Chapter 4: Fractions and Decimals

Ans: Given fraction is $\dfrac{{129}}{8}$

Now divide the numbers and quotient and reminder of the numbers is $16{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\text{and}}{\kern 1pt} \,{\kern 1pt} 1$

So, the mixed fraction of the $\dfrac{{129}}{8} = 16\dfrac{1}{8}$

Ans: $20.8$is the nearest round off $20.83$

Ans: $75.20$is the nearest round off $75.195$

Solution:

$28.0$is the nearest round off $27.981$

Ans: Given fraction $\dfrac{3}{8}$ and $\dfrac{2}{3}$

Denominator is different so need to cross multiply

Cross multiply the both fraction with each other.

$\dfrac{3}{8} + \dfrac{2}{3} = \dfrac{{3 \times 3 + 8 \times 2}}{{8 \times 3}}$

$= \dfrac{{9 + 16}}{{24}} = \dfrac{{25}}{{24}}$

The addition of fraction $\dfrac{3}{8}$ and $\dfrac{2}{3}$ is $\dfrac{{25}}{{24}}$.

Ans: Given fraction is $\dfrac{3}{8}$ and $6\dfrac{3}{4}$

Now, rewrite the mixed fraction

$6\dfrac{3}{4} = \dfrac{{(6 \times 4) + 3}}{4} = \dfrac{{24 + 3}}{4} = \dfrac{{27}}{4}$

Add the following fraction $\dfrac{3}{8}$ and $\dfrac{{27}}{4}$

Cross multiply the both fraction with each other.

$\dfrac{{3 \times 4 + 27 \times 8}}{{8 \times 4}} = \dfrac{{12 + 216}}{{32}}$

$= \dfrac{{228}}{{32}} = \dfrac{{228 \div 4}}{{32 \div 4}}$

$= \dfrac{{57}}{8} = 7\dfrac{1}{8}$ 

The addition of fractions $\dfrac{3}{8}$ and $6\dfrac{3}{4}$ is $7\dfrac{1}{8}$

Ans: Given fraction $\dfrac{1}{6}$ and $\dfrac{1}{2}$

Cross multiply the both fraction with each other.

$\dfrac{1}{2} - \dfrac{1}{6} = \dfrac{{1 \times 6 - 1 \times 2}}{{2 \times 6}}$

$= \dfrac{{6 - 2}}{{12}}$

$= \dfrac{4}{{12}} = \dfrac{{4 \div 4}}{{12 \div 4}}$

$= \dfrac{1}{3}$ 

The subtraction of $\dfrac{1}{6}$ and $\dfrac{1}{2}$ is $\dfrac{1}{6}$.

Ans: Given fraction $8\dfrac{1}{3}$ and $\dfrac{{100}}{9}$

Now, rewrite the mixed fraction

$8\dfrac{1}{3} = \dfrac{{(8 \times 3) + 1}}{3} = \dfrac{{24 + 1}}{3} = \dfrac{{25}}{3}$

Subtract the following fraction, $\dfrac{{25}}{3}$ from $\dfrac{{100}}{9}$

Cross multiply the both fraction with each other.

$= \dfrac{{100}}{9} - \dfrac{{25}}{3}$

$= \dfrac{{100}}{9} - \dfrac{{25 \times 3}}{{3 \times 3}}$

$= \dfrac{{100}}{9} - \dfrac{{75}}{9}$

$= \dfrac{{100 - 75}}{9}$

$= \dfrac{{25}}{9} = 2\dfrac{7}{9}$

The subtraction of $\dfrac{{100}}{9} - 8\dfrac{1}{3} = 2\dfrac{7}{9}$.

Ans: Given fraction $1\dfrac{1}{4}$ and $6\dfrac{1}{2}$

 Now, rewrite the mixed fraction

Now, $1\dfrac{1}{4}$ and $6\dfrac{1}{2}$

$\Rightarrow \dfrac{{(4 \times 1) + 1}}{4} = \dfrac{{4 + 1}}{4}$

$= \dfrac{5}{4}$ 

Now, $6\dfrac{1}{2}$

$\Rightarrow \dfrac{{(6 \times 2) + 1}}{2} = \dfrac{{12 + 1}}{2}$

$= \dfrac{{13}}{2}$

Subtract the following fraction, $\dfrac{5}{4}$ from $\dfrac{{13}}{6}$

$\dfrac{{13}}{2} - \dfrac{5}{4} = \dfrac{{13 \times 2}}{{2 \times 2}} - \dfrac{5}{4}$

$= \dfrac{{26}}{4} - \dfrac{5}{4}$

$= \dfrac{{26 - 5}}{4}$

$= \dfrac{{21}}{4} = 5\dfrac{1}{4}$

The subtraction of the $\dfrac{{13}}{2} - \dfrac{5}{4} = 5\dfrac{1}{4}$.

Ans: The given fraction $1\dfrac{1}{2}$ and $6\dfrac{1}{2}$

Now, rewrite the mixed fraction

$1\dfrac{1}{4} = \dfrac{{4 + 1}}{4} = \dfrac{5}{4}$ 

$6\dfrac{1}{2} = \dfrac{{12 + 1}}{2} = \dfrac{{13}}{2}$ 

Now, $\dfrac{5}{4} + \dfrac{{13}}{2} = \dfrac{5}{4} + \dfrac{{13 \times 2}}{{2 \times 2}}$ 

$= \dfrac{5}{4} + \dfrac{{26}}{4}$ 

$= \dfrac{{5 + 26}}{4}$ 

$= \dfrac{{31}}{4} = 7\dfrac{3}{4}$

 The addition of the $\dfrac{5}{4} + \dfrac{{13}}{2} = 7\dfrac{3}{4}$.