multiplying and dividing decimals by whole numbers worksheets

Teaching Notes

Practice focus: multiplying and dividing decimals by whole numbers worksheets. Focus: Tenths × Whole Number. Use the worked example and teaching sequence below to explain the reasoning before independent practice.

Before You Begin

• Read the numbers and identify the operation.

Teaching Steps for Parents and Teachers

1. First multiply using the digits as whole numbers.
2. Count the decimal places in both original factors.
3. Their total tells you where to place the decimal point in the product.
4. Include leading zeros after the decimal point when needed, then remove unnecessary trailing zeros only when the value stays unchanged.
5. If the divisor has decimal places, multiply both numbers by the same power of ten until the divisor is a whole number.
6. The quotient stays the same.
7. Divide using place value, keeping track of the decimal point in the quotient.
8. These worksheets use the answers supplied by the existing calculation bank; do not round unless a question explicitly asks you to.

Worked Examples

Evaluate 1.2 × 3.

1. Calculate the whole-number product: 12 × 3 = 36.
2. The factors have 1 decimal places altogether. Divide the product by 10.
3. The product is 3.6.

Answer: 3.6

Evaluate 3.6/3.

1. Multiply both numbers by 1: 3.6 ÷ 3.
2. Divide to get 1.2.
3. Check: 1.2 × 3 = 3.6.

Answer: 1.2

Common Mistakes and How to Help

Do not align decimal points as you would for addition. Multiplying by a positive number less than one makes a positive quantity smaller, so a large answer may indicate a misplaced point.

Estimate the product before calculating. Divide the product by a nonzero factor to check the other factor.

Moving only the divisor’s decimal point changes the problem. Apply the same shift to the dividend, and keep any zero needed to hold a quotient place.

Multiply the quotient by the original divisor. The result should return the original dividend.

Questions to Check Understanding

• Estimate the product before calculating. Divide the product by a nonzero factor to check the other factor.
• Which step explains your answer?
• Can you apply the same reasoning when the numbers change?

Practice Advice

Work through the example together. Ask the learner to explain the first two problems, then try three independently. Review the first incorrect step before assigning more practice.

Next Practice

• Use New Numbers to practice the same skill with different values.
• If the learner needs help, return to the example and model each step before trying again.