Question

dear family. this week your child is learning to multiply fractions to find the area of rectangles. your child might see a problem like this: kareem has a square placemat that measures 1 foot on each side. he divides it in half vertically and in thirds horizontally. he wants to decorate each part with a different pattern. what is the area of each part of the placemat? to understand the problem, your child could draw and label a picture. the dashed lines show 6 equal parts. each part is 1/2 foot long and 1/3 foot wide. each part is 1/6 of the whole. multiply to find the area of each part. 1/2 foot × 1/3 foot = 1/6 square foot the area of each part of the placemat is 1/6 square foot. invite your child to share what they know about multiplying fractions to find the area of rectangles by doing the following activity together.

Explanation:

Step1: Identify side - lengths of each part

The square is divided vertically in half, so the vertical side - length of each part is $\frac{1}{2}$ foot. It is divided horizontally in thirds, so the horizontal side - length of each part is $\frac{1}{3}$ foot.

Step2: Apply area formula for rectangle

The area formula for a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. Here, $l=\frac{1}{2}$ foot and $w = \frac{1}{3}$ foot. So $A=\frac{1}{2}\times\frac{1}{3}$.

Step3: Multiply the fractions

When multiplying fractions, we multiply the numerators together and the denominators together. $\frac{1}{2}\times\frac{1}{3}=\frac{1\times1}{2\times3}=\frac{1}{6}$ square foot.

Answer:

$\frac{1}{6}$ square foot