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**Analyze a Base ten Diagram in Division.**

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.

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**Explore Long Division Method.**

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?

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(4). 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

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(5). 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

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**Practice Base ten Diagrams in Division.**

Find the quotient of 511 ÷ 5 by drawing base-ten diagrams or by using the partial quotients method. Show your reasoning.

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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.

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**Complete the calculations so that each shows the correct difference.**

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

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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.

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