Question 11 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$9$
$9$
Answer
View full question & answer→ Multiplicative inverse of $9=\frac{1}{9}$
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Question 21 Mark
Name the property of multiplication of rational numbers illustrated by the following statements: $\frac{13}{-17}\times1=\frac{13}{-17}=1\times\frac{13}{-17}$
Answer
View full question & answer→$\frac{13}{-17}\times1=\frac{13}{-17}$ $=1\times\frac{13}{-17}$ It is multiplicative identity.
Question 31 Mark
Multiply: $\frac{-3}{17}\ \text{by}\ \frac{-5}{-4}$
Answer
View full question & answer→$\frac{-3}{17}\ \text{by}\ \frac{-5}{-4}=\frac{-3\times(-5)}{17\times(-4)}=\frac{15}{-68}$
Question 41 Mark
Fill in the blanks: The product of two positive rational numbers is always ______.
Answer
View full question & answer→The product of two positive rational number is alway positive.
Question 51 Mark
Fill in the blanks:
$(17 × 12)^{-1} = 17^{-1}$ × _____.
$(17 × 12)^{-1} = 17^{-1}$ × _____.
Answer
View full question & answer→$(17 × 12)^{-1} = 17^{-1} × 12^{-1}$
Question 61 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{-3}{-5}$
Answer
View full question & answer→Multiplicative inverse of $=\frac{-5}{-3}=\frac{5}{3}$
Question 71 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{0}{3}$
Answer
View full question & answer→Multiplicative inverse of $0=$ Does not exist as division by $0$ is not admissible.
Question 81 Mark
Write the additive inverse of the following rational number: $1$
Answer
View full question & answer→$1$ Negative inverse of $1$ is $-1.$
Question 91 Mark
Write the additive inverse of the following rational number:
$0$
$0$
Answer
View full question & answer→$0$
Negative inverse of $0$ is $0.$
Negative inverse of $0$ is $0.$
Question 101 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $1$
Answer
View full question & answer→Multiplicative inverse of $1=1$
Question 111 Mark
Multiply: $-\frac{3}{5}\ \text{by}\ -\frac{4}{7}$
Answer
View full question & answer→$-\frac{3}{5}\ \text{by}\ -\frac{4}{7}=\frac{-3\times(-4}{5\times7}=\frac{12}{35}$
Question 121 Mark
Name the property of multiplication of rational numbers illustrated by the following statements: $\frac{-5}{16}\times\frac{8}{15}=\frac{8}{15}\times\frac{-5}{16}$
Answer
View full question & answer→$\frac{-5}{16}\times\frac{8}{15}=\frac{8}{15}\times\frac{-5}{16}$ It is commutative property.
Question 131 Mark
Fill in the blanks: The product of a positive rational number and a negative rational number is always _____.
Answer
View full question & answer→The product of a positive rational number and a negative rational number is always negative.
Question 141 Mark
Multiply: $\frac{9}{-7}\ \text{by}\ \frac{36}{-11}$
Answer
View full question & answer→$\frac{9}{-7}\ \text{by}\ \frac{36}{-11}=\frac{9\times36}{(-7)\times(-11)}=\frac{324}{77}$
Question 151 Mark
Fill in the blanks: The number $0$ is _________ the reciprocal of any number.
Answer
View full question & answer→The number $0$ is not the reciprocal of any number.
Question 161 Mark
Find the value and express as a rational number in standard form:
$\frac{-36}{126}\div\frac{-3}{75}$
$\frac{-36}{126}\div\frac{-3}{75}$
Answer
View full question & answer→ $\frac{-36}{126}\div\frac{-3}{75}=\frac{-36}{125}\times\frac{75}{-3}$
$=\frac{-36\times75}{125\times(-3)}=\frac{-12\times3}{5\times(-1)}$
$=\frac{-36}{-5}=\frac{36}{5}$
$=\frac{-36\times75}{125\times(-3)}=\frac{-12\times3}{5\times(-1)}$
$=\frac{-36}{-5}=\frac{36}{5}$
Question 171 Mark
Divide: $\frac{2}{3}\ \text{by}\ \frac{-7}{12}$
Answer
View full question & answer→$\frac{2}{3}\ \text{by}\ \frac{-7}{12}$ $=\frac{2}{3}\div\frac{-7}{12}=\frac{2}{3}\times\frac{12}{-7}$ $=\frac{2\times4}{1\times(-7)}=\frac{8}{-7}$ $=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
Question 181 Mark
Simplify: $0+\frac{-3}{5}$
Answer
View full question & answer→$0+\frac{-3}{5}$ $=\frac{-3}{5}$
Question 191 Mark
Multiply: $\frac{-8}{9}\ \text{by}\ \frac{3}{64}$
Answer
View full question & answer→$\frac{-8}{9}\ \text{by}\ \frac{3}{64}$ $=\frac{-8\times3}{9\times64}=\frac{-1\times1}{3\times8}=\frac{-1}{24}$
Question 201 Mark
Write the additive inverse of the following rational number: $-1$
Answer
View full question & answer→$1$ Negative inverse of $-1$ is $(-1) = 1.$
Question 211 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $-2\times\frac{-3}{5}$
Answer
View full question & answer→Multiplicative inverse of $-2\times\frac{-3}{5}$ $=\frac{1}{-2}\times\frac{5}{-3}=\frac{1\times5}{(-2)\times(-3)}$ $=\frac{5}{6}$
Question 221 Mark
Fill in the blanks: The product of two negative rational numbers is always __________.
Answer
View full question & answer→The product of two negative rational numbers is always positive.
Question 231 Mark
Simplify the following and express the result as a rational number in standard form: $\frac{-13}{9}\times\frac{27}{-26}$
Answer
View full question & answer→$\frac{-13}{9}\times\frac{27}{-26}=\frac{-13\times27}{9\times(-26)}$ $=\frac{-1\times3}{-\times(-2)}=\frac{-3}{-2}=\frac{3}{2}$
Question 241 Mark
Find the value and express as a rational number in standard form: $\frac{-40}{99}\div(-20)$
Answer
View full question & answer→$\frac{-40}{99}\div(-20)=\frac{-40}{99}\times\frac{1}{-20}$ $=\frac{-2\times1}{99\times(-1)}=\frac{-2}{99}=\frac{2}{99}$
Question 251 Mark
Simplify the following and express the result as a rational number in standard form: $\frac{-9}{16}\times\frac{-64}{-27}$
Answer
View full question & answer→$\frac{-9}{16}\times\frac{-64}{-27}$ $=\frac{(-9)\times(-64)}{16\times(-27)}$ $=\frac{-1\times(-4)}{1\times(-3)}=\frac{4}{-3}$ $=\frac{4\times(-1)}{-3(-1)}=\frac{-4}{3}$
Question 261 Mark
Name the property of multiplication of rational numbers illustrated by the following statements: $\frac{-5}{9}\times\Big(\frac{4}{15}\times\frac{-9}{8}\Big)=\Big(\frac{-5}{9}\times\frac{4}{15}\Big)\times\frac{-9}{8}$
Answer
View full question & answer→$\frac{-5}{9}\times\Big(\frac{4}{15}\times\frac{-9}{8}\Big)$ $=\Big(\frac{-5}{9}\times\frac{4}{15}\Big)\times\frac{-9}{8}$ It is associativem property.
