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Question 11 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$9$
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
$\frac{13}{-17}\times1=\frac{13}{-17}$
$=1\times\frac{13}{-17}$
It is multiplicative identity.
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Question 31 Mark
Multiply:
$\frac{-3}{17}\ \text{by}\ \frac{-5}{-4}$
Answer
$\frac{-3}{17}\ \text{by}\ \frac{-5}{-4}=\frac{-3\times(-5)}{17\times(-4)}=\frac{15}{-68}$
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Question 41 Mark
Fill in the blanks:
The product of two positive rational numbers is always ______.
Answer
The product of two positive rational number is alway positive.
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Question 51 Mark
Fill in the blanks:
$(17 \times 12)^{-1}=17^{-1} \times$_____.
Answer
$(17 \times 12)^{-1}=17^{-1} \times 1 2 ^{-1}$
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Question 61 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$\frac{-3}{-5}$
Answer
Multiplicative inverse of $=\frac{-5}{-3}=\frac{5}{3}$
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Question 71 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$\frac{0}{3}$
Answer
Multiplicative inverse of $0=$ Does not exist as division by 0 is not admissible.
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Question 101 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$1$
Answer
Multiplicative inverse of $1=1$
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Question 111 Mark
Multiply:
$-\frac{3}{5}\ \text{by}\ -\frac{4}{7}$
Answer
$-\frac{3}{5}\ \text{by}\ -\frac{4}{7}=\frac{-3\times(-4}{5\times7}=\frac{12}{35}$
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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
$\frac{-5}{16}\times\frac{8}{15}=\frac{8}{15}\times\frac{-5}{16}$
It is commutative property.
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Question 131 Mark
Fill in the blanks:
The product of a positive rational number and a negative rational number is always _____.
Answer
The product of a positive rational number and a negative rational number is always negative.
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Question 141 Mark
Multiply:
$\frac{9}{-7}\ \text{by}\ \frac{36}{-11}$
Answer
$\frac{9}{-7}\ \text{by}\ \frac{36}{-11}=\frac{9\times36}{(-7)\times(-11)}=\frac{324}{77}$
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Question 151 Mark
Fill in the blanks:
The number 0 is _________ the reciprocal of any number.
Answer
The number 0 is not the reciprocal of any number.
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Question 161 Mark
Find the value and express as a rational number in standard form:
$\frac{-36}{126}\div\frac{-3}{75}$
Answer
$\frac{-36}{126}\div\frac{-3}{75}=\frac{-36}{125}\times\frac{75}{-3}$
$=\frac{-36\times75}{125\times(-3)}=\frac{-12\times3}{5\times(-1)}$
$=\frac{-36}{-5}=\frac{36}{5}$
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Question 171 Mark
Divide:
$\frac{2}{3}\ \text{by}\ \frac{-7}{12}$
Answer
$\frac{2}{3}\ \text{by}\ \frac{-7}{12}$
$=\frac{2}{3}\div\frac{-7}{12}=\frac{2}{3}\times\frac{12}{-7}$
$=\frac{2\times4}{1\times(-7)}=\frac{8}{-7}$
$=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
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Question 191 Mark
Multiply:
$\frac{-8}{9}\ \text{by}\ \frac{3}{64}$
Answer
$\frac{-8}{9}\ \text{by}\ \frac{3}{64}$
$=\frac{-8\times3}{9\times64}=\frac{-1\times1}{3\times8}=\frac{-1}{24}$
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Question 201 Mark
Write the additive inverse of the following rational number:
-1
Answer
1
Negative inverse of -1 is (-1) = 1.
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Question 211 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$-2\times\frac{-3}{5}$
Answer
Multiplicative inverse of $-2\times\frac{-3}{5}$
$=\frac{1}{-2}\times\frac{5}{-3}=\frac{1\times5}{(-2)\times(-3)}$
$=\frac{5}{6}$
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Question 221 Mark
Fill in the blanks:
The product of two negative rational numbers is always __________.
