Question 11 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$9$
Answer Multiplicative inverse of $9=\frac{1}{9}$
View full question & answer→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.
View full question & answer→Question 31 Mark
Multiply: $\frac{-3}{17}\ \text{by}\ \frac{-5}{-4}$
Answer$\frac{-3}{17}\ \text{by}\ \frac{-5}{-4}=\frac{-3\times(-5)}{17\times(-4)}=\frac{15}{-68}$
View full question & answer→Question 41 Mark
Fill in the blanks: The product of two positive rational numbers is always ______.
AnswerThe product of two positive rational number is alway positive.
View full question & answer→Question 51 Mark
Fill in the blanks:
$(17 × 12)^{-1} = 17^{-1}$ × _____.
Answer$(17 × 12)^{-1} = 17^{-1} × 12^{-1}$
View full question & answer→Question 61 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{-3}{-5}$
AnswerMultiplicative inverse of $=\frac{-5}{-3}=\frac{5}{3}$
View full question & answer→Question 71 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{0}{3}$
AnswerMultiplicative inverse of $0=$ Does not exist as division by $0$ is not admissible.
View full question & answer→Question 81 Mark
Write the additive inverse of the following rational number: $1$
Answer$1$ Negative inverse of $1$ is $-1.$
View full question & answer→Question 91 Mark
Write the additive inverse of the following rational number:
$0$
Answer$0$
Negative inverse of $0$ is $0.$
View full question & answer→Question 101 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $1$
AnswerMultiplicative inverse of $1=1$
View full question & answer→Question 111 Mark
Multiply: $-\frac{3}{5}\ \text{by}\ -\frac{4}{7}$
Answer$-\frac{3}{5}\ \text{by}\ -\frac{4}{7}=\frac{-3\times(-4}{5\times7}=\frac{12}{35}$
View full question & answer→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.
View full question & answer→Question 131 Mark
Fill in the blanks: The product of a positive rational number and a negative rational number is always _____.
AnswerThe product of a positive rational number and a negative rational number is always negative.
View full question & answer→Question 141 Mark
Multiply: $\frac{9}{-7}\ \text{by}\ \frac{36}{-11}$
Answer$\frac{9}{-7}\ \text{by}\ \frac{36}{-11}=\frac{9\times36}{(-7)\times(-11)}=\frac{324}{77}$
View full question & answer→Question 151 Mark
Fill in the blanks: The number $0$ is _________ the reciprocal of any number.
AnswerThe number $0$ is not the reciprocal of any number.
View full question & answer→Question 161 Mark
Find the value and express as a rational number in standard form:
$\frac{-36}{126}\div\frac{-3}{75}$
Answer $\frac{-36}{126}\div\frac{-3}{75}=\frac{-36}{125}\times\frac{75}{-3}$
$=\frac{-36\times75}{125\times(-3)}=\frac{-12\times3}{5\times(-1)}$
$=\frac{-36}{-5}=\frac{36}{5}$
View full question & answer→Question 171 Mark
Divide: $\frac{2}{3}\ \text{by}\ \frac{-7}{12}$
Answer$\frac{2}{3}\ \text{by}\ \frac{-7}{12}$ $=\frac{2}{3}\div\frac{-7}{12}=\frac{2}{3}\times\frac{12}{-7}$ $=\frac{2\times4}{1\times(-7)}=\frac{8}{-7}$ $=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
View full question & answer→Question 181 Mark
Simplify: $0+\frac{-3}{5}$
Answer$0+\frac{-3}{5}$ $=\frac{-3}{5}$
View full question & answer→Question 191 Mark
Multiply: $\frac{-8}{9}\ \text{by}\ \frac{3}{64}$
Answer$\frac{-8}{9}\ \text{by}\ \frac{3}{64}$ $=\frac{-8\times3}{9\times64}=\frac{-1\times1}{3\times8}=\frac{-1}{24}$
View full question & answer→Question 201 Mark
Write the additive inverse of the following rational number: $-1$
Answer$1$ Negative inverse of $-1$ is $(-1) = 1.$
View full question & answer→Question 211 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $-2\times\frac{-3}{5}$
AnswerMultiplicative inverse of $-2\times\frac{-3}{5}$ $=\frac{1}{-2}\times\frac{5}{-3}=\frac{1\times5}{(-2)\times(-3)}$ $=\frac{5}{6}$
View full question & answer→Question 221 Mark
Fill in the blanks: The product of two negative rational numbers is always __________.
AnswerThe product of two negative rational numbers is always positive.
View full question & answer→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$\frac{-13}{9}\times\frac{27}{-26}=\frac{-13\times27}{9\times(-26)}$ $=\frac{-1\times3}{-\times(-2)}=\frac{-3}{-2}=\frac{3}{2}$
View full question & answer→Question 241 Mark
Find the value and express as a rational number in standard form: $\frac{-40}{99}\div(-20)$
Answer$\frac{-40}{99}\div(-20)=\frac{-40}{99}\times\frac{1}{-20}$ $=\frac{-2\times1}{99\times(-1)}=\frac{-2}{99}=\frac{2}{99}$
View full question & answer→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$\frac{-9}{16}\times\frac{-64}{-27}$ $=\frac{(-9)\times(-64)}{16\times(-27)}$ $=\frac{-1\times(-4)}{1\times(-3)}=\frac{4}{-3}$ $=\frac{4\times(-1)}{-3(-1)}=\frac{-4}{3}$
View full question & answer→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.