Question 271 Mark
Simplify the following and express the result as a rational number in standard form: $\frac{-50}{7}\times\frac{14}{3}$
Answer
View full question & answer→$\frac{-50}{7}\times\frac{14}{3}=\frac{-50\times14}{7\times3}$ $=\frac{-50\times2}{1\times3}=\frac{-100}{3}$
Question 281 Mark
Fill in the blanks: $\frac{-4}{5}\times\Big(\frac{5}{7}\times\frac{-8}{9}\Big)=\Big(\frac{-4}{5}\times$___$\Big)\times\frac{-8}{9}$
Answer
View full question & answer→$\frac{-4}{5}\times\Big(\frac{5}{7}\times\frac{-8}{9}\Big)=\Big(\frac{-4}{5}\times\frac{5}{7}\Big)\times\frac{-8}{9}$
Question 291 Mark
Divide: $\frac{-3}{13}\ \text{by}\ \frac{-4}{65}$
Answer
View full question & answer→$\frac{-3}{13}\ \text{by}\ \frac{-4}{65}$ $=\frac{-3}{13}\div\frac{-4}{65}=\frac{-3}{13}\times\frac{65}{-4}$ $=\frac{-3\times5}{1\times(-4)}=\frac{-15}{-4}=\frac{15}{4}$
Question 301 Mark
Fill in the blanks: If $a$ is reciprocal of $b,$ then the reciprocal of $b$ is __________.
Answer
View full question & answer→If a is reciprocal of $b,$ then the reciprocal of $b$ is $a.$
Question 311 Mark
Find the value and express as a rational number in standard form: $-6\div\frac{-8}{17}$
Answer
View full question & answer→$-6\div\frac{-8}{17}=-6\times\frac{17}{-8}$ $=\frac{-3\times17}{-4}$ $=\frac{-51}{4}=\frac{51}{4}$
Question 321 Mark
Find the value and express as a rational number in standard form: $\frac{-22}{27}\div\frac{-110}{18}$
Answer
View full question & answer→$\frac{-22}{27}\div\frac{-110}{18}=\frac{-22}{27}\times\frac{18}{-110}$ $=\frac{-22\times18}{27\times(-110)}=\frac{-1\times2}{34\times(-5)}$ $=\frac{-2}{-15}=\frac{2}{15}$
Question 331 Mark
Fill in the blanks:
The reciprocal of a positive rational number is _______.
The reciprocal of a positive rational number is _______.
Answer
View full question & answer→ The reciprocal of a positive rational number is positive.
Question 341 Mark
Find the value and express as a rational number in standard form: $\frac{2}{5}\div\frac{26}{15}$
Answer
View full question & answer→$\frac{2}{5}\div\frac{26}{15}=\frac{2}{5}\times\frac{15}{26}=\frac{2\times15}{5\times26}$ $=\frac{1\times3}{1\times13}=\frac{3}{13}$
Question 351 Mark
Fill in the blanks: Zero has _____________ reciprocal.
Answer
View full question & answer→Zero has no reciprocal.
Question 361 Mark
Name the property of multiplication of rational numbers illustrated by the following statements: $\frac{2}{13}\times0=0=0\times\frac{2}{13}$
Answer
View full question & answer→$\frac{2}{13}\times0=0=0\times\frac{2}{13}$ It is zero property of multiplication.
Question 371 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{12}{5}$
Answer
View full question & answer→Multiplicative inverse of $\frac{12}{5}=\frac{5}{12}$
Question 381 Mark
Write the negative (additive inverse) of the following: $\frac{-2}{5}$
Answer
View full question & answer→$\frac{-2}{5}$ Negative of $\frac{-2}{5}$ is $-\Big(\frac{-2}{5}\Big)=\frac{2}{5}$
Question 391 Mark
Add the following ration numbers:
$\frac{-5}{7}$ and $\frac{3}{7}$
$\frac{-5}{7}$ and $\frac{3}{7}$
Answer
View full question & answer→ $\frac{-5}{7}+\frac{3}{7}=\frac{-5+3}{7}=\frac{-2}{7}$
Question 401 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$-7$
$-7$
Answer
View full question & answer→ Multiplicative inverse of $-7=\frac{1}{-7}$
Question 411 Mark
Add the following ration numbers:
$\frac{6}{13}$ and $\frac{-9}{13}$
$\frac{6}{13}$ and $\frac{-9}{13}$
Answer
View full question & answer→ $\frac{6}{13}+\frac{-9}{13}=\frac{6-9}{13}=\frac{-3}{13}$
Question 421 Mark
Write the additive inverse of the following rational number: $\frac{7}{-9}$
Answer
View full question & answer→$\frac{7}{-9}$ Nagative of $\frac{7}{-9}$ is $-\Big(\frac{7}{-9}\Big)=\frac{7}{9}$
Question 431 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{2}{3}\times\frac{9}{4}$
Answer
View full question & answer→Multiplicative inverse of $\frac{2}{3}\times\frac{9}{4}$ $=\frac{3}{2}\times\frac{4}{9}$ $\frac{3\times4}{2\times9}=\frac{1\times2}{1\times3}$ $=\frac{2}{3}$
Question 441 Mark
Name the property of multiplication of rational numbers illustrated by the following statements: $\frac{-3}{2}\times\frac{5}{4}+\frac{-3}{2}\times\frac{-7}{6}=\frac{-3}{2}\times\Big(\frac{5}{4}+\frac{-7}{6}\Big)$
Answer
View full question & answer→$\frac{-3}{2}\times\frac{5}{4}+\frac{-3}{2}\times\frac{-7}{6}$ $=\frac{-3}{2}\times\Big(\frac{5}{4}+\frac{-7}{6}\Big)$ It is destributive law of multiplication over addition.
