Question

The model shown was used to find the product of two fractions: A rectangle divided into nine columns of equal size and 4 rows of equal size. The length of a column is labeled as one ninth and the width of a row is labeled as one fourth. Two columns are fully shaded in grey. The cells in three full rows are covered with dots. Which equation does the model represent? (1 point) a the equation with the fractions two ninths times three fourths is equal to six thirty sixths b the equation with the fractions one ninth times one fourth is equal to two thirty sixths c the equation with the fractions two ninths times three fourths is equal to five thirty sixths d the equation with the fractions nine ninths times four fourths is equal to twenty nine thirty sixths

Answer 1

The equation that represents the array (rectangles and area) multiplication model that sows two grey shaded columns of length one ninth each and three rows with dots of width one fourth each is option a

a) The equation with fractions two ninths times three fourths is equal to six thirty sixths

$\dfrac{2}{9} \times \dfrac{3}{4} = \dfrac{6}{36}$

What is an array (area) multiplication model?

An array representation of a multiplication is a rectangular visual order of positioning of rows and columns that indicates the terms of a multiplication equation.

Please find attached the area model to multiply the fractions

The terms of the equation represented by the model are indicated by the two columns of length one ninth each shaded grey and the three rows of width one fourth each covered with dots, such that the equation can be presented as follows;

$\left(\dfrac{1}{9} +\dfrac{1}{9}\right) \times \left(\dfrac{1}{4} +\dfrac{1}{4} + \dfrac{1}{4} \right) = \dfrac{2}{9} \times \dfrac{3}{4} =\dfrac{6}{36}$

The equation that the model represents is therefore;

• The equation with fractions two ninths times three fourths is equal to six thirty sixths

Learn more about multiplication models here:

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