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 $-\Big(\frac{3}{-11}\Big)=\frac{3}{11}$
View full question & answer→Question 521 Mark
Add the following ration numbers:
$\frac{-15}{4}$ and $\frac{7}{4}$
Answer$\frac{-15}{7}+\frac{7}{4}=\frac{-15+7}{4}=\frac{-8}{4}=-2$
View full question & answer→Question 531 Mark
Multiply:
$-\frac{15}{11}\ \text{by}\ 7$
Answer$-\frac{15}{11}\ \text{by}\ 7=\frac{-15\times7}{11}=\frac{-105}{11}$
View full question & answer→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 $-\Big(\frac{-16}{13}\Big)=\frac{16}{13}$
View full question & answer→Question 551 Mark
Divide:
$0\ \text{by}\ \frac{-7}{5}$
Answer$0\ \text{by}\ \frac{-7}{5}=0\div\frac{-7}{5}=0\times\frac{5}{-7}=0$
View full question & answer→Question 561 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$\frac{-7}{9}$
AnswerMultiplicative inverse of $\frac{-7}{9}=\frac{9}{-7}$
View full question & answer→Question 571 Mark
Multiply:
$\frac{5}{7}\ \text{by}\ \frac{-3}{4}$
Answer$\frac{5}{7}\ \text{by}\ \frac{-3}{4}=\frac{5\times(-3)}{7\times4}=\frac{-15}{28}$
View full question & answer→Question 581 Mark
Write the additive inverse of the following rational number:
$\frac{-11}{-25}$
Answer$\frac{-11}{-25}$
Additive inverse of $\frac{-11}{-25}=\Big(\frac{-11}{-25}\Big)$
$=-\Big(\frac{11}{25}\Big)=\frac{-11}{25}$
View full question & answer→Question 591 Mark
Add the following ration numbers:
$\frac{-8}{11}$ and $\frac{-4}{11}$
Answer$\frac{-8}{11}+\frac{-4}{11}=\frac{-8-4}{11}=\frac{-12}{11}$
View full question & answer→Question 601 Mark
Find the value and express as a rational number in standard form:
$\frac{10}{3}\div\frac{-35}{12}$
Answer$\frac{10}{3}\div\frac{-35}{12}=\frac{10}{3}\times\frac{12}{-35}$
$=\frac{10\times12}{3\times(-35)}$
$=\frac{2\times4}{1\times(-7)}=\frac{8}{-7}$
$=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
View full question & answer→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$\frac{-5}{9}\times\frac{72}{-25}=\frac{-5\times72}{9\times(-25)}$
$=\frac{-1\times8}{1\times(-5)}=\frac{-8}{-5}$
$=\frac{8}{5}$
View full question & answer→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 $-\Big(\frac{-2}{17}\Big)=\frac{2}{17}$
View full question & answer→Question 631 Mark
Fill in the blanks:
The product of a rational number and its reciprocal is ______________.
AnswerThe product of a rational number and its reciprocal is 1.
View full question & answer→Question 641 Mark
Fill in the blanks:
The numbers __________ and _______ are their own reciprocals.
AnswerThe numbers -1 and 1 are their own reciprocals.
View full question & answer→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$\frac{7}{6}\times\frac{-3}{28}=\frac{7\times(-3)}{6\times28}$
$=\frac{1\times(-1)}{2\times4}=\frac{-1}{8}$
View full question & answer→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.
View full question & answer→Question 671 Mark
Multiply:
$\frac{-11}{13}\ \text{by}\ \frac{-21}{7}$
Answer$\frac{-11}{13}\ \text{by}\ \frac{-21}{7}=\frac{(-11)\times(-21)}{13\times7}$
$=\frac{231}{91}=\frac{231\div7}{91\div7}=\frac{33}{13}$
View full question & answer→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 $-\Big(\frac{-5}{1}\Big)={5}$
View full question & answer→Question 691 Mark
Fill in the blanks:
$\frac{5}{11}\times\frac{-3}{8}=\frac{-3}{8}\times$ ___________.
Answer$\frac{5}{11}\times\frac{-3}{8}=\frac{-3}{8}\times\frac{5}{11}$
View full question & answer→Question 701 Mark
Fill in the blanks:
Reciprocal of $\frac{1}{\text{a}},a\neq0$ is _________.
AnswerReciprocal of $\frac{1}{\text{a}},a\neq0$ is a.
View full question & answer→Question 711 Mark
Multiply:
$\frac{-2}{9}\ \text{by}\ \frac{5}{11}$
Answer$\frac{-2}{9}\ \text{by}\ \frac{5}{11}=\frac{-2\times5}{9\times11}=\frac{-10}{99}$
View full question & answer→Question 721 Mark
Divide:
$-4\ \text{by}\ \frac{-3}{5}$
Answer$-4\ \text{by}\ \frac{-3}{5}$
$=-4\div\frac{-3}{5}$
$=-4\times\frac{5}{-3}$
$=\frac{-4\times5}{-3}$
$=\frac{-20}{-3}=\frac{20}{3}$
$=\frac{8\times(-1)}{-7\times(-1)}=\frac{-8}{7}$
View full question & answer→Question 731 Mark
Find the multiplicative inverse (reciprocal) of the following rational numbers:
$-1$
AnswerMultiplicative inverse of $-1=-1$
View full question & answer→Question 741 Mark
Multiply:
$\frac{7}{11}\ \text{by}\ \frac{5}{4}$
Answer$\frac{7}{11}\ \text{by}\ \frac{5}{4}=\frac{7\times5}{11\times4}=\frac{35}{44}$
View full question & answer→Question 751 Mark
Fill in the blanks:
$-4\times\frac{7}{9}=\frac{7}{9}\times$ ___________.
AnswerFill in the blanks:
$-4\times\frac{7}{9}=\frac{7}{9}\times$ -4.
View full question & answer→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.
View full question & answer→Question 771 Mark
Simplify the following and express the result as a rational number in standard form:
$\frac{-19}{36}\times16$
Answer$\frac{-19}{36}\times16=\frac{-19\times16}{36}$
$=\frac{-19\times4}{9}=\frac{-76}{9}$
View full question & answer→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$\frac{1}{2}\times\Big(\frac{3}{4}+\frac{-5}{12}\Big)=\frac{1}{2}\times\frac{3}{4}+\frac{1}{2}\times\frac{-5}{12}$
View full question & answer→Question 791 Mark
Divide:
$\frac{-3}{4}\ \text{by}\ -6$
Answer$\frac{-3}{4}\ \text{by}\ -6=\frac{-3}{4}\div\frac{-6}{1}=\frac{-3}{1}\times\frac{1}{-6}$
$=\frac{-1\times1}{4\times(-2)}=\frac{-1}{-8}=\frac{1}{8}$
View full question & answer→Question 801 Mark
Multiply:
$\frac{6}{7}\ \text{by}\ \frac{-49}{36}$
Answer$\frac{6}{7}\ \text{by}\ \frac{-49}{36}=\frac{6}{7}\times\frac{-49}{36}$
$=\frac{6\times(-49)}{7\times36}=\frac{1\times(-7)}{1\times6}=\frac{-7}{6}$
View full question & answer→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$\frac{-16}{21}\times\frac{14}{5}=\frac{-16\times14}{21\times5}$
$=\frac{-16\times2}{3\times5}=\frac{-32}{15}$
View full question & answer→Question 821 Mark
Fill in the blanks:
The reciprocal of a negative rational number is ____________.
AnswerThe reciprocal of a negative rational number is negative.
View full question & answer→