Write the following mixed numbers as fractions : Class 6

Write the following mixed numbers as fractions : Class 6

Question 1.

Write the following mixed numbers as fractions : Class 6

(a) 3[latex]\frac{1}{4}[/latex]

(b) 7[latex]\frac{2}{3}[/latex]

(c) 9[latex]\frac{4}{9}[/latex]

(d) 3[latex]\frac{1}{6}[/latex]

(e) 2[latex]\frac{3}{11}[/latex]

(f) 3[latex]\frac{9}{10}[/latex]

Solution:

(a)

$\begin{aligned} & 3 \frac{1}{4}=1+1+1+\frac{1}{4} \\ & =\left(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}\right)+\left(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}\right) \\ & +\left(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}\right)+\frac{1}{4} \\ & =4 \times \frac{1}{4}+4 \times \frac{1}{4}+4 \times \frac{1}{4}+1 \times \frac{1}{4} \\ & =\frac{13}{4} .\end{aligned}$

$\begin{aligned} & \text { (b) } 7 \frac{2}{3}=1+1+1+1+1+1+1+\frac{2}{3} \\ & =\left(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}\right)+\left(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}\right)+\left(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}\right) \\ & +\left(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}\right)+\left(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}\right)+\left(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}\right) \\ & +\left(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}\right)+\left(\frac{1}{3}+\frac{1}{3}\right) \\ & =3 \times \frac{1}{3}+3 \times \frac{1}{3}+3 \times \frac{1}{3}+3 \times \frac{1}{3}+3 \times \frac{1}{3}+3 \times \frac{1}{3} \\ & +3 \times \frac{1}{3}+2 \times \frac{1}{3}\end{aligned}$

$\begin{aligned} &= \frac{23}{3} \\ & \text { (c) } 9 \frac{4}{9}=1+1+1+1+1+1+1+1+1+\frac{4}{9} \\ &=\left(\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}\right) \\ &+\left(\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}\right) \\ &+\ldots 9 \text { times }+\left(\frac{1}{9}+\frac{1}{9}+\frac{1}{9}+\frac{1}{9}\right) \\ &= 9 \times \frac{1}{9}+9 \times \frac{1}{9}+9 \times \frac{1}{9}+9 \times \frac{1}{9}+9 \times \frac{1}{9}+9 \times \frac{1}{9} \\ &+9 \times \frac{1}{9}+9 \times \frac{1}{9}+9 \times \frac{1}{9}+4 \times \frac{1}{9} \\ &= \frac{85}{9}\end{aligned}$

(d) 3[latex]\frac{1}{4}[/latex] = 1 + 1 + 1 + [latex]\frac{1}{6}[/latex]

$\begin{aligned}= & \left(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\right) \\ & +\left(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\right) \\ & +\left(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\right)+1 \times \frac{1}{6} \\ = & 6 \times \frac{1}{6}+6 \times \frac{1}{6}+6 \times \frac{1}{6}+1 \times \frac{1}{6}=\frac{19}{6} .\end{aligned}$

$\begin{aligned} 2 \frac{3}{11} & =1+1+\frac{3}{11} \\ & =11 \times \frac{1}{11}+11 \times \frac{1}{11}+3 \times \frac{1}{11}=\frac{25}{11} \\ \text { (f) } 3 \frac{9}{10} & =1+1+1+\frac{9}{10} \\ = & 10 \times \frac{1}{10}+10 \times \frac{1}{10}+10 \times \frac{1}{10}+9 \times \frac{1}{10} \\ = & \frac{39}{10}\end{aligned}$