1 Mark Question

Question 11 Mark

Write three rational numbers that lie between the two given numbers. : $0, \frac{-3}{4}$

Answer

$0, \frac{-3}{4}$
The three numbers between 0 and $\frac{-3}{4}$ are $\frac{-1}{8}, \frac{-2}{8}, \frac{-5}{8}$

Question 21 Mark

Write three rational numbers that lie between the two given numbers. : $\frac{5}{7}, \frac{11}{7}$

Answer

$\frac{5}{7}, \frac{11}{7}$
The three numbers between $\frac{5}{7}$ and $\frac{11}{7}$ are $\frac{6}{7}, \frac{8}{7}, \frac{9}{7}$

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Question 31 Mark

Write three rational numbers that lie between the two given numbers. : $\frac{7}{8}, \frac{-5}{3}$

Answer

$\frac{7}{8}, \frac{-5}{3}$
$\frac{7}{8}=\frac{21}{24}, \frac{-5}{3}=\frac{-40}{24}$
The three numbers between $\frac{7}{8}$ and $\frac{-5}{3}$ are $\frac{17}{24}, \frac{11}{24}, \frac{-13}{24}$

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Question 41 Mark

Write three rational numbers that lie between the two given numbers. : $\frac{-3}{4}, \frac{+5}{4}$

Answer

$\frac{-3}{4}, \frac{+5}{4}$
The three numbers between $\frac{-3}{4}$ and $\frac{+5}{4}$ are $\frac{-2}{4}, \frac{-1}{4}, \frac{3}{4}$

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Question 51 Mark

Write three rational numbers that lie between the two given numbers. : $\frac{7}{9},-\frac{5}{9}$

Answer

$\frac{7}{9},-\frac{5}{9}$
The three numbers between $\frac{7}{9}$ and $\frac{-5}{9}$ are $\frac{6}{9}, 0,\frac{-4}{9}$

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Question 61 Mark

Write three rational numbers that lie between the two given numbers. : $-\frac{2}{3}, \frac{4}{5}$

Answer

$-\frac{2}{3}, \frac{4}{5}$
$\frac{-2}{3}=\frac{-10}{15}, \frac{4}{5}=\frac{12}{15}$
The three numbers between $\frac{-2}{3}$ and $\frac{4}{5}$ are $\frac{-9}{15}, \frac{-7}{15}, \frac{4}{15}$

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Question 71 Mark

Write three rational numbers that lie between the two given numbers. : $\frac{4}{5}, \frac{2}{3}$

Answer

$\frac{4}{5}, \frac{2}{3}$
$\frac{4}{5}=\frac{24}{30}, \frac{2}{3}=\frac{20}{30}$
The three numbers between $\frac{4}{5}$ and $\frac{2}{3}$ are $\frac{21}{30},
\frac{22}{30}, \frac{23}{30}$

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Question 81 Mark

Write three rational numbers that lie between the two given numbers. : $\frac{2}{7}, \frac{6}{7}$

Answer

$\frac{2}{7}, \frac{6}{7}$
The three numbers lying between $\frac{2}{7}$ and $\frac{6}{7}$ are $\frac{3}{7}, \frac{4}{7}, \frac{5}{7}$

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Question 91 Mark

Carry out the divisions of rational numbers : $5 \div \frac{2}{5}$

Answer

\begin{aligned}
& 5 \div \frac{2}{5} \\
& =\frac{5}{1} \times \frac{5}{2}=\frac{25}{2}
\end{aligned}

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Question 101 Mark

Carry out the divisions of rational numbers : $\frac{9}{11} \div(-8)$

Answer

\begin{aligned}
& \frac{9}{11} \div(-8) \\
& =\frac{9}{11} \times \frac{-1}{8}=\frac{-9}{88}
\end{aligned}

