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6.04 Multiply decimals by single digit numbers

Lesson

Are you ready?

Do you remember how to multiply numbers using a standard algorithm? Let's try this problem to practice.

Find $213\times45$213×45.

Vocabulary:
  • You might notice that sometimes the standard algorithm is called the 'vertical algorithm'. Let's think about why. When we use the standard algorithm, we line our numbers up in 'vertical' place value columns.

Learn

This video looks at using visual models for multiplying decimals. 

Apply

Question 1

Use the area model to find $1.27\times8$1.27×8.

  1. Fill in the areas of each rectangle.

            $1$1           $0.2$0.2       $0.07$0.07  
    $8$8       $\editable{}$           $\editable{}$       $\editable{}$  
                           
  2. What is the total area of all three rectangles, and therefore the answer to $8\times1.27$8×1.27?

 

Learn

This video uses the standard algorithm and a couple of methods to check if our answers are reasonable. While this doesn't always tell us our answer is correct, it can definitely help us check our decimal point is in the correct position.

Apply

Question 2

We want to find $1.07\times8$1.07×8.

  1. Will $1.07\times8$1.07×8 be less than or greater than $8$8?

    $1.07\times8$1.07×8 is less than $8$8

    A

    $1.07\times8$1.07×8 is greater than $8$8

    B
  2. Find $1.07\times8$1.07×8, giving your answer as a decimal.

 

Remember!

When using a standard algorithm, we multiply the digits together one pair at a time starting from the column that is furthest to the right.

Outcomes

5.NBT.B.7

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations. Assess the reasonableness of answers using estimation strategies. (Limit multiplication problems so that the product does not exceed thousandths. Limit division problems so that either the dividend or the divisor is a whole number.)

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