Unit 5, Lesson 25

Divide Decimals by Decimals

Grade 5

Warm-up

Find the value of each expression mentally.

Jada draws this diagram to find the value of .

Two diagrams. Each squares. Each partitioned into 10 rows of 10 of the same size squares. On left, 1 hundred squares shaded. On right, sixty squares shaded. Each column of 10 squares shading alternates, blue, orange.
1. Describe how the diagram shows 1.6.
2. Describe how the diagram shows 16 groups of 1 tenth.
3. Describe how the diagram shows the value of .
4. Describe how the diagram also represents the expression .
1. Describe how this diagram represents .
  
  Two diagrams. Each squares. Each partitioned into 10 rows of 10 of the same size squares. On left, 1 hundred squares shaded. On right, 30 squares shaded. For each square shading alternates, blue, orange.
2. What is the value of ? Explain or show your reasoning.

Find the value of each expression. Explain or show your reasoning.

We learned different strategies for dividing with decimals.

We used diagrams. This diagram shows there are 10 groups of 0.1 in each whole. So, there are or 30 groups of 0.1 in 3 wholes.

We thought about place value. Since 3 is 30 tenths and 0.1 is 1 tenth, is equivalent to . Both have the value 30.

We also used the relationship between multiplication and division. We know that . So, .

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