Question 451 Mark
If $24$ trousers of equal size can be prepared in $54$ metres of cloth, what length of cloth is required for each trouser$?$
Answer
View full question & answer→Cloth required for $24$ trousers $= 54m$
$\therefore$ Cloth required for $1$ trouser $=(54\div24)\text{m}$
$=\frac{54}{24}=\frac{9}{4}=2\frac{1}{4}\text{m}$
$\therefore$ Cloth required for $1$ trouser $=(54\div24)\text{m}$
$=\frac{54}{24}=\frac{9}{4}=2\frac{1}{4}\text{m}$
Question 461 Mark
Multiply:
$\frac{-8}{25}\ \text{by}\ \frac{-5}{16}$
$\frac{-8}{25}\ \text{by}\ \frac{-5}{16}$
Answer
View full question & answer→ $\frac{-8}{25}\ \text{by}\ \frac{-5}{16}=\frac{(-8)\times(-5)}{25\times16}$
$=\frac{(-1)\times(-1)}{5\times2}=\frac{1}{10}$
$=\frac{(-1)\times(-1)}{5\times2}=\frac{1}{10}$
Question 471 Mark
Divide: $1\ \text{by}\ \frac{1}{2}$
Answer
View full question & answer→$1\ \text{by}\ \frac{1}{2}=1\div\frac{1}{2}=1\times\frac{2}{1}=2$
Question 481 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{-11}{16}\times\frac{16}{-11}=1$
$\frac{-11}{16}\times\frac{16}{-11}=1$
Answer
View full question & answer→ $\frac{-11}{16}\times\frac{16}{-11}=1$
It is existanceof multiplicative inverse.
It is existanceof multiplicative inverse.
Question 491 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{-17}{5}\times9=9\times\frac{-17}{5}$
$\frac{-17}{5}\times9=9\times\frac{-17}{5}$
Answer
View full question & answer→ $\frac{-17}{5}\times9=9\times\frac{-17}{5}$
It is commutative property.
It is commutative property.
Question 501 Mark
Write the additive inverse of the following rational number: $\frac{-17}{5}$
Answer
View full question & answer→$\frac{-17}{5}$ Additive inverse of $\frac{-17}{5}$ is $-\Big(\frac{-17}{5}\Big)=\frac{17}{5}$
Question 511 Mark
Write the additive inverse of the following rational number: $\frac{3}{-11}$
Answer
View full question & answer→$\frac{3}{-11}$Additive inverse of $\frac{3}{-11}$ is $-\Big(\frac{3}{-11}\Big)=\frac{3}{11}$
Question 521 Mark
Add the following ration numbers: $\frac{-15}{4}$ and $\frac{7}{4}$
Answer
View full question & answer→$\frac{-15}{7}+\frac{7}{4}=\frac{-15+7}{4}=\frac{-8}{4}=-2$
Question 531 Mark
Multiply: $-\frac{15}{11}\ \text{by}\ 7$
Answer
View full question & answer→$-\frac{15}{11}\ \text{by}\ 7=\frac{-15\times7}{11}=\frac{-105}{11}$
Question 541 Mark
Write the additive inverse of the following rational number:
$\frac{-16}{13}$
$\frac{-16}{13}$
Answer
View full question & answer→ $\frac{-16}{13}$
Negative of $\frac{-16}{13}$ is $-\Big(\frac{-16}{13}\Big)=\frac{16}{13}$
Negative of $\frac{-16}{13}$ is $-\Big(\frac{-16}{13}\Big)=\frac{16}{13}$
Question 551 Mark
Divide: $0\ \text{by}\ \frac{-7}{5}$
Answer
View full question & answer→$0\ \text{by}\ \frac{-7}{5}=0\div\frac{-7}{5}=0\times\frac{5}{-7}=0$
Question 561 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{-7}{9}$
Answer
View full question & answer→Multiplicative inverse of $\frac{-7}{9}=\frac{9}{-7}$
Question 571 Mark
Multiply: $\frac{5}{7}\ \text{by}\ \frac{-3}{4}$
Answer
View full question & answer→$\frac{5}{7}\ \text{by}\ \frac{-3}{4}=\frac{5\times(-3)}{7\times4}=\frac{-15}{28}$
Question 581 Mark
Write the additive inverse of the following rational number: $\frac{-11}{-25}$
Answer
View full question & answer→$\frac{-11}{-25}$ Additive inverse of $\frac{-11}{-25}=\Big(\frac{-11}{-25}\Big)$ $=-\Big(\frac{11}{25}\Big)=\frac{-11}{25}$
Question 591 Mark
Add the following ration numbers: $\frac{-8}{11}$ and $\frac{-4}{11}$
Answer
View full question & answer→$\frac{-8}{11}+\frac{-4}{11}=\frac{-8-4}{11}=\frac{-12}{11}$
Question 601 Mark
Find the value and express as a rational number in standard form: $\frac{10}{3}\div\frac{-35}{12}$
Answer
View full question & answer→$\frac{10}{3}\div\frac{-35}{12}=\frac{10}{3}\times\frac{12}{-35}$ $=\frac{10\times12}{3\times(-35)}$ $=\frac{2\times4}{1\times(-7)}=\frac{8}{-7}$ $=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
Question 611 Mark
Simplify the following and express the result as a rational number in standard form:
$\frac{-5}{9}\times\frac{72}{-25}$
$\frac{-5}{9}\times\frac{72}{-25}$
Answer
View full question & answer→ $\frac{-5}{9}\times\frac{72}{-25}=\frac{-5\times72}{9\times(-25)}$
$=\frac{-1\times8}{1\times(-5)}=\frac{-8}{-5}$
$=\frac{8}{5}$
$=\frac{-1\times8}{1\times(-5)}=\frac{-8}{-5}$
$=\frac{8}{5}$
Question 621 Mark
Write the additive inverse of the following rational number: $\frac{-2}{17}$
Answer
View full question & answer→$\frac{-2}{17}$ Additive inverse of $\frac{-2}{17}$ is $-\Big(\frac{-2}{17}\Big)=\frac{2}{17}$
Question 631 Mark
Fill in the blanks: The product of a rational number and its reciprocal is ______________.
Answer
View full question & answer→The product of a rational number and its reciprocal is $1.$
Question 641 Mark
Fill in the blanks:
The numbers __________ and _______ are their own reciprocals.
The numbers __________ and _______ are their own reciprocals.
Answer
View full question & answer→The numbers $-1$ and $1$ are their own reciprocals.
Question 651 Mark
Simplify the following and express the result as a rational number in standard form: $\frac{7}{6}\times\frac{-3}{28}$
Answer
View full question & answer→$\frac{7}{6}\times\frac{-3}{28}=\frac{7\times(-3)}{6\times28}$ $=\frac{1\times(-1)}{2\times4}=\frac{-1}{8}$
Question 661 Mark
Name the property of multiplication of rational numbers illustrated by the following statements: $\frac{7}{4}\times\Big(\frac{-8}{3}+\frac{-13}{12}\Big)=\frac{7}{4}\times\frac{-8}{3}+\frac{7}{4}+\frac{-13}{12}$
Answer
View full question & answer→$\frac{7}{4}\times\Big(\frac{-8}{3}+\frac{-13}{12}\Big)$ $=\frac{7}{4}\times\frac{-8}{3}+\frac{7}{4}+\frac{-13}{12}$ It is distributive property over addition.
