Case study (4 Marks)

Question 14 Marks

Find the multiplicative inverse of the following:$\frac{1}{5}$

Answer

We know that multiplicative inverse of a rational number a is $\Big(\frac{1}{\text{a}}\Big),$
such that $\text{a}\times\frac{1}{\text{a}}=1$
Multiplicative inverse of $\frac{1}{5}\text{ is }5$

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Question 24 Marks

Find the multiplicative inverse of the following:$-1$

Answer

We know that multiplicative inverse of a rational number a is $\Big(\frac{1}{\text{a}}\Big),$
such that $\text{a}\times\frac{1}{\text{a}}=1$
Multiplicative inverse of $-1\text{ is }\frac{1}{-1}=-1$

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Question 34 Marks

Name the property under multiplication used in the following:$-\frac{13}{17}\times\frac{-2}{7}=\frac{-2}{7}\times\frac{-13}{17}$

Answer

Commutativity property.

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Question 44 Marks

Name the property under multiplication used in the following: $\frac{-4}{5}\times1=1\times\frac{-4}{5}=-\frac{4}{5}$

Answer

$1$ is the multiplicative identity.

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Question 54 Marks

Name the property under multiplication used in the following:$\frac{-19}{29}\times\frac{29}{-19}=1$

Answer

Multiplicative Inverse property.

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Question 64 Marks

Write five rational numbers which are smaller than $2.$

Answer

$2$ Can be represented as $\frac{14}{7}$
Therefore, five rational numbers smaller than $2$ are,
$\frac{13}{7},\frac{12}{7},\frac{11}{7},\frac{10}{7},\frac{9}{7}$

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Question 74 Marks

Find ten rational numbers between $\frac{3}{5}\ \text{and}\ \frac{3}{4}$

Answer

$\frac{3}{5}\text{ and }\frac{3}{4}$ can be represented as $\frac{48}{80}\text{ and }\frac{60}{80}$ respectively.
Therefore, ten rational numbers between $\frac{3}{5}\text{ and }\frac{3}{4}$ are
$\frac{49}{80},\frac{50}{80},\frac{51}{80},\frac{52}{80},\frac{53}{80},\frac{54}{80},\frac{55}{80},\frac{56}{80},\frac{57}{80},\frac{58}{80}$

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Question 84 Marks

Represent these numbers on the number line.

Answer

$\frac{7}{4}$ can be represented on the number line as follows.

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Question 94 Marks

Multiply $\frac{6}{13}$ by the reciprocal of $\frac{-7}{16}$

Answer

The reciprocal of $\frac{-7}{16}\text{ is }\frac{-16}{7}$
According to the question, $\frac{6}{13}\times\Big(\frac{-16}{7}\Big)=\frac{-96}{91}$

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Question 104 Marks

Find ten retional numbers between $\frac{-2}{5}\text{and}\frac{1}{2}$

Answer

$\frac{-2}{5}\text{ and }\frac{1}{2}$ can be respresented as $-\frac{8}{20}\text{ and }\frac{10}{20}$ respectively.
Therefore, ten rational numbers between $\frac{-2}{5}\text{ and }\frac{1}{2}$ are
$-\frac{7}{20},-\frac{6}{20},-\frac{5}{20},-\frac{4}{20},-\frac{3}{20}-\frac{2}{20},-\frac{1}{20},0,\frac{1}{20},\frac{2}{20}$

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Question 114 Marks

Find five rational numbers between $\frac{-3}{2}\ \text{and}\ \frac{5}{3}$

Answer

$-\frac{3}{2}\text{ and }\frac{5}{3}$
can be respresented as $-\frac{9}{6}\text{ and }\frac{10}{6}$
respectively.
Therefore, five rational numbers between $-\frac{3}{2}\text{ and }\frac{5}{3}$ are
$-\frac{8}{6},-\frac{7}{6}.-1,-\frac{5}{6},-\frac{4}{6}$

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Question 124 Marks

Is $0.3$ the multiplicative inverse of $3\frac{1}{3}$? wha or why not?

Answer

Since multiplicative inverse of a rational number a is $\Big(\frac{1}{\text{a}}\Big),\text{ if }\text{ a}\times\frac{1}{\text{a}}=1$
Therefore, $0.3\times3\frac{1}{3}=\frac{3}{10}\times\frac{10}{3}=1$
Therefore, Yes $0.3$ is the multiplicative inverse of $3\frac{1}{3}$

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Question 134 Marks

Tell what property allows you to computer? $\frac{1}{3}\times\Big(6\times\frac{4}{3}\Big)\text{as}\Big(\frac{1}{3}\times6\Big)\times\frac{4}{3}$

Answer

By using associative property of multiplication, We will compute as $a \times (b \times c) = (a \times b) \times c$

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Question 144 Marks

Is $\frac{8}{9 }$ the multiplicative inverse or $-1\frac{1}{8}$? Why or why not?

Answer

Since multiplicative inverse of a rational number a is $\Big(\frac{1}{\text{a}}\Big),\text{ if }\text{a}\times\frac{1}{\text{a}}=1$
Therefore, $\frac{8}{9}\times\Big(-1\frac{1}{8}\Big)=\frac{8}{9}\times\frac{-9}{8}=-1$
But its product must be positive $1$.
Therefore, $\frac{8}{9}$ is not the multiplicative inverse of $\Big(-1\frac{1}{8}\Big)$

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Question 154 Marks

Write five rational numbers greater then $-2.$

Answer

$-2$ can be represented as $-\frac{14}{7}$ Therefore, five rational numbers greater than $-2$ are $-\frac{13}{7},-\frac{12}{7},-\frac{-11}{7},-\frac{10}{7},-\frac{9}{7}$

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Question 164 Marks

Find five rational numbers between$\frac{2}{3}\text{and}\frac{4}{5}$

Answer

$\frac{2}{3}\text{ and }\frac{4}{5}$ can be represented as $\frac{30}{45}\text{ and }\frac{36}{45}$ respectively.
Therefore, five rational numbers between $\frac{2}{3}\text{ and }\frac{4}{5}$ are
$\frac{31}{45},\frac{32}{45},\frac{33}{45},\frac{34}{45},\frac{35}{45}$

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Question 174 Marks

Find five rational numbers between$\frac{1}{4}\ \text{and}\ \frac{1}{2}$

Answer

$\frac{1}{4}\text{ and }\frac{1}{2}$ can be represented as $\frac{8}{32}\text{ and }\frac{16}{32}$ respectively.
Therefore, five rational numbers between $\frac{1}{4}\text{ and }\frac{1}{2}$ are,
$\frac{9}{32},\frac{10}{32},\frac{11}{32},\frac{12}{32},\frac{13}{32}$

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Maths Case study (4 Marks)

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