Question

create a story problem for the problem 3,422 + 2,987.
solve 821 x 54 using an area model.

Explanation:

Story Problem for \( 3,422 + 2,987 \)

To create a story problem, we can use a real - life context like the number of items in two groups. For example, we can consider the number of books in two libraries or the number of people in two places. Let's use a library context.

Step 1: Decompose the numbers

We decompose \( 821 \) into \( 800 + 20+1 \) and \( 54 \) into \( 50 + 4 \). The area model for multiplication is based on the distributive property of multiplication over addition, i.e., \((a + b + c)\times(d+e)=a\times d+a\times e + b\times d + b\times e + c\times d + c\times e\). So we create a table with the decomposed parts of the two numbers.

	50	4
20	\( 20\times50 = 1000 \)	\( 20\times4 = 80 \)
1	\( 1\times50=50 \)	\( 1\times4 = 4 \)

Step 2: Sum up all the products

First, we calculate the sum of the products in each row and then add them together.

• Sum of the first row: \( 40000+3200=43200 \)
• Sum of the second row: \( 1000 + 80=1080 \)
• Sum of the third row: \( 50+4 = 54 \)

Then we add these three sums together: \( 43200+1080 + 54\)
\(43200+1080=44280\)
\(44280 + 54=44334\)

Answer:

There are two libraries. The first library has 3,422 books, and the second library has 2,987 books. How many books do the two libraries have in total?

Solve \( 821\times54 \) using an area model