Answer
The product of two negative rational numbers is always positive.
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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
$\frac{-13}{9}\times\frac{27}{-26}=\frac{-13\times27}{9\times(-26)}$
$=\frac{-1\times3}{-\times(-2)}=\frac{-3}{-2}=\frac{3}{2}$
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Question 241 Mark
Find the value and express as a rational number in standard form:
$\frac{-40}{99}\div(-20)$
Answer
$\frac{-40}{99}\div(-20)=\frac{-40}{99}\times\frac{1}{-20}$
$=\frac{-2\times1}{99\times(-1)}=\frac{-2}{99}=\frac{2}{99}$
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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
$\frac{-9}{16}\times\frac{-64}{-27}$
$=\frac{(-9)\times(-64)}{16\times(-27)}$
$=\frac{-1\times(-4)}{1\times(-3)}=\frac{4}{-3}$
$=\frac{4\times(-1)}{-3(-1)}=\frac{-4}{3}$
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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
$\frac{-5}{9}\times\Big(\frac{4}{15}\times\frac{-9}{8}\Big)$
$=\Big(\frac{-5}{9}\times\frac{4}{15}\Big)\times\frac{-9}{8}$
It is associativem property.
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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
$\frac{-50}{7}\times\frac{14}{3}=\frac{-50\times14}{7\times3}$
$=\frac{-50\times2}{1\times3}=\frac{-100}{3}$
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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
$\frac{-4}{5}\times\Big(\frac{5}{7}\times\frac{-8}{9}\Big)=\Big(\frac{-4}{5}\times\frac{5}{7}\Big)\times\frac{-8}{9}$
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Question 291 Mark
Divide:
$\frac{-3}{13}\ \text{by}\ \frac{-4}{65}$
Answer
$\frac{-3}{13}\ \text{by}\ \frac{-4}{65}$
$=\frac{-3}{13}\div\frac{-4}{65}=\frac{-3}{13}\times\frac{65}{-4}$
$=\frac{-3\times5}{1\times(-4)}=\frac{-15}{-4}=\frac{15}{4}$
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Question 301 Mark
Fill in the blanks:
If a is reciprocal of b, then the reciprocal of b is __________.
Answer
If a is reciprocal of b, then the reciprocal of b is a.
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Question 311 Mark
Find the value and express as a rational number in standard form:
$-6\div\frac{-8}{17}$
Answer
$-6\div\frac{-8}{17}=-6\times\frac{17}{-8}$
$=\frac{-3\times17}{-4}$
$=\frac{-51}{4}=\frac{51}{4}$
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Question 321 Mark
Find the value and express as a rational number in standard form:
$\frac{-22}{27}\div\frac{-110}{18}$
Answer
$\frac{-22}{27}\div\frac{-110}{18}=\frac{-22}{27}\times\frac{18}{-110}$
$=\frac{-22\times18}{27\times(-110)}=\frac{-1\times2}{34\times(-5)}$
$=\frac{-2}{-15}=\frac{2}{15}$
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Question 331 Mark
Fill in the blanks:
The reciprocal of a positive rational number is _______.
Answer
The reciprocal of a positive rational number is positive.
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Question 341 Mark
Find the value and express as a rational number in standard form:
$\frac{2}{5}\div\frac{26}{15}$
Answer
$\frac{2}{5}\div\frac{26}{15}=\frac{2}{5}\times\frac{15}{26}=\frac{2\times15}{5\times26}$
$=\frac{1\times3}{1\times13}=\frac{3}{13}$
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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
$\frac{2}{13}\times0=0=0\times\frac{2}{13}$
It is zero property of multiplication.
