# Dividing Numbers that Result in Decimals

Warmup

Activity #1

Analyze a Base ten Diagram in Division.

In this unit, we have introduced three techniques to divide whole numbers that result in a terminating decimal: base-ten diagrams, partial quotients, and long division. • Examine the method below of base-ten blocks used by Mai, and answer the questions that follow.

Mai used base-ten diagrams to calculate 62 ÷ 5. She started by representing 62. She then made 5 groups, each with 1 ten. There was 1 ten left. She unbundled it into 10 ones and distributed the ones across the 5 groups.

Here below is Mai’s diagram from 62 ÷ 5. (1.) Mai should have a total of 12 ones, but her diagram shows only 10. Why?

(2.) She did not originally have tenths, but in her diagram each group has 4 tenths. Why?

(3.) What value has Mai found for 62 ÷ 5? Explain your reasoning.

Activity #2

Explore Long Division Method. • Examine here below, the long division method used by Lin to divide the same numbers Mai used above, and answer the questions that follow.

Here is how Lin calculated 62 ÷ 5.

(1.) Lin put a 0 after the remainder of 2. Why? Why does this 0 not change the value of the quotient?

(2.) Lin subtracted 5 groups of 4 from 20. What value does the 4 in the quotient represent?

(3.) What value did Lin find for 62 ÷ 5?

• Use long division in the applet below to find the value of each expression on the work sheet below.

(a.) 126 ÷ 8

(b.) 90 ÷ 12

• Use long division in the applet below to show that:

(a.) 5 ÷ 4, or is 1.25

(b.) 4 ÷ 5, or is 0.8

(c.) 1 ÷ 8, or is 0.125

Activity #3

Practice Base ten Diagrams in Division. • Find the quotient of 511 ÷ 5 by drawing base-ten diagrams or by using the partial quotients method.

Four students share a \$271 prize from a science competition. How much does each student get if the prize is shared equally?

• Show your reasoning using the applet below.

Challenge #1

Complete the calculations so that each shows the correct difference.

Challenge #2

Use long division to show that the fraction and decimal in each pair are equal.

Challenge #3

Noah said we cannot use long division to calculate 10 ÷ 3 because there will always be a remainder.

(1.) What do you think Noah meant by “there will always be a remainder”?

(2.) Do you agree with him? Explain your reasoning.

Quiz Time