3 Mark Question

Question 13 Marks

In the following, find an equivalent form of the rational number having common denominator:
$\frac{5}{7},\frac{3}{8},\frac{9}{14}\text{ and }\frac{20}{21}$

Answer

Equivalent forms of the rational number having common denominator are:
$\Rightarrow\frac{5}{7}=\frac{5\times24}{7\times24}=\frac{120}{168}$
$\Rightarrow\frac{3}{8}=\frac{3\times21}{8\times21}=\frac{63}{168}$
$\Rightarrow\frac{9}{14}=\frac{9\times12}{14\times12}=\frac{108}{168}$
and
$\Rightarrow\frac{20}{21}=\frac{20\times8}{21\times8}=\frac{160}{168}$
$\text{Forms are }\frac{120}{168},\frac{63}{168},\frac{108}{168}\text{ and }\frac{160}{168}$

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Question 23 Marks

Arrange the following rational numbers in ascending order:
$\frac{3}{5},\frac{-17}{30},\frac{8}{-15},-\frac{7}{10}$

Answer

Ascending order:
Since, LCM of 5, -30, -15, 10 is 30.
Multiplying the numerators and denominators to get the denominator equal to the LCM $\frac{3}{5}$
$=\frac{3\times6}{5\times6}=\frac{18}{30},\frac{17}{30}=\frac{17\times1}{30\times1}=\frac{17}{30}$
$\frac{8}{-15}=\frac{-8\times2}{15\times2}=\frac{-16}{30},$
$\frac{-7}{10}=\frac{-7\times3}{10\times3}=\frac{-21}{30}$
Order is $-21<-16<17<8$
Order is $\frac{-7}{10}<\frac{8}{-15}<\frac{17}{30}<\frac{3}{5}$

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Question 33 Marks

Arrange the following rational numbers in ascending order:
$-\frac{4}{9},\frac{5}{-12},\frac{7}{-18},\frac{2}{-3}$

Answer

Since, LCM of 9, -12, -18, 3 is 36. Multiplying the numerators and denominators to get the denominator to get the denominator equal to the LCM. $\frac{-4}{9}=\frac{-4\times4}{9\times4}=\frac{-16}{36},$$\frac{5}{-12}=\frac{-5\times3}{12\times3}=\frac{-15}{36},$ $\frac{7}{-18}=\frac{-7\times2}{8\times2}=\frac{-14}{36},$$\frac{2}{-3}=\frac{-2\times12}{3\times12}=\frac{-24}{36}$ Order is $-24<-16<-15<-14$Order is $\frac{2}{-3}<\frac{-4}{9}<\frac{5}{-12}<\frac{7}{-18}$

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Question 43 Marks

Arrange the following rational numbers in descending order:
$\frac{7}{8},\frac{64}{16},\frac{36}{-12},\frac{5}{-4},\frac{140}{28}$

Answer

We have to arrange them in descending order.
Since, LCM of 8, 16, -12, -4, 28 is 336.
Multiplying the numerators and denominators to get the denominator to get the denominator equal to the LCM, $\frac{7}{8}$
$=\frac{7\times42}{8\times42}=\frac{294}{336},\frac{64}{16}=\frac{64\times121}{16\times21}=\frac{1344}{336}$
$\frac{36}{-12}=\frac{-36\times28}{12\times28}=\frac{-1008}{336},\frac{5}{-4}=\frac{-5\times84}{4\times84}=\frac{-420}{336},$
$\frac{140}{28}=\frac{140\times12}{28\times12}=\frac{180}{336}$
Order is: $1680>1344>294>-420>-1008$
Order is: $4>36-12$
Order is: $\frac{140}{28}>\frac{64}{16}>\frac{7}{8}>\frac{5}{-4}>\frac{36}{-12}$

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Question 53 Marks

Select those rational numbers which can be written as a rational number with denominator 4:
$\frac{7}{8},\frac{64}{16},\frac{36}{-12},\frac{-16}{17},\frac{5}{-4},\frac{-140}{28}$

Answer

Given rational numbers that can be written as a rational number with denominator 4 are:
$\frac{7}{8}$ (On multiplying by 2) $=\frac{3.5}{4}$
$\frac{64}{16}$ (On multiplying by 4) $=\frac{16}{4}$
$\frac{36}{-12}$ (On multiplying by 3) $=\frac{12}{-4}=\frac{-12}{4}$
$=\frac{-16}{17}$ Can,t be expressed with a denominator 4.
$\frac{5}{-4}$ (On multiplying by -1) $=\frac{-5}{4}$
$\frac{140}{28}$ (On multiplying by 7) $=\frac{20}{4}$

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