Relating Decimal and Whole Number Multiplication
Relating Decimal and Whole Number Multiplication is a Grade 5 math skill from Illustrative Mathematics Chapter 5 (Place Value Patterns and Decimal Operations) that teaches students to use known whole number facts to solve decimal multiplication problems. Multiply the digits as whole numbers first, then place the decimal point so the product has the same number of decimal places as the decimal factor.
Key Concepts
Property To multiply a decimal by a whole number, first multiply the numbers as if they were whole numbers. Then, place the decimal point in the product so that it has the same number of decimal places as the decimal factor.
Examples To solve $0.3 \times 4$, first calculate the whole number fact $3 \times 4 = 12$. Since $0.3$ has one decimal place, the product will also have one decimal place: $1.2$. To solve $1.25 \times 3$, first calculate the whole number fact $125 \times 3 = 375$. Since $1.25$ has two decimal places, the product will also have two decimal places: $3.75$.
Explanation This skill helps you use your knowledge of whole number multiplication to solve decimal problems. By temporarily ignoring the decimal point, you can calculate the digits of the answer using familiar facts. Then, you simply place the decimal point correctly in the final product. The number of decimal places in your answer must match the number of decimal places in the decimal factor you started with.
Common Questions
How does whole number multiplication help with decimal multiplication?
First multiply the digits while ignoring the decimal point, using a known whole number fact. Then place the decimal point in the product so it has the same number of decimal places as the decimal factor. For example, 0.3 × 4: use 3 × 4 = 12, then place 1 decimal: 1.2.
What is the rule for placing the decimal in a product?
The number of decimal places in the product equals the number of decimal places in the decimal factor. For example, 1.25 × 3: use 125 × 3 = 375, then place 2 decimal places: 3.75.
What chapter covers relating decimal and whole number multiplication in Illustrative Mathematics Grade 5?
Relating decimal and whole number multiplication is covered in Chapter 5 of Illustrative Mathematics Grade 5, titled Place Value Patterns and Decimal Operations.
Why can you use whole number facts to multiply decimals?
Multiplying a decimal by a whole number is like multiplying the whole-number part and then scaling down by the appropriate power of 10. Ignoring the decimal does the multiplication; counting decimal places applies the scaling.
What is an example of relating decimal and whole number multiplication?
To solve 1.25 × 3: recognize that 125 × 3 = 375. Since 1.25 has 2 decimal places, the answer is 3.75. To solve 0.3 × 4: use 3 × 4 = 12, apply 1 decimal place to get 1.2.