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Question 371 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$\frac{12}{5}$
Answer
Multiplicative inverse of $\frac{12}{5}=\frac{5}{12}$
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Question 381 Mark
Write the negative (additive inverse) of the following:
$\frac{-2}{5}$
Answer
$\frac{-2}{5}$
Negative of $\frac{-2}{5}$ is $-\Big(\frac{-2}{5}\Big)=\frac{2}{5}$
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Question 391 Mark
Add the following ration numbers:
$\frac{-5}{7}$ and $\frac{3}{7}$
Answer
$\frac{-5}{7}+\frac{3}{7}=\frac{-5+3}{7}=\frac{-2}{7}$
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Question 401 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$-7$
Answer
Multiplicative inverse of $-7=\frac{1}{-7}$
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Question 411 Mark
Add the following ration numbers:
$\frac{6}{13}$ and $\frac{-9}{13}$
Answer
$\frac{6}{13}+\frac{-9}{13}=\frac{6-9}{13}=\frac{-3}{13}$
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Question 421 Mark
Write the additive inverse of the following rational number:
$\frac{7}{-9}$
Answer
$\frac{7}{-9}$
Nagative of $\frac{7}{-9}$ is $-\Big(\frac{7}{-9}\Big)=\frac{7}{9}$
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Question 431 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$\frac{2}{3}\times\frac{9}{4}$
Answer
Multiplicative inverse of $\frac{2}{3}\times\frac{9}{4}$
$=\frac{3}{2}\times\frac{4}{9}$
$\frac{3\times4}{2\times9}=\frac{1\times2}{1\times3}$
$=\frac{2}{3}$
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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
$\frac{-3}{2}\times\frac{5}{4}+\frac{-3}{2}\times\frac{-7}{6}$
$=\frac{-3}{2}\times\Big(\frac{5}{4}+\frac{-7}{6}\Big)$
It is destributive law of multiplication over addition.
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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
Cloth required for 24 trousers = 54m$\therefore$ Cloth required for 1 trouser $=(54\div24)\text{m}$
$=\frac{54}{24}=\frac{9}{4}=2\frac{1}{4}\text{m}$
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Question 461 Mark
Multiply:
$\frac{-8}{25}\ \text{by}\ \frac{-5}{16}$
Answer
$\frac{-8}{25}\ \text{by}\ \frac{-5}{16}=\frac{(-8)\times(-5)}{25\times16}$
$=\frac{(-1)\times(-1)}{5\times2}=\frac{1}{10}$
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Question 471 Mark
Divide:
$1\ \text{by}\ \frac{1}{2}$
Answer
$1\ \text{by}\ \frac{1}{2}=1\div\frac{1}{2}=1\times\frac{2}{1}=2$
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Question 481 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{-11}{16}\times\frac{16}{-11}=1$
Answer
$\frac{-11}{16}\times\frac{16}{-11}=1$
It is existanceof multiplicative inverse.
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Question 491 Mark
Name the property of multiplication of rational numbers illustrated by the following statements:
$\frac{-17}{5}\times9=9\times\frac{-17}{5}$
Answer
$\frac{-17}{5}\times9=9\times\frac{-17}{5}$
It is commutative property.
