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

`(4)/(7)*(13)/(9) = (52)/(63)`

Explanation:

Given

See attachment for model

Required

Determine
`(4)/(7)*(13)/(9)` from the model

The model is represented by:

`(4)/(7)*(13)/(9) = (4)/(7)*(9)/(9) + (4)/(7)*(4)/(9)`

To get:
`(4)/(7)*(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:

`(4)/(7)*(9)/(9) = (36)/(63)`

To get:
`(4)/(7)*(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:

`(4)/(7)*(4)/(9) =(16)/(63)`

The equation becomes:

`(4)/(7)*(13)/(9) = (4)/(7)*(9)/(9) + (4)/(7)*(4)/(9)`

`(4)/(7)*(13)/(9) = (36)/(63) + (16)/(63)`

`(4)/(7)*(13)/(9) = (36+16)/(63)`

`(4)/(7)*(13)/(9) = (52)/(63)`