# 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 , we can decompose the 5,342 into its expanded form, , and then use a diagram or an algorithm to help us multiply.

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 . The 31 is decomposed into and 15 is decomposed into .

## Problem 1 (Lesson 5)

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

1. Does Mai have more or less than 100 stickers? Explain your reasoning.

2. Find how many stickers Mai has. Explain or show your reasoning.

## Problem 2 (Lesson 6)

Find the value of . Use a diagram if it is helpful.

## Problem 3 (Lesson 7)

1. Use the diagram to find the value of .

2. Find the value of .

## Problem 4 (Lesson 8)

1. Use the diagram to find the value of .

2. Would this diagram be helpful to find the value of ? Explain your reasoning.

## Problem 5 (Lesson 9)

The diagram and calculations show two ways for finding the value of .

1. How does each part of the vertical calculation relate to the diagram?

2. Find the value of using a method of your choice.

## Problem 6 (Lesson 10)

Here is an incomplete calculation that uses partial products of .

1. Write multiplication expressions that the numbers 15, 180, 200, and 2,400 each represent. Then, find the value of .

2. Find the value of the product .

## Problem 7 (Lesson 11)

Here is how Elena calculated the value of .

1. Where does the 9 in Elena’s calculation come from? What about the 6?

2. Where do the 2 and the 1 in calculation come from?

3. Use Elena’s method to find the value of .

## 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?

## Problem 10 (Exploration)

Here is Mai’s strategy to find the value of .