View full question & answer→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$\frac{-50}{7}\times\frac{14}{3}=\frac{-50\times14}{7\times3}$ $=\frac{-50\times2}{1\times3}=\frac{-100}{3}$
View full question & answer→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$\frac{-4}{5}\times\Big(\frac{5}{7}\times\frac{-8}{9}\Big)=\Big(\frac{-4}{5}\times\frac{5}{7}\Big)\times\frac{-8}{9}$
View full question & answer→Question 291 Mark
Divide: $\frac{-3}{13}\ \text{by}\ \frac{-4}{65}$
Answer$\frac{-3}{13}\ \text{by}\ \frac{-4}{65}$ $=\frac{-3}{13}\div\frac{-4}{65}=\frac{-3}{13}\times\frac{65}{-4}$ $=\frac{-3\times5}{1\times(-4)}=\frac{-15}{-4}=\frac{15}{4}$
View full question & answer→Question 301 Mark
Fill in the blanks: If $a$ is reciprocal of $b,$ then the reciprocal of $b$ is __________.
AnswerIf a is reciprocal of $b,$ then the reciprocal of $b$ is $a.$
View full question & answer→Question 311 Mark
Find the value and express as a rational number in standard form: $-6\div\frac{-8}{17}$
Answer$-6\div\frac{-8}{17}=-6\times\frac{17}{-8}$ $=\frac{-3\times17}{-4}$ $=\frac{-51}{4}=\frac{51}{4}$
View full question & answer→Question 321 Mark
Find the value and express as a rational number in standard form: $\frac{-22}{27}\div\frac{-110}{18}$
Answer$\frac{-22}{27}\div\frac{-110}{18}=\frac{-22}{27}\times\frac{18}{-110}$ $=\frac{-22\times18}{27\times(-110)}=\frac{-1\times2}{34\times(-5)}$ $=\frac{-2}{-15}=\frac{2}{15}$
View full question & answer→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.
View full question & answer→Question 341 Mark
Find the value and express as a rational number in standard form: $\frac{2}{5}\div\frac{26}{15}$
Answer$\frac{2}{5}\div\frac{26}{15}=\frac{2}{5}\times\frac{15}{26}=\frac{2\times15}{5\times26}$ $=\frac{1\times3}{1\times13}=\frac{3}{13}$
View full question & answer→Question 351 Mark
Fill in the blanks: Zero has _____________ 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$\frac{2}{13}\times0=0=0\times\frac{2}{13}$ It is zero property of multiplication.
View full question & answer→Question 371 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{12}{5}$
AnswerMultiplicative inverse of $\frac{12}{5}=\frac{5}{12}$
View full question & answer→Question 381 Mark
Write the negative (additive inverse) of the following: $\frac{-2}{5}$
Answer$\frac{-2}{5}$ Negative of $\frac{-2}{5}$ is $-\Big(\frac{-2}{5}\Big)=\frac{2}{5}$
View full question & answer→Question 391 Mark
Add the following ration numbers:
$\frac{-5}{7}$ and $\frac{3}{7}$
Answer $\frac{-5}{7}+\frac{3}{7}=\frac{-5+3}{7}=\frac{-2}{7}$
View full question & answer→Question 401 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$-7$
Answer Multiplicative inverse of $-7=\frac{1}{-7}$
View full question & answer→Question 411 Mark
Add the following ration numbers:
$\frac{6}{13}$ and $\frac{-9}{13}$
Answer $\frac{6}{13}+\frac{-9}{13}=\frac{6-9}{13}=\frac{-3}{13}$
View full question & answer→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 $-\Big(\frac{7}{-9}\Big)=\frac{7}{9}$
View full question & answer→Question 431 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers: $\frac{2}{3}\times\frac{9}{4}$
AnswerMultiplicative inverse of $\frac{2}{3}\times\frac{9}{4}$ $=\frac{3}{2}\times\frac{4}{9}$ $\frac{3\times4}{2\times9}=\frac{1\times2}{1\times3}$ $=\frac{2}{3}$
View full question & answer→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.
View full question & answer→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$?$
AnswerCloth required for $24$ trousers $= 54m$
$\therefore$ Cloth required for $1$ trouser $=(54\div24)\text{m}$
$=\frac{54}{24}=\frac{9}{4}=2\frac{1}{4}\text{m}$
View full question & answer→Question 461 Mark
Multiply:
$\frac{-8}{25}\ \text{by}\ \frac{-5}{16}$
Answer $\frac{-8}{25}\ \text{by}\ \frac{-5}{16}=\frac{(-8)\times(-5)}{25\times16}$
$=\frac{(-1)\times(-1)}{5\times2}=\frac{1}{10}$
View full question & answer→Question 471 Mark
Divide: $1\ \text{by}\ \frac{1}{2}$
Answer$1\ \text{by}\ \frac{1}{2}=1\div\frac{1}{2}=1\times\frac{2}{1}=2$
View full question & answer→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.
View full question & answer→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.
View full question & answer→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 $-\Big(\frac{-17}{5}\Big)=\frac{17}{5}$
View full question & answer→