IM 6.5.11 Lesson: Dividing Numbers that Result in Decimals
Find the quotients mentally.
Mai used base-ten diagrams to calculate . 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 is Mai's diagram from .
Discuss these questions with a partner and write down your answers:
Mai should have a total of 12 ones, but her diagram shows only 10. Why?
She did not originally have tenths, but in her diagram each group has 4 tenths. Why?
What value has Mai found for ? Explain your reasoning.
Find the quotient of 511 ÷ 5 by drawing base-ten diagrams or by using the partial quotients method. Show your reasoning. If you get stuck, work with your partner to find a solution.
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 to your answer above.
Here is how Lin calculated 62 ÷ 5.
Discuss with your partner:
Lin put a 0 after the remainder of 2. Why? Why does this 0 not change the value of the quotient?
Lin subtracted 5 groups of 4 from 20. What value does the 4 in the quotient represent?
What value did Lin find for ?
Use long division to find the value of each expression.
Use long division to show that:
, or , is 1.25.
, or , is 0.8.
, or , is 0.125.
, or , 0.04.
Noah said we cannot use long division to calculate 10 ÷ 3 because there will always be a remainder.
What do you think Noah meant by “there will always be a remainder”?
Do you agree with him? Explain your reasoning.