Question

B.match illustrate by using rectangular regions then solve

Answer 1

Fractions can be represented by shading parts of a rectangular region

The simplified expressions are:

• $\frac 28 + \frac 24 = \frac 34$.
• $\frac 9{10} - \frac 35 =\frac{2}{5}$.
• $\frac 46 -\frac{2}{6}=\frac{2}{6}$.
• $-\frac{2}{12} + \frac 26 = \frac{2}{12}$.
• $\frac{9}{18} - \frac{3}{9} = \frac{1}{6}$

Complete number sentence

To start with, we simplify the fraction expressions as follows:

(1) $\frac 28 + \frac 24 =$

Take LCM

$\frac 28 + \frac 24 = \frac{2 + 4}8$

$\frac 28 + \frac 24 = \frac{6}8$

Simplify

$\frac 28 + \frac 24 = \frac 34$

(2) $\frac 9{10} - \frac 35 =$

Take LCM

$\frac 9{10} - \frac 35 =\frac{9 - 6}{10}$

$\frac 9{10} - \frac 35 =\frac{4}{10}$

Simplify

$\frac 9{10} - \frac 35 =\frac{2}{5}$

(3) $\frac 46 - [\ ]=\frac{2}{6}$

Replace the blank with x

$\frac 46 -x=\frac{2}{6}$

Collect like terms

$x = \frac 46 -\frac{2}{6}$

Take LCM

$x = \frac{4 - 2}{6}$

$x = \frac{2}{6}$

Simplify

$x = \frac{1}{3}$

(4) $\frac{}{12} + \frac 26 = \frac{2}{12}$

Replace the blank with x

$\frac{x}{12} + \frac 26 = \frac{2}{12}$

Collect like terms

$\frac{x}{12} = \frac{2}{12} -\frac 26$

Take LCM

$\frac{x}{12} = \frac{2 - 4}{12}$

$\frac{x}{12} = -\frac{2}{12}$

Multiply both sides by 12

$x=-2$

(5) $\frac{9}{18} - \frac{3}{9}$

Take LCM

$\frac{9}{18} - \frac{3}{9} = \frac{9 - 6}{18}$

$\frac{9}{18} - \frac{3}{9} = \frac{3}{18}$

Reduce fraction

$\frac{9}{18} - \frac{3}{9} = \frac{1}{6}$

Missing fractions

So, the simplified expressions that contain the missing fractions are:

• $\frac 28 + \frac 24 = \frac 34$.
• $\frac 9{10} - \frac 35 =\frac{2}{5}$.
• $\frac 46 -\frac{2}{6}=\frac{2}{6}$.
• $-\frac{2}{12} + \frac 26 = \frac{2}{12}$.
• $\frac{9}{18} - \frac{3}{9} = \frac{1}{6}$

Shaded regions

See attachment for the shaded regions

Read more about fractions at:

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