Question 671 Mark
Multiply: $\frac{-11}{13}\ \text{by}\ \frac{-21}{7}$
Answer
View full question & answer→$\frac{-11}{13}\ \text{by}\ \frac{-21}{7}=\frac{(-11)\times(-21)}{13\times7}$ $=\frac{231}{91}=\frac{231\div7}{91\div7}=\frac{33}{13}$
Question 681 Mark
Write the additive inverse of the following rational number: $\frac{-5}{1}$
Answer
View full question & answer→$\frac{-5}{1}$ Negative of $\frac{-5}{1}$ is $-\Big(\frac{-5}{1}\Big)={5}$
Question 691 Mark
Fill in the blanks: $\frac{5}{11}\times\frac{-3}{8}=\frac{-3}{8}\times$ ___________.
Answer
View full question & answer→$\frac{5}{11}\times\frac{-3}{8}=\frac{-3}{8}\times\frac{5}{11}$
Question 701 Mark
Fill in the blanks: Reciprocal of $\frac{1}{\text{a}},a\neq0$ is _________.
Answer
View full question & answer→Reciprocal of $\frac{1}{\text{a}},a\neq0$ is a.
Question 711 Mark
Multiply: $\frac{-2}{9}\ \text{by}\ \frac{5}{11}$
Answer
View full question & answer→$\frac{-2}{9}\ \text{by}\ \frac{5}{11}=\frac{-2\times5}{9\times11}=\frac{-10}{99}$
Question 721 Mark
Divide: $-4\ \text{by}\ \frac{-3}{5}$
Answer
View full question & answer→$-4\ \text{by}\ \frac{-3}{5}$ $=-4\div\frac{-3}{5}$ $=-4\times\frac{5}{-3}$ $=\frac{-4\times5}{-3}$ $=\frac{-20}{-3}=\frac{20}{3}$ $=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
Question 731 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $-1$
Answer
View full question & answer→Multiplicative inverse of $-1=-1$
Question 741 Mark
Multiply: $\frac{7}{11}\ \text{by}\ \frac{5}{4}$
Answer
View full question & answer→$\frac{7}{11}\ \text{by}\ \frac{5}{4}=\frac{7\times5}{11\times4}=\frac{35}{44}$
Question 751 Mark
Fill in the blanks: $-4\times\frac{7}{9}=\frac{7}{9}\times$ ___________.
Answer
View full question & answer→Fill in the blanks: $-4\times\frac{7}{9}=\frac{7}{9}\times$ -4.
Question 761 Mark
Verify the property: $x \times (y \times z) = (x \times y) \times z$ by taking: $\text{x}=\frac{5}{7},\text{y}=\frac{-12}{13},\text{z=}\frac{-7}{18}$
Answer
View full question & answer→$\text{x}=\frac{5}{7},\text{y}=\frac{-12}{13},\text{z}=\frac{-7}{18}$
$\text{x}(\text{y}\times\text{z})=\frac{5}{7}\times\Big(\frac{-12}{13}\times\frac{-7}{18}\Big)$
$=\frac{5}{7}\times\frac{14}{39}=\frac{10}{39}$
$(\text{x}\times\text{y})\times\text{z}=\frac{5}{7}\times\frac{-12}{13}\times\frac{-7}{18}$
$=\frac{-60}{91}\times\frac{-7}{18}=\frac{10}{39}$
$\therefore\frac{5}{7}\times\Big(\frac{-12}{13}\times\frac{-7}{18}\Big)$
$\Big(\frac{5}{7}\times\frac{-12}{13}\Big)\times\frac{-7}{18}$ Hence verified.
$\text{x}(\text{y}\times\text{z})=\frac{5}{7}\times\Big(\frac{-12}{13}\times\frac{-7}{18}\Big)$
$=\frac{5}{7}\times\frac{14}{39}=\frac{10}{39}$
$(\text{x}\times\text{y})\times\text{z}=\frac{5}{7}\times\frac{-12}{13}\times\frac{-7}{18}$
$=\frac{-60}{91}\times\frac{-7}{18}=\frac{10}{39}$
$\therefore\frac{5}{7}\times\Big(\frac{-12}{13}\times\frac{-7}{18}\Big)$
$\Big(\frac{5}{7}\times\frac{-12}{13}\Big)\times\frac{-7}{18}$ Hence verified.
Question 771 Mark
Simplify the following and express the result as a rational number in standard form: $\frac{-19}{36}\times16$
Answer
View full question & answer→$\frac{-19}{36}\times16=\frac{-19\times16}{36}$ $=\frac{-19\times4}{9}=\frac{-76}{9}$
Question 781 Mark
Fill in the blanks: $\frac{1}{2}\times\Big(\frac{3}{4}+\frac{-5}{12}\Big)=\frac{1}{2}\times$ ___________ + ____________ $\times\frac{-5}{12}$
Answer
View full question & answer→$\frac{1}{2}\times\Big(\frac{3}{4}+\frac{-5}{12}\Big)=\frac{1}{2}\times\frac{3}{4}+\frac{1}{2}\times\frac{-5}{12}$
Question 791 Mark
Divide: $\frac{-3}{4}\ \text{by}\ -6$
Answer
View full question & answer→$\frac{-3}{4}\ \text{by}\ -6=\frac{-3}{4}\div\frac{-6}{1}=\frac{-3}{1}\times\frac{1}{-6}$ $=\frac{-1\times1}{4\times(-2)}=\frac{-1}{-8}=\frac{1}{8}$
Question 801 Mark
Multiply: $\frac{6}{7}\ \text{by}\ \frac{-49}{36}$
Answer
View full question & answer→$\frac{6}{7}\ \text{by}\ \frac{-49}{36}=\frac{6}{7}\times\frac{-49}{36}$ $=\frac{6\times(-49)}{7\times36}=\frac{1\times(-7)}{1\times6}=\frac{-7}{6}$
Question 811 Mark
Simplify the following and express the result as a rational number in standard form: $\frac{-16}{21}\times\frac{14}{5}$
Answer
View full question & answer→$\frac{-16}{21}\times\frac{14}{5}=\frac{-16\times14}{21\times5}$ $=\frac{-16\times2}{3\times5}=\frac{-32}{15}$
Question 821 Mark
Fill in the blanks:
The reciprocal of a negative rational number is ____________.
The reciprocal of a negative rational number is ____________.
Answer
View full question & answer→ The reciprocal of a negative rational number is negative.