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Question 501 Mark
Write the additive inverse of the following rational number:
$\frac{-17}{5}$
Answer
$\frac{-17}{5}$
Additive inverse of $\frac{-17}{5}$ is $-\Big(\frac{-17}{5}\Big)=\frac{17}{5}$
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Question 511 Mark
Write the additive inverse of the following rational number:
$\frac{3}{-11}$
Answer
$\frac{3}{-11}$Additive inverse of $\frac{3}{-11}$ is $-\Big(\frac{3}{-11}\Big)=\frac{3}{11}$
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Question 521 Mark
Add the following ration numbers:
$\frac{-15}{4}$ and $\frac{7}{4}$
Answer
$\frac{-15}{7}+\frac{7}{4}=\frac{-15+7}{4}=\frac{-8}{4}=-2$
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Question 531 Mark
Multiply:
$-\frac{15}{11}\ \text{by}\ 7$
Answer
$-\frac{15}{11}\ \text{by}\ 7=\frac{-15\times7}{11}=\frac{-105}{11}$
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Question 541 Mark
Write the additive inverse of the following rational number:
$\frac{-16}{13}$
Answer
$\frac{-16}{13}$
Negative of $\frac{-16}{13}$ is $-\Big(\frac{-16}{13}\Big)=\frac{16}{13}$
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Question 551 Mark
Divide:
$0\ \text{by}\ \frac{-7}{5}$
Answer
$0\ \text{by}\ \frac{-7}{5}=0\div\frac{-7}{5}=0\times\frac{5}{-7}=0$
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Question 561 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$\frac{-7}{9}$
Answer
Multiplicative inverse of $\frac{-7}{9}=\frac{9}{-7}$
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Question 571 Mark
Multiply:
$\frac{5}{7}\ \text{by}\ \frac{-3}{4}$
Answer
$\frac{5}{7}\ \text{by}\ \frac{-3}{4}=\frac{5\times(-3)}{7\times4}=\frac{-15}{28}$
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Question 581 Mark
Write the additive inverse of the following rational number:
$\frac{-11}{-25}$
Answer
$\frac{-11}{-25}$
Additive inverse of $\frac{-11}{-25}=\Big(\frac{-11}{-25}\Big)$
$=-\Big(\frac{11}{25}\Big)=\frac{-11}{25}$
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Question 591 Mark
Add the following ration numbers:
$\frac{-8}{11}$ and $\frac{-4}{11}$
Answer
$\frac{-8}{11}+\frac{-4}{11}=\frac{-8-4}{11}=\frac{-12}{11}$
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Question 601 Mark
Find the value and express as a rational number in standard form:
$\frac{10}{3}\div\frac{-35}{12}$
Answer
$\frac{10}{3}\div\frac{-35}{12}=\frac{10}{3}\times\frac{12}{-35}$
$=\frac{10\times12}{3\times(-35)}$
$=\frac{2\times4}{1\times(-7)}=\frac{8}{-7}$
$=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
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Question 611 Mark
Simplify the following and express the result as a rational number in standard form:
$\frac{-5}{9}\times\frac{72}{-25}$
Answer
$\frac{-5}{9}\times\frac{72}{-25}=\frac{-5\times72}{9\times(-25)}$
$=\frac{-1\times8}{1\times(-5)}=\frac{-8}{-5}$
$=\frac{8}{5}$
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Question 621 Mark
Write the additive inverse of the following rational number:
$\frac{-2}{17}$
Answer
$\frac{-2}{17}$
Additive inverse of $\frac{-2}{17}$ is $-\Big(\frac{-2}{17}\Big)=\frac{2}{17}$
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Question 631 Mark
Fill in the blanks:
The product of a rational number and its reciprocal is ______________.
Answer
The product of a rational number and its reciprocal is 1.
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Question 641 Mark
Fill in the blanks:
The numbers __________ and _______ are their own reciprocals.
Answer
The numbers -1 and 1 are their own reciprocals.
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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
$\frac{7}{6}\times\frac{-3}{28}=\frac{7\times(-3)}{6\times28}$
$=\frac{1\times(-1)}{2\times4}=\frac{-1}{8}$
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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
$\frac{7}{4}\times\Big(\frac{-8}{3}+\frac{-13}{12}\Big)$
$=\frac{7}{4}\times\frac{-8}{3}+\frac{7}{4}+\frac{-13}{12}$
It is distributive property over addition.
