Question

Find 45 divided by 9 by describing two ways you can model it using equal groups. Then tell how 9 means something diffetent in each model.

Answer 1

Here are two ways to model 45 divided by 9 using equal groups:

Method 1: Division by Grouping

We can use division by grouping to model 45 divided by 9. Here’s how it works:

Start with 45 dots or counters.

Collect the dots or counters into groups of 9.

Count the number of groups you have. The number of groups is the answer to the division.

We can group the dots or counters as follows:

| . . . . . . . . . . | . . . . . . . . . . |

| . . . . . . . . . . | . . . . . . . . . . |

| . . . . . . . . . . | . . . . . . . . . . |

| . . . . . . . . . . | . . . . . . . . . . |

| . . . . . . . . . . | . . . . . . . . . . |

We have 5 groups of 9 dots or counters, so the answer to the division is 5.

In this model, 9 represents the number of dots or counters in each group.

Method 2: Repeated Subtraction

We can also use repeated subtraction to model 45 divided by 9. Here’s how it works:

Start with 45.

Subtract 9 from 45.

Repeat step 2 until you reach 0.

Count the number of times you subtracted 9. This is the answer to the division.

We can subtract 9 from 45 as follows:

45 - 9 = 36

36 - 9 = 27

27 - 9 = 18

18 - 9 = 9

9 - 9 = 0

We subtracted 9 a total of 5 times, so the answer to the division is 5.

In this model, 9 represents the amount we are subtracting each time.