Answer to Question #139470 in Algebra for Precious

Question

Multiply the following using a diagrammatical representation:
1. 2/3 *6/8
2. 3/4 * 4/5
3. 3/5 * 2/3
4. 3/4 * 2/2

Answer 1

1. The boxes coloured black represents $\frac{2}{3}$ and the boxes coloured red represents $\frac{6}{8}$ .

N.B: Some boxes contain both colours and some do not contain any colour.

Number of boxes that contain both colours = 12

Total number of boxes = 24

$\frac{2}{3} × \frac{6}{8}$ = $\frac{12}{24} = \frac{1}{2}$

2. The boxes coloured blue represents $\frac{3}{4}$ and the boxes coloured red represents $\frac{4}{5}$ .

N.B: Some boxes contain both colours and one box does not contain any colour.

Number of boxes that contain both colours = 12

Total number of boxes = 20

$\frac{3}{4} × \frac{4}{5} = \frac{12}{20} = \frac{3}{5}$

3. The boxes coloured blue represents $\frac{2}{3}$ and the boxes coloured red represents $\frac{3}{5}$ .

N.B: Some boxes contain both colours and some do not contain any colour.

Number of boxes that contain both colours = 6

Total number of boxes = 15

$\frac{3}{5} × \frac{2}{3} = \frac{6}{15} = \frac{2}{5}$

4. The boxes coloured blue represents $\frac{2}{2}$ and the boxes coloured red represents $\frac{3}{4}$ .

N.B: Some boxes contain both colours.

Number of boxes that contain both colours = 6

Total number of boxes = 8

$\frac{3}{4} × \frac{2}{2} = \frac{6}{8} = \frac{3}{4}$