Question 831 Mark
Write the negative (additive inverse) of the following:
$\frac{-2}{5}$
$\frac{-2}{5}$
Answer
View full question & answer→$\frac{-2}{5}$
Negative of$\frac{-2}{5}$is$-\Big(\frac{-2}{5}\Big)=\frac{2}{5}$
Negative of$\frac{-2}{5}$is$-\Big(\frac{-2}{5}\Big)=\frac{2}{5}$
Question 841 Mark
Write the additive inverse of the following rational number:
$\frac{7}{-9}$
$\frac{7}{-9}$
Answer
View full question & answer→$\frac{7}{-9}$
Nagative of$\frac{7}{-9}$is$-\Big(\frac{7}{-9}\Big)=\frac{7}{9}$
Nagative of$\frac{7}{-9}$is$-\Big(\frac{7}{-9}\Big)=\frac{7}{9}$
Question 851 Mark
Write the additive inverse of the following rational number:
$\frac{-5}{1}$
$\frac{-5}{1}$
Answer
View full question & answer→$\frac{-5}{1}$
Negative of$\frac{-5}{1}$is$-\Big(\frac{-5}{1}\Big)={5}$
Negative of$\frac{-5}{1}$is$-\Big(\frac{-5}{1}\Big)={5}$
Question 861 Mark
Write the additive inverse of the following rational number:
$\frac{3}{-11}$
$\frac{3}{-11}$
Answer
View full question & answer→$\frac{3}{-11}$
Additive inverse of$\frac{3}{-11}$is$-\Big(\frac{3}{-11}\Big)=\frac{3}{11}$
Additive inverse of$\frac{3}{-11}$is$-\Big(\frac{3}{-11}\Big)=\frac{3}{11}$
Question 871 Mark
Write the additive inverse of the following rational number:
$\frac{-2}{17}$
$\frac{-2}{17}$
Answer
View full question & answer→$\frac{-2}{17}$
Additive inverse of$\frac{-2}{17}$is$-\Big(\frac{-2}{17}\Big)=\frac{2}{17}$
Additive inverse of$\frac{-2}{17}$is$-\Big(\frac{-2}{17}\Big)=\frac{2}{17}$
Question 881 Mark
Write the additive inverse of the following rational number:
$\frac{-17}{5}$
$\frac{-17}{5}$
Answer
View full question & answer→$\frac{-17}{5}$
Additive inverse of$\frac{-17}{5}$is$-\Big(\frac{-17}{5}\Big)=\frac{17}{5}$
Additive inverse of$\frac{-17}{5}$is$-\Big(\frac{-17}{5}\Big)=\frac{17}{5}$
Question 891 Mark
Write the additive inverse of the following rational number:
$\frac{-16}{13}$
$\frac{-16}{13}$
Answer
View full question & answer→$\frac{-16}{13}$
Negative of$\frac{-16}{13}$is$-\Big(\frac{-16}{13}\Big)=\frac{16}{13}$
Negative of$\frac{-16}{13}$is$-\Big(\frac{-16}{13}\Big)=\frac{16}{13}$
Question 901 Mark
Write the additive inverse of the following rational number:
$\frac{-11}{-25}$
$\frac{-11}{-25}$
Answer
View full question & answer→$\frac{-11}{-25}$
Additive inverse of$\frac{-11}{-25}=\Big(\frac{-11}{-25}\Big)$
$=-\Big(\frac{11}{25}\Big)=\frac{-11}{25}$
Additive inverse of$\frac{-11}{-25}=\Big(\frac{-11}{-25}\Big)$
$=-\Big(\frac{11}{25}\Big)=\frac{-11}{25}$
Question 911 Mark
Write the additive inverse of the following rational number:
1
1
Answer
View full question & answer→1
Negative inverse of 1 is -1.
Negative inverse of 1 is -1.
Question 921 Mark
Write the additive inverse of the following rational number:
-1
-1
Answer
View full question & answer→1
Negative inverse of -1 is (-1) = 1.
Negative inverse of -1 is (-1) = 1.
Question 931 Mark
Write the additive inverse of the following rational number:
0
0
Answer
View full question & answer→0
Negative inverse of 0 is 0.
Negative inverse of 0 is 0.
Question 941 Mark
Verify the property: x × (y × z) = (x × y) × z by taking:
$\text{x}=\frac{5}{7},\text{y}=\frac{-12}{13},\text{z=}\frac{-7}{18}$
$\text{x}=\frac{5}{7},\text{y}=\frac{-12}{13},\text{z=}\frac{-7}{18}$
Answer
View full question & answer→$\text{x}=\frac{5}{7},\text{y}=\frac{-12}{13},\text{z}=\frac{-7}{18}$
$\text{x}(\text{y}\times\text{z})=\frac{5}{7}\times\Big(\frac{-12}{13}\times\frac{-7}{18}\Big)$
$=\frac{5}{7}\times\frac{14}{39}=\frac{10}{39}$
$(\text{x}\times\text{y})\times\text{z}=\frac{5}{7}\times\frac{-12}{13}\times\frac{-7}{18}$
$=\frac{-60}{91}\times\frac{-7}{18}=\frac{10}{39}$
$\therefore\frac{5}{7}\times\Big(\frac{-12}{13}\times\frac{-7}{18}\Big)$
$\Big(\frac{5}{7}\times\frac{-12}{13}\Big)\times\frac{-7}{18}$
Hence verified.
$\text{x}(\text{y}\times\text{z})=\frac{5}{7}\times\Big(\frac{-12}{13}\times\frac{-7}{18}\Big)$
$=\frac{5}{7}\times\frac{14}{39}=\frac{10}{39}$
$(\text{x}\times\text{y})\times\text{z}=\frac{5}{7}\times\frac{-12}{13}\times\frac{-7}{18}$
$=\frac{-60}{91}\times\frac{-7}{18}=\frac{10}{39}$
$\therefore\frac{5}{7}\times\Big(\frac{-12}{13}\times\frac{-7}{18}\Big)$
$\Big(\frac{5}{7}\times\frac{-12}{13}\Big)\times\frac{-7}{18}$
Hence verified.
