In this Grade 6 Illustrative Mathematics lesson from Unit 5, students learn how to multiply decimals by expressing them as fractions with powers of ten, such as rewriting 0.7 × 0.09 as (7 × 1/10) × (9 × 1/100) to determine the correct placement of the decimal point in the product. Students explore how multiplying by 0.1, 0.01, and other powers of ten shifts the decimal point and practice applying this reasoning to multi-digit decimal multiplication. The lesson builds fluency with equivalent expressions and connects fraction concepts to decimal arithmetic.
Section 1
Multiply Decimals by Converting to Fractions
To multiply decimals, you can convert each decimal to its equivalent fraction. Then, multiply the fractions by multiplying the numerators and the denominators. The resulting fraction can be converted back to a decimal to find the product.
Section 2
Model Multiplying Two Decimals Less Than One
To multiply two decimals less than one, you can use a 10x10 grid to model the area of a rectangle. The product of the two decimals is represented by the overlapping shaded area.
Section 3
How to Multiply Decimal Numbers
How to multiply decimal numbers:
Step 1. Write the numbers in vertical format, lining up the numbers on the right.
Step 2. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.
Step 3. Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors. If needed, use zeros as placeholders.
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Section 1
Multiply Decimals by Converting to Fractions
To multiply decimals, you can convert each decimal to its equivalent fraction. Then, multiply the fractions by multiplying the numerators and the denominators. The resulting fraction can be converted back to a decimal to find the product.
Section 2
Model Multiplying Two Decimals Less Than One
To multiply two decimals less than one, you can use a 10x10 grid to model the area of a rectangle. The product of the two decimals is represented by the overlapping shaded area.
Section 3
How to Multiply Decimal Numbers
How to multiply decimal numbers:
Step 1. Write the numbers in vertical format, lining up the numbers on the right.
Step 2. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.
Step 3. Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors. If needed, use zeros as placeholders.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter