Question 11 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$9$
AnswerMultiplicative 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:
$(17 \times 12)^{-1}=17^{-1} \times$_____.
Answer$(17 \times 12)^{-1}=17^{-1} \times 1 2 ^{-1}$
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
Answer1
Negative inverse of 1 is -1.
View full question & answer→Question 91 Mark
Write the additive inverse of the following rational number:
0
Answer0
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
Answer1
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 _______.
AnswerThe 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:
$-7$
AnswerMultiplicative 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→