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Question 671 Mark
Multiply:
$\frac{-11}{13}\ \text{by}\ \frac{-21}{7}$
Answer
$\frac{-11}{13}\ \text{by}\ \frac{-21}{7}=\frac{(-11)\times(-21)}{13\times7}$
$=\frac{231}{91}=\frac{231\div7}{91\div7}=\frac{33}{13}$
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Question 681 Mark
Write the additive inverse of the following rational number:
$\frac{-5}{1}$
Answer
$\frac{-5}{1}$
Negative of $\frac{-5}{1}$ is $-\Big(\frac{-5}{1}\Big)={5}$
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Question 691 Mark
Fill in the blanks:
$\frac{5}{11}\times\frac{-3}{8}=\frac{-3}{8}\times$ ___________.
Answer
$\frac{5}{11}\times\frac{-3}{8}=\frac{-3}{8}\times\frac{5}{11}$
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Question 701 Mark
Fill in the blanks:
Reciprocal of $\frac{1}{\text{a}},a\neq0$ is _________.
Answer
Reciprocal of $\frac{1}{\text{a}},a\neq0$ is a.
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Question 711 Mark
Multiply:
$\frac{-2}{9}\ \text{by}\ \frac{5}{11}$
Answer
$\frac{-2}{9}\ \text{by}\ \frac{5}{11}=\frac{-2\times5}{9\times11}=\frac{-10}{99}$
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Question 721 Mark
Divide:
$-4\ \text{by}\ \frac{-3}{5}$
Answer
$-4\ \text{by}\ \frac{-3}{5}$
$=-4\div\frac{-3}{5}$
$=-4\times\frac{5}{-3}$
$=\frac{-4\times5}{-3}$
$=\frac{-20}{-3}=\frac{20}{3}$
$=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
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Question 731 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$-1$
Answer
Multiplicative inverse of $-1=-1$
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Question 741 Mark
Multiply:
$\frac{7}{11}\ \text{by}\ \frac{5}{4}$
Answer
$\frac{7}{11}\ \text{by}\ \frac{5}{4}=\frac{7\times5}{11\times4}=\frac{35}{44}$
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Question 751 Mark
Fill in the blanks:
$-4\times\frac{7}{9}=\frac{7}{9}\times$ ___________.
Answer
Fill in the blanks:
$-4\times\frac{7}{9}=\frac{7}{9}\times$ -4.
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Question 761 Mark
Verify the property: x × (y × z) = (x × y) × z by taking:
$\text{x}=\frac{5}{7},\text{y}=\frac{-12}{13},\text{z=}\frac{-7}{18}$
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.
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Question 771 Mark
Simplify the following and express the result as a rational number in standard form:
$\frac{-19}{36}\times16$
Answer
$\frac{-19}{36}\times16=\frac{-19\times16}{36}$
$=\frac{-19\times4}{9}=\frac{-76}{9}$
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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
$\frac{1}{2}\times\Big(\frac{3}{4}+\frac{-5}{12}\Big)=\frac{1}{2}\times\frac{3}{4}+\frac{1}{2}\times\frac{-5}{12}$
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Question 791 Mark
Divide:
$\frac{-3}{4}\ \text{by}\ -6$
Answer
$\frac{-3}{4}\ \text{by}\ -6=\frac{-3}{4}\div\frac{-6}{1}=\frac{-3}{1}\times\frac{1}{-6}$
$=\frac{-1\times1}{4\times(-2)}=\frac{-1}{-8}=\frac{1}{8}$
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Question 801 Mark
Multiply:
$\frac{6}{7}\ \text{by}\ \frac{-49}{36}$
Answer
$\frac{6}{7}\ \text{by}\ \frac{-49}{36}=\frac{6}{7}\times\frac{-49}{36}$
$=\frac{6\times(-49)}{7\times36}=\frac{1\times(-7)}{1\times6}=\frac{-7}{6}$
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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
$\frac{-16}{21}\times\frac{14}{5}=\frac{-16\times14}{21\times5}$
$=\frac{-16\times2}{3\times5}=\frac{-32}{15}$
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Question 821 Mark
Fill in the blanks:
The reciprocal of a negative rational number is ____________.
Answer
The reciprocal of a negative rational number is negative.
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