Question 951 Mark
Simplify the following and express the result as a rational number in standard form:
$\frac{-9}{16}\times\frac{-64}{-27}$
$\frac{-9}{16}\times\frac{-64}{-27}$
Answer
View full question & answer→$\frac{-9}{16}\times\frac{-64}{-27}$
$=\frac{(-9)\times(-64)}{16\times(-27)}$
$=\frac{-1\times(-4)}{1\times(-3)}=\frac{4}{-3}$
$=\frac{4\times(-1)}{-3(-1)}=\frac{-4}{3}$
$=\frac{(-9)\times(-64)}{16\times(-27)}$
$=\frac{-1\times(-4)}{1\times(-3)}=\frac{4}{-3}$
$=\frac{4\times(-1)}{-3(-1)}=\frac{-4}{3}$
Question 961 Mark
Simplify the following and express the result as a rational number in standard form:
$\frac{7}{6}\times\frac{-3}{28}$
$\frac{7}{6}\times\frac{-3}{28}$
Answer
View full question & answer→$\frac{7}{6}\times\frac{-3}{28}=\frac{7\times(-3)}{6\times28}$
$=\frac{1\times(-1)}{2\times4}=\frac{-1}{8}$
$=\frac{1\times(-1)}{2\times4}=\frac{-1}{8}$
Question 971 Mark
Simplify the following and express the result as a rational number in standard form:
$\frac{-5}{9}\times\frac{72}{-25}$
$\frac{-5}{9}\times\frac{72}{-25}$
Answer
View full question & answer→$\frac{-5}{9}\times\frac{72}{-25}=\frac{-5\times72}{9\times(-25)}$
$=\frac{-1\times8}{1\times(-5)}=\frac{-8}{-5}$
$=\frac{8}{5}$
$=\frac{-1\times8}{1\times(-5)}=\frac{-8}{-5}$
$=\frac{8}{5}$
Question 981 Mark
Simplify the following and express the result as a rational number in standard form:
$\frac{-50}{7}\times\frac{14}{3}$
$\frac{-50}{7}\times\frac{14}{3}$
Answer
View full question & answer→$\frac{-50}{7} \times \frac{14}{3}=\frac{-50 \times 14}{7 \times 3}$
$=\frac{-50\times2}{1\times3}=\frac{-100}{3}$
$=\frac{-50\times2}{1\times3}=\frac{-100}{3}$
Question 991 Mark
Simplify the following and express the result as a rational number in standard form:
$\frac{-19}{36}\times16$
$\frac{-19}{36}\times16$
Answer
View full question & answer→$\frac{-19}{36}\times16=\frac{-19\times16}{36}$
$=\frac{-19\times4}{9}=\frac{-76}{9}$
$=\frac{-19\times4}{9}=\frac{-76}{9}$
Question 1001 Mark
Simplify the following and express the result as a rational number in standard form:
$\frac{-16}{21}\times\frac{14}{5}$
$\frac{-16}{21}\times\frac{14}{5}$
Answer
View full question & answer→$\frac{-16}{21}\times\frac{14}{5}=\frac{-16\times14}{21\times5}$
$=\frac{-16\times2}{3\times5}=\frac{-32}{15}$
$=\frac{-16\times2}{3\times5}=\frac{-32}{15}$
Question 1011 Mark
Simplify the following and express the result as a rational number in standard form:
$\frac{-13}{9}\times\frac{27}{-26}$
$\frac{-13}{9}\times\frac{27}{-26}$
Answer
View full question & answer→$\frac{-13}{9}\times\frac{27}{-26}=\frac{-13\times27}{9\times(-26)}$
$=\frac{-1\times3}{-\times(-2)}=\frac{-3}{-2}=\frac{3}{2}$
$=\frac{-1\times3}{-\times(-2)}=\frac{-3}{-2}=\frac{3}{2}$
Question 1021 Mark
Simplify:
$0+\frac{-3}{5}$
$0+\frac{-3}{5}$
Answer
View full question & answer→$0+\frac{-3}{5}$
$=\frac{-3}{5}$
$=\frac{-3}{5}$
Question 1031 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{7}{4}\times\Big(\frac{-8}{3}+\frac{-13}{12}\Big)=\frac{7}{4}\times\frac{-8}{3}+\frac{7}{4}+\frac{-13}{12}$
$\frac{7}{4}\times\Big(\frac{-8}{3}+\frac{-13}{12}\Big)=\frac{7}{4}\times\frac{-8}{3}+\frac{7}{4}+\frac{-13}{12}$
Answer
View full question & answer→$\frac{7}{4} \times\left(\frac{-8}{3}+\frac{-13}{12}\right)$
$=\frac{7}{4}\times\frac{-8}{3}+\frac{7}{4}+\frac{-13}{12}$
$=\frac{7}{4}\times\frac{-8}{3}+\frac{7}{4}+\frac{-13}{12}$
Question 1041 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{-5}{9}\times\Big(\frac{4}{15}\times\frac{-9}{8}\Big)=\Big(\frac{-5}{9}\times\frac{4}{15}\Big)\times\frac{-9}{8}$
$\frac{-5}{9}\times\Big(\frac{4}{15}\times\frac{-9}{8}\Big)=\Big(\frac{-5}{9}\times\frac{4}{15}\Big)\times\frac{-9}{8}$
Answer
View full question & answer→$\frac{-5}{9}\times\Big(\frac{4}{15}\times\frac{-9}{8}\Big)$
$=\Big(\frac{-5}{9}\times\frac{4}{15}\Big)\times\frac{-9}{8
It is associativem property.
$=\Big(\frac{-5}{9}\times\frac{4}{15}\Big)\times\frac{-9}{8
It is associativem property.
Question 1051 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{-5}{16}\times\frac{8}{15}=\frac{8}{15}\times\frac{-5}{16}$
$\frac{-5}{16}\times\frac{8}{15}=\frac{8}{15}\times\frac{-5}{16}$
Answer
View full question & answer→$\frac{-5}{16}\times\frac{8}{15}=\frac{8}{15}\times\frac{-5}{16}$
It is commutative property.
It is commutative property.
Question 1061 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{-3}{2}\times\frac{5}{4}+\frac{-3}{2}\times\frac{-7}{6}=\frac{-3}{2}\times\Big(\frac{5}{4}+\frac{-7}{6}\Big)$
$\frac{-3}{2}\times\frac{5}{4}+\frac{-3}{2}\times\frac{-7}{6}=\frac{-3}{2}\times\Big(\frac{5}{4}+\frac{-7}{6}\Big)$
Answer
View full question & answer→$\frac{-3}{2}\times\frac{5}{4}+\frac{-3}{2}\times\frac{-7}{6}$
$=\frac{-3}{2}\times\Big(\frac{5}{4}+\frac{-7}{6}\Big)$
It is destributive law of multiplication over addition.
$=\frac{-3}{2}\times\Big(\frac{5}{4}+\frac{-7}{6}\Big)$
It is destributive law of multiplication over addition.
Question 1071 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{2}{13}\times0=0=0\times\frac{2}{13}$
$\frac{2}{13}\times0=0=0\times\frac{2}{13}$
Answer
View full question & answer→$\frac{2}{13}\times0=0=0\times\frac{2}{13}$
It is zero property of multiplication.
It is zero property of multiplication.
Question 1081 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{-17}{5}\times9=9\times\frac{-17}{5}$
$\frac{-17}{5}\times9=9\times\frac{-17}{5}$
Answer
View full question & answer→$\frac{-17}{5}\times9=9\times\frac{-17}{5}$
It is commutative property.
It is commutative property.
Question 1091 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{13}{-17}\times1=\frac{13}{-17}=1\times\frac{13}{-17}$
$\frac{13}{-17}\times1=\frac{13}{-17}=1\times\frac{13}{-17}$
Answer
View full question & answer→$\frac{13}{-17}\times1=\frac{13}{-17}$
$=1\times\frac{13}{-17}$
It is multiplicative identity.
