Section B: Practice Problems Multi-digit Multiplication

Section Summary

Details

In this section, we learned to multiply factors whose products are greater than 100, using different representations and strategies to do so.

When working with multi-digit factors, it helps to decompose them by place value before multiplying. For example, to find $4 \times 5, 342$ , we can decompose the 5,342 into its expanded form, $5, 000 + 300 + 40 + 2$ , and then use a diagram or an algorithm to help us multiply.

multiply. 5 thousand 3 hundred 42 times 4.

In both the diagram and the algorithm, the 20,000, 1,200, 160, and 8 are called the partial products. They are the result of multiplying each decomposed part of 5,342 by 4.

We can do the same to multiply a two-digit number by another two-digit number. For example, here are two ways to find $31 \times 15$ . The 31 is decomposed into $30 + 1$ and 15 is decomposed into $10 + 5$ .

Problem 1 (Lesson 5)

Mai has a sheet of stickers with 23 rows and 8 stickers in each row.

Does Mai have more or less than 100 stickers? Explain your reasoning.
Find how many stickers Mai has. Explain or show your reasoning.

Problem 2 (Lesson 6)

Find the value of $7 \times 64$ . Use a diagram if it is helpful.

Problem 3 (Lesson 7)

Use the diagram to find the value of $8 \times 573$ .
Find the value of $4 \times 3, 516$ .

Problem 4 (Lesson 8)

Use the diagram to find the value of $47 \times 62$ .
Would this diagram be helpful to find the value of $47 \times 62$ ? Explain your reasoning.

Problem 5 (Lesson 9)

The diagram and calculations show two ways for finding the value of $2, 518 \times 6$ .

Diagram, rectangle partitioned vertically into 4 rectangles.

multiply. 2 thousand 5 hundred 18 times 6.

How does each part of the vertical calculation relate to the diagram?
Find the value of $3, 172 \times 5$ using a method of your choice.

Problem 6 (Lesson 10)

Here is an incomplete calculation that uses partial products of $65 \times 43$ .

Write multiplication expressions that the numbers 15, 180, 200, and 2,400 each represent. Then, find the value of $65 \times 43$ .
Find the value of the product $45 \times 38$ .

Problem 7 (Lesson 11)

Here is how Elena calculated the value of $723 \times 3$ .

multiply. 7 hundred 23 times 3, equals 2 thousand 1 hundred sixty 9.

Where does the 9 in Elena’s calculation come from? What about the 6?
Where do the 2 and the 1 in calculation come from?
Use Elena’s method to find the value of $534 \times 2$ .

Problem 8 (Lesson 12)

There are 4,218 students in school district A. School district B has 3 times as many students as school district A. How many students are in school district B? Explain or show your reasoning.

Problem 9 (Exploration)

Clare was double checking her answers for some products. Without doing the computation again, she knew that these answers were incorrect. How might Clare have known?

$5 \times 5, 783 = 27, 914$
$7 \times 8, 419 = 54, 253$
$9 \times 9, 999 = 99, 999$

Problem 10 (Exploration)

Here is Mai’s strategy to find the value of $9 \times 8, 235$ .

Explain why Mai’s method works.
Use Mai’s method to find the value of $9 \times 6, 789$ .
Find the value of $9 \times 6, 789$ using a strategy you learned. How is Mai’s method like yours? How is it different than yours?