Reasoning about Multiplication with Decimals
5.NBT.7
What expression can you write about this representation?
Pose the Problem:
Key:
= 1
You may have written + + or 3 x or 3 x 0.2
We can see that this equals or 0.6
Debrief
What equation can you write about this representation?
Pose the Problem: Letβs try another one.
You may have written
or or 4 x 0.6 = 2.4
Debrief
What multiplication equation can you write about this representation?
Pose the Problem: Letβs try one more.
You may have written
or 8 x 0.4 = 3.2
Debrief
What do you notice about the product when you multiply a whole number by a decimal?
0.2 x 3 = 0.6
0.6 x 4 = 2.4
0.4 x 8 = 3.2
0.2 x 3 = 0.6
0.6 x 4 = 2.4
0.4 x 8 = 3.2
We can think about the expression 0.2 x 3 as βtwo-tenths of 3.β We can reason that the product will be less than 3, so the product six-tenths makes sense.
Letβs investigate what happens when we multiply a decimal by a decimal.
Use the Decimal Squares virtual manipulative to show 0.3 x 0.4
Ensure that you select 100 for the Number of Tiles and Paint By Rows to shade in horizontally or Columns to shade in vertically. Use a different color to represent each decimal.
Did you get 0.12 as a product? When we think back and connect decimals to fractions, this makes sense because
Letβs investigate what happens when we multiply a decimal by a decimal.
Use the Decimal Squares virtual manipulative to show 0.5 x 0.6
Ensure that you select 100 for the Number of Tiles and Paint By Rows to shade in horizontally or Columns to shade in vertically. Use a different color to represent each decimal.
Did you get 0.30 as a product? When we think back and connect decimals to fractions, this makes sense because
How could we use reasoning to estimate the product of
5.48 x 8?
Write an equation to estimate the product and explain your reasoning.
5.48 x 8
Since 5.48 is between 5 and 6. We can reason that the product must be between 5 x 8 and 6 x 8. Since 5 x 8 = 40 and 6 x 8 = 48, the product of 5.48 x 8 will be between 40 and 48.
How could we use reasoning to estimate the product of
3.2 x 8.5?
Write an equation to estimate the
product and explain your reasoning.
3.2 x 8.5
We can round 3.2 to 3 and 8.5 to 9. Since 3 x 9 = 27 we can reason that the product will be close to 27.
Practice: What is the most reasonable estimate for
0.5 x 10 ?
Practice:
Draw a model and solve for:
5 x 0.3
Practice: What is the most reasonable estimate for
0.2 x 0.4 ?
Practice:
Draw a model and solve for:
0.2 x 0.6
Reasoning about Multiplication with Decimals
5.NBT.7