Question

Barry made the model to show multiplying a fraction by a fraction. Which multiplication sentence does the model show? A grid with 3 rows of 6 columns showing 18 squares total. The 12 squares in the top two rows are shaded yellow, the 15 squares in the first 5 columns are shaded blue. The shading overaps to make green in 10 squares. 13×23=29 26×56=518 13×26=19 23×56=59

Answer 1

Given:

Number of rows = 3

Number of columns = 6

Number of square boxes = 18

yellow square boxes in the top two rows = 12

Blue square boxes in the first 5 columns = 15

Number of green boxes (shading overlaps) = 10

To find:

The model to show multiplying a fraction by a fraction.

Solution:

2 rows out of 3 are shaded yellow.

Fraction for yellow = $\dfrac{2}{3}$

5 columns out of 6 are shaded blue.

Faction for blue = $\dfrac{5}{6}$

10 out of 18 squares are green.

Faction for green =  $\dfrac{10}{18}=\dfrac{5}{9}$

Now,

$\dfrac{2}{3}\times \dfrac{5}{6}=\dfrac{10}{18}$

$\dfrac{2}{3}\times \dfrac{5}{6}=\dfrac{5}{9}$

Therefore, the correct option is D.

Answer 2

The correct option is D.

• The calculation is as follows:

2 rows out of 3 are shaded yellow.

Fraction should be $2\div 3$

Now

5 columns out of 6 are shaded blue.

Fraction should be $5 \div 6$

And,

10 out of 18 squares are green.

Fraction should be  $10 \div 18 = 5\div 9$

Now

$\frac{2}{3} \times \frac{5}{6} = \frac{10}{18}\\\\ \frac{2}{3} \times \frac{5}{6} = \frac{5}{9}$

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