# Solve multiplication and division problems involving objects or words

Lesson

## Word Problems

You may have already looked at how to solve written multiplication and division problems by changing them into number sentences. To do this, we looked for key words and values in the question. If we need to work out a total, we can use multiplication. If we need to share our total, we can use division.

The next step is to work on problems with larger numbers. Once we've written our problem out numerically, it's time to solve it.

### methods to solve problems

Working with larger numbers means we may choose to use one of these methods to solve number problems:

• a vertical multiplication algorithm, or setting our work out down the page
• partitioning a number for multiplication or division
• the area method of multiplication, or division
• short division or long division
• a calculator!

### Let's get started

Our first job is to identify the key words, or clues, and then we can solve the number problems. We'll also look at how we might be able to solve our number problems using some tips along the way. When it comes to solving our problem, we can choose which method to use. In the first video, we look at how to multiply a large number in our head. How do we do this? Come and have a look.

### Ignoring things that aren't relevant

Sometimes there may be pieces of information that are not relevant to our problem. How do we know which things we need? The best thing to do is to highlight the key words, and then think about what they are suggesting. When we do this, we can see which things don't help at all, and then exclude those from our calculations.

In the second video, we look at what information is relevant, and then how we might solve a multiplication in the millions.

Remember!

Identifying the clues helps us work out how to write out our number problem. We can also look for pieces of information that may not be useful, and ignore those.

#### Worked Examples

##### Question 1

A rock climber descends from the top of a wall to the ground in $5$5 stages, dropping $109$109 feet each time.

What is the height of the wall?

##### Question 2

The Queen of Angleterre has $4$4 sons and she wants to give each an equal share of the kingdom's goats. The last census showed there were $4684$4684 goats in the kingdom.

1. Which number sentence correctly describes the number of goats that the Queen would give to each son?

$4684\times4$4684×4

A

$4\div4684$4÷​4684

B

$4684\div4$4684÷​4

C

$4+4684$4+4684

D

$4684\times4$4684×4

A

$4\div4684$4÷​4684

B

$4684\div4$4684÷​4

C

$4+4684$4+4684

D

##### Question 3

A real estate agency has portfolio of $6$6 properties that it manages. The total value of the properties is $\$35184003518400.

1. If each property is valued equally, what is the cost of one of the properties in the portfolio?

### Outcomes

#### 5.NN3.01

Solve problems involving the addition, subtraction, and multiplication of whole numbers, using a variety of mental strategies (e.g., use the commutative property: 5 x 18 x 2 = 5 x 2 x 18, which gives 10 x 18 = 180)