$=1\times\frac{13}{-17}$
It is multiplicative identity.
Question 1101 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{-11}{16}\times\frac{16}{-11}=1$
$\frac{-11}{16}\times\frac{16}{-11}=1$
Answer
View full question & answer→$\frac{-11}{16}\times\frac{16}{-11}=1$
It is existanceof multiplicative inverse.
It is existanceof multiplicative inverse.
Question 1111 Mark
Multiply: $\frac{9}{-7}\ \text{by}\ \frac{36}{-11}$
Answer
View full question & answer→$\frac{9}{-7}\ \text{by}\ \frac{36}{-11}=\frac{9\times36}{(-7)\times(-11)}=\frac{324}{77}$
Question 1121 Mark
Multiply: $\frac{-8}{9}\ \text{by}\ \frac{3}{64}$
Answer
View full question & answer→$\frac{-8}{9}\ \text{by}\ \frac{3}{64}$
$=\frac{-8\times3}{9\times64}=\frac{-1\times1}{3\times8}=\frac{-1}{24}$
$=\frac{-8\times3}{9\times64}=\frac{-1\times1}{3\times8}=\frac{-1}{24}$
Question 1131 Mark
Multiply: $\frac{-8}{25}\ \text{by}\ \frac{-5}{16}$
Answer
View full question & answer→$\frac{-8}{25}\ \text{by}\ \frac{-5}{16}=\frac{(-8)\times(-5)}{25\times16}$
$=\frac{(-1)\times(-1)}{5\times2}=\frac{1}{10}$
$=\frac{(-1)\times(-1)}{5\times2}=\frac{1}{10}$
Question 1141 Mark
Multiply: $\frac{7}{11}\ \text{by}\ \frac{5}{4}$
Answer
View full question & answer→$\frac{7}{11}\ \text{by}\ \frac{5}{4}=\frac{7\times5}{11\times4}=\frac{35}{44}$
Question 1151 Mark
Multiply: $\frac{6}{7}\ \text{by}\ \frac{-49}{36}$
Answer
View full question & answer→$\frac{6}{7}\ \text{by}\ \frac{-49}{36}=\frac{6}{7}\times\frac{-49}{36}$
$=\frac{6\times(-49)}{7\times36}=\frac{1\times(-7)}{1\times6}=\frac{-7}{6}$
$=\frac{6\times(-49)}{7\times36}=\frac{1\times(-7)}{1\times6}=\frac{-7}{6}$
Question 1161 Mark
Multiply: $\frac{5}{7}\ \text{by}\ \frac{-3}{4}$
Answer
View full question & answer→$\frac{5}{7}\ \text{by}\ \frac{-3}{4}=\frac{5\times(-3)}{7\times4}=\frac{-15}{28}$
Question 1171 Mark
Multiply: $-\frac{3}{5}\ \text{by}\ -\frac{4}{7}$
Answer
View full question & answer→$-\frac{3}{5}\ \text{by}\ -\frac{4}{7}=\frac{-3\times(-4}{5\times7}=\frac{12}{35}$
Question 1181 Mark
Multiply: $\frac{-3}{17}\ \text{by}\ \frac{-5}{-4}$
Answer
View full question & answer→$\frac{-3}{17}\ \text{by}\ \frac{-5}{-4}=\frac{-3\times(-5)}{17\times(-4)}=\frac{15}{-68}$
Question 1191 Mark
Multiply: $\frac{-2}{9}\ \text{by}\ \frac{5}{11}$
Answer
View full question & answer→$\frac{-2}{9}\ \text{by}\ \frac{5}{11}=\frac{-2\times5}{9\times11}=\frac{-10}{99}$
Question 1201 Mark
Multiply: $-\frac{15}{11}\ \text{by}\ 7$
Answer
View full question & answer→$-\frac{15}{11}\ \text{by}\ 7=\frac{-15\times7}{11}=\frac{-105}{11}$
Question 1211 Mark
Multiply: $\frac{-11}{13}\ \text{by}\ \frac{-21}{7}$
Answer
View full question & answer→$\frac{-11}{13}\ \text{by}\ \frac{-21}{7}=\frac{(-11)\times(-21)}{13\times7}$
$=\frac{231}{91}=\frac{231\div7}{91\div7}=\frac{33}{13}$
$=\frac{231}{91}=\frac{231\div7}{91\div7}=\frac{33}{13}$
Question 1221 Mark
If 24 trousers of equal size can be prepared in 54 metres of cloth, what length of cloth is required for each trouser?
Answer
View full question & answer→Cloth required for 24 trousers = 54m
$\therefore$Cloth required for 1 trouser$=(54\div24)\text{m}$
$=\frac{54}{24}=\frac{9}{4}=2\frac{1}{4}\text{m}$
$\therefore$Cloth required for 1 trouser$=(54\div24)\text{m}$
$=\frac{54}{24}=\frac{9}{4}=2\frac{1}{4}\text{m}$
Question 1231 Mark
Find the value and express as a rational number in standard form: $\frac{-36}{126}\div\frac{-3}{75}$
Answer
View full question & answer→$\frac{-36}{126}\div\frac{-3}{75}=\frac{-36}{125}\times\frac{75}{-3}$ $=\frac{-36\times75}{125\times(-3)}=\frac{-12\times3}{5\times(-1)}$ $=\frac{-36}{-5}=\frac{36}{5}$
Question 1241 Mark
Find the value and express as a rational number in standard form: $\frac{2}{5}\div\frac{26}{15}$
Answer
View full question & answer→$\frac{2}{5}\div\frac{26}{15}=\frac{2}{5}\times\frac{15}{26}=\frac{2\times15}{5\times26}$ $=\frac{1\times3}{1\times13}=\frac{3}{13}$
Question 1251 Mark
Find the value and express as a rational number in standard form: $\frac{-22}{27}\div\frac{-110}{18}$
Answer
View full question & answer→$\frac{-22}{27}\div\frac{-110}{18}=\frac{-22}{27}\times\frac{18}{-110}$ $=\frac{-22\times18}{27\times(-110)}=\frac{-1\times2}{34\times(-5)}$ $=\frac{-2}{-15}=\frac{2}{15}$
Question 1261 Mark
Find the value and express as a rational number in standard form: $\frac{10}{3}\div\frac{-35}{12}$
Answer
View full question & answer→$\frac{10}{3}\div\frac{-35}{12}=\frac{10}{3}\times\frac{12}{-35}$ $=\frac{10\times12}{3\times(-35)}$ $=\frac{2\times4}{1\times(-7)}=\frac{8}{-7}$ $=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
Question 1271 Mark
Find the value and express as a rational number in standard form:
$\frac{-40}{99}\div(-20)$
$\frac{-40}{99}\div(-20)$
Answer
View full question & answer→$\frac{-40}{99}\div(-20)=\frac{-40}{99}\times\frac{1}{-20}$ $=\frac{-2\times1}{99\times(-1)}=\frac{-2}{99}=\frac{2}{99}$
Question 1281 Mark
Find the value and express as a rational number in standard form: $-6\div\frac{-8}{17}$
Answer
View full question & answer→$-6\div\frac{-8}{17}=-6\times\frac{17}{-8}$ $=\frac{-3\times17}{-4}$ $=\frac{-51}{4}=\frac{51}{4}$
Question 1291 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{-7}{9}$
Answer
View full question & answer→Multiplicative inverse of$\frac{-7}{9}=\frac{9}{-7}$
Question 1301 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{-3}{-5}$
Answer
View full question & answer→Multiplicative inverse of$=\frac{-5}{-3}=\frac{5}{3}$
Question 1311 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{2}{3}\times\frac{9}{4}$
Answer
View full question & answer→Multiplicative inverse of$\frac{2}{3}\times\frac{9}{4}$ $=\frac{3}{2}\times\frac{4}{9}$ $\frac{3\times4}{2\times9}=\frac{1\times2}{1\times3}$ $=\frac{2}{3}$
Question 1321 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{12}{5}$
Answer
View full question & answer→Multiplicative inverse of$\frac{12}{5}=\frac{5}{12}$
Question 1331 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{0}{3}$
Answer
View full question & answer→Multiplicative inverse of $0=$Does not exist as division by 0 is not admissible.
