Question

John made this model to show \frac{4}{7}\times\frac{13}{9} 7 4 ​ × 9 13 ​ Using John's model, what is \frac{4}{7}\times\frac{13}{9} 7 4 ​ × 9 13 ​ ? You may use the scratchpad to show your work.

Answer 1

Answer:

$\frac{4}{7}\times\frac{13}{9} = \frac{52}{63}$

Step-by-step explanation:

Given

See attachment for model

Required

Determine $\frac{4}{7}\times\frac{13}{9}$ from the model

The model is represented by:

$\frac{4}{7}\times\frac{13}{9} = \frac{4}{7}\times\frac{9}{9} + \frac{4}{7}\times\frac{4}{9}$

To get: $\frac{4}{7}\times\frac{9}{9}$, we consider the first partition

The number of shaded box is 63 ---- this represents the denominator

The total boxes shaded at the bottom is 36 ---- this represents the numerator

So, we have:

$\frac{4}{7}\times\frac{9}{9} = \frac{36}{63}$

To get: $\frac{4}{7}\times\frac{9}{9}$, we consider the first partition

The number of shaded box is 63 ---- this represents the denominator

The total boxes shaded at the bottom is 16 (do not count the gray boxes) ---- this represents the numerator

So, we have:

$\frac{4}{7}\times\frac{4}{9} =\frac{16}{63}$

The equation becomes:

$\frac{4}{7}\times\frac{13}{9} = \frac{4}{7}\times\frac{9}{9} + \frac{4}{7}\times\frac{4}{9}$

$\frac{4}{7}\times\frac{13}{9} = \frac{36}{63} + \frac{16}{63}$

$\frac{4}{7}\times\frac{13}{9} = \frac{36+16}{63}$

$\frac{4}{7}\times\frac{13}{9} = \frac{52}{63}$