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Question 111 Mark

Carry out the divisions of rational numbers : $\frac{-5}{13} \div \frac{7}{26}$

Answer

\begin{aligned}
& \frac{-5}{13} \div \frac{7}{26} \\
& =\frac{-5}{13} \times \frac{26}{7}=\frac{-10}{7}
\end{aligned}

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Question 121 Mark

Carry out the divisions of rational numbers : $2 \frac{1}{5} \div 5 \frac{3}{6}$

Answer

\begin{aligned}
& 2 \frac{1}{5} \div 5 \frac{3}{6} \\
& =\frac{11}{5} \div \frac{33}{6}=\frac{11}{5} \times \frac{6}{33}=\frac{1}{5} \times \frac{6}{3}=\frac{2}{5}
\end{aligned}

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Question 131 Mark

Carry out the divisions of rational numbers : $\frac{2}{3} \div(-4)$

Answer

\begin{aligned}
& \frac{2}{3} \div(-4) \\
& =\frac{2}{3} \times \frac{-1}{4}=\frac{1}{3} \times \frac{-1}{2}=\frac{-1}{6}
\end{aligned}

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Question 141 Mark

Carry out the divisions of rational numbers : $\frac{-7}{8} \div \frac{-3}{6}$

Answer

$\frac{-7}{8} \div \frac{-3}{6}$
$=\frac{-7}{8} \times \frac{-6}{3}=\frac{-7}{4} \times \frac{-3}{3}=\frac{7}{4}$

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Question 151 Mark

Carry out the divisions of rational numbers : $\frac{-10}{11} \div \frac{-11}{10}$

Answer

\begin{aligned}
& \frac{-10}{11} \div \frac{-11}{10} \\
& =\frac{-10}{11} \times \frac{-10}{11}=\frac{100}{121}
\end{aligned}

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Question 161 Mark

Carry out the divisions of rational numbers : $\frac{40}{12} \div \frac{10}{4}$

Answer

\begin{aligned}
& \frac{40}{12} \div \frac{10}{4} \\
& =\frac{40}{12} \times \frac{4}{10}=\frac{4}{3}
\end{aligned}

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Question 171 Mark

Write the multiplicative inverse of. : $-7 \frac{1}{3}$

Answer

$\frac{-3}{22}$

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Question 181 Mark

Write the multiplicative inverse of. : 7

Answer

$\frac{1}{7}$

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Question 191 Mark

Write the multiplicative inverse of. : $\frac{-17}{39}$

Answer

$\frac{-39}{17}$

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Question 201 Mark

Write the multiplicative inverse of. : $\frac{-3}{8}$

Answer

$\frac{-8}{3}$

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Question 211 Mark

Write the multiplicative inverse of. : $\frac{2}{5}$

Answer

$\frac{5}{2}$

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Question 221 Mark

Multiply the following rational numbers. : $\frac{0}{6} \times \frac{3}{4}$

Answer

$\frac{0}{6} \times \frac{3}{4}$ $=0 \times \frac{3}{4}=0$

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Question 231 Mark

Multiply the following rational numbers. : $\frac{(-8)}{9} \times \frac{3}{4}$

Answer

$\begin{aligned} & \frac{(-8)}{9} \times \frac{3}{4} \\ &=\frac{(-2)}{3} \times \frac{1}{1}=\frac{-2}{3}\end{aligned}$

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Question 241 Mark

Multiply the following rational numbers. : $\frac{12}{5} \times \frac{4}{15}$

Answer

$\begin{aligned}
&\frac{12}{5} \times \frac{4}{15} \\
& =\frac{4}{5} \times \frac{4}{5}=\frac{4 \times 4}{5 \times 5}=\frac{16}{25}
\end{aligned}$

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Question 251 Mark

Multiply the following rational numbers. : $\frac{3}{11} \times \frac{2}{5}$

Answer

$\begin{aligned}
&\frac{3}{11} \times \frac{2}{5} \\
& =\frac{3 \times 2}{11 \times 5}=\frac{6}{55}
\end{aligned}$

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