Grade 6Mathmedium
Multiply & Divide Decimals
Multiply & Divide Decimals — Decimals worksheet for Grade 6.
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What Your Child Will Learn
- Multiply decimal numbers by whole numbers and other decimals using the standard algorithm, correctly placing the decimal point in the product
- Divide decimals by whole numbers and by other decimals, using long division or the equivalent fractions strategy to find accurate quotients
- Apply understanding of place value to explain why the decimal point moves when multiplying and dividing by powers of 10
- Solve real-world problems involving multiplication and division of decimals, such as calculating costs, measurements, and unit rates
How to Use This Worksheet
- Step 1: Before starting, have your student review the concept of place value in decimals and review one or two worked examples of decimal multiplication and division. This refresher takes 3-5 minutes but builds confidence.
- Step 2: Have your student work through the first 3-4 problems slowly, writing out all steps clearly. Encourage them to estimate the answer first (rounding to whole numbers), then compute, then check if the actual answer is reasonable compared to the estimate.
- Step 3: For multiplication problems, remind students to count the total number of decimal places in both factors and place the decimal point that many places from the right in their product. Have them circle or highlight the decimal point placement step.
- Step 4: For division problems, have your student rewrite the problem so the divisor is a whole number (multiplying both numerator and denominator by 10, 100, etc. if needed), then complete the long division. This reduces decimal-related errors significantly.
- Step 5: After completing all 10 problems, have your student go back and verify 3-4 answers using a different method (such as estimation, a calculator, or solving with a peer) to identify and correct any remaining errors before finishing.
Tips for Parents & Teachers
Address the common mistake of placing the decimal point incorrectly by teaching students to count total decimal places in the factors (multiplication) or to use the equivalent fractions method for division. Have students check their work by estimating first—for example, 3.2 × 4.1 should be close to 3 × 4 = 12, not 1.2 or 120.
Help students understand that dividing by a decimal (like 2.5) is easier if they multiply both the dividend and divisor by a power of 10 to create a whole number divisor. For example, 5 ÷ 2.5 becomes 50 ÷ 25. This avoids confusion and reduces errors in the division process.
Use area models or grid diagrams to visualize multiplication of decimals, especially when multiplying two decimals. This concrete representation helps students see why 0.3 × 0.4 = 0.12 rather than 0.12 appearing arbitrary. Visual learners benefit greatly from this approach.
Encourage students to use a calculator to check their work after solving by hand. This builds confidence and helps them identify computational errors, but ensure they understand the 'why' behind each step before relying on technology.
Frequently Asked Questions
Why do I need to count decimal places when multiplying decimals instead of just multiplying the numbers?
When you multiply 2.3 × 1.5, you're not multiplying 23 × 15 (which would give 345). You're multiplying numbers that are 10 times smaller and 10 times smaller, so the answer should be 100 times smaller than 345. That's why 2.3 × 1.5 = 3.45. Counting decimal places ensures your answer has the correct size. Without placing the decimal correctly, your answer would be off by powers of 10.
How do I divide by a decimal like 4.2 when I've only learned to divide by whole numbers?
You can convert the problem to one with a whole number divisor! If you multiply both the dividend and divisor by 10 (or 100, depending on how many decimal places are in the divisor), the division stays the same but becomes easier. For example, 8.4 ÷ 4.2 becomes 84 ÷ 42, which equals 2. This works because you're multiplying by equivalent fractions (like multiplying by 10/10, which equals 1).
My child got 0.08 but I think the answer should be 0.8. How do I know which is correct?
Check using estimation! If the problem is 0.4 × 0.2, round to whole numbers: 0 × 0 doesn't help here, so try a different method. Think of it as 4 tenths × 2 tenths, which should give you hundredths (much smaller). So 0.4 × 0.2 = 0.08 is correct, not 0.8. Always estimate first to check if your decimal point is in the right place.
Should my sixth grader be using a calculator for these problems?
Calculators are best used as a checking tool after solving by hand, not during the problem-solving process. The goal is for students to understand WHY the decimal point moves and HOW the algorithm works. Once they've solved it correctly on paper, a calculator confirms their answer and builds confidence. This ensures they're building deep understanding, not just getting answers.
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