Question 1341 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$-7$
$-7$
Answer
View full question & answer→Multiplicative inverse of$-7=\frac{1}{-7}$
Question 1351 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $9$
Answer
View full question & answer→Multiplicative inverse of$9=\frac{1}{9}$![]()
Question 1361 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $-2\times\frac{-3}{5}$
Answer
View full question & answer→Multiplicative inverse of $-2\times\frac{-3}{5}$ $=\frac{1}{-2}\times\frac{5}{-3}=\frac{1\times5}{(-2)\times(-3)}$ $=\frac{5}{6}$
Question 1371 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $1$
Answer
View full question & answer→Multiplicative inverse of$1=1$
Question 1381 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $-1$
Answer
View full question & answer→Multiplicative inverse of $-1=-1$
Question 1391 Mark
Divide:
$\frac{-3}{4}\ \text{by}\ -6$
$\frac{-3}{4}\ \text{by}\ -6$
Answer
View full question & answer→$\frac{-3}{4}\ \text{by}\ -6=\frac{-3}{4}\div\frac{-6}{1}=\frac{-3}{1}\times\frac{1}{-6}$
$=\frac{-1\times1}{4\times(-2)}=\frac{-1}{-8}=\frac{1}{8}$
$=\frac{-1\times1}{4\times(-2)}=\frac{-1}{-8}=\frac{1}{8}$
Question 1401 Mark
Divide:
$\frac{-3}{13}\ \text{by}\ \frac{-4}{65}$
$\frac{-3}{13}\ \text{by}\ \frac{-4}{65}$
Answer
View full question & answer→$\frac{-3}{13}\ \text{by}\ \frac{-4}{65}$
$=\frac{-3}{13}\div\frac{-4}{65}=\frac{-3}{13}\times\frac{65}{-4}$
$=\frac{-3\times5}{1\times(-4)}=\frac{-15}{-4}=\frac{15}{4}$
$=\frac{-3}{13}\div\frac{-4}{65}=\frac{-3}{13}\times\frac{65}{-4}$
$=\frac{-3\times5}{1\times(-4)}=\frac{-15}{-4}=\frac{15}{4}$
Question 1411 Mark
Divide:
$\frac{2}{3}\ \text{by}\ \frac{-7}{12}$
$\frac{2}{3}\ \text{by}\ \frac{-7}{12}$
Answer
View full question & answer→$\frac{2}{3}\ \text{by}\ \frac{-7}{12}$
$=\frac{2}{3}\div\frac{-7}{12}=\frac{2}{3}\times\frac{12}{-7}$
$=\frac{2\times4}{1\times(-7)}=\frac{8}{-7}$
$=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
$=\frac{2}{3}\div\frac{-7}{12}=\frac{2}{3}\times\frac{12}{-7}$
$=\frac{2\times4}{1\times(-7)}=\frac{8}{-7}$
$=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
Question 1421 Mark
Divide:
$-4\ \text{by}\ \frac{-3}{5}$
$-4\ \text{by}\ \frac{-3}{5}$
Answer
View full question & answer→$-4\ \text{by}\ \frac{-3}{5}$
$=-4\div\frac{-3}{5}$
$=-4\times\frac{5}{-3}$
$=\frac{-4\times5}{-3}$
$=\frac{-20}{-3}=\frac{20}{3}$
$=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
$=-4\div\frac{-3}{5}$
$=-4\times\frac{5}{-3}$
$=\frac{-4\times5}{-3}$
$=\frac{-20}{-3}=\frac{20}{3}$
$=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
Question 1431 Mark
Divide:
$1\ \text{by}\ \frac{1}{2}$
$1\ \text{by}\ \frac{1}{2}$
Answer
View full question & answer→$1\ \text{by}\ \frac{1}{2}=1\div\frac{1}{2}=1\times\frac{2}{1}=2$
Question 1441 Mark
Divide:
$0\ \text{by}\ \frac{-7}{5}$
$0\ \text{by}\ \frac{-7}{5}$
Answer
View full question & answer→$0\ \text{by}\ \frac{-7}{5}=0\div\frac{-7}{5}=0\times\frac{5}{-7}=0$
Question 1451 Mark
Add the following ration numbers:
$\frac{-8}{11}$ and $\frac{-4}{11}$
$\frac{-8}{11}$ and $\frac{-4}{11}$
Answer
View full question & answer→$\frac{-8}{11}+\frac{-4}{11}=\frac{-8-4}{11}=\frac{-12}{11}$
Question 1461 Mark
Add the following ration numbers:
$\frac{6}{13}$ and $\frac{-9}{13}$
$\frac{6}{13}$ and $\frac{-9}{13}$
Answer
View full question & answer→$\frac{6}{13}+\frac{-9}{13}=\frac{6-9}{13}=\frac{-3}{13}$
Question 1471 Mark
Add the following ration numbers:
$\frac{-5}{7}$ and $\frac{3}{7}$
$\frac{-5}{7}$ and $\frac{3}{7}$
Answer
View full question & answer→$\frac{-5}{7}+\frac{3}{7}=\frac{-5+3}{7}=\frac{-2}{7}$
Question 1481 Mark
Add the following ration numbers:
$\frac{-15}{4}$ and $\frac{7}{4}$
$\frac{-15}{4}$ and $\frac{7}{4}$
Answer
View full question & answer→$\frac{-15}{7}+\frac{7}{4}=\frac{-15+7}{4}=\frac{-8}{4}=-2$