Using the Distributive Property with Decimals and Mixed Numbers - worksheet and answer key

Sep 30, 2026

Uploaded by Bulrr

Worksheet and answer key for practicing the distributive property with decimals and mixed numbers. Students break each product into two parts by separating whole-number and fractional/decimal components, then add the partial products to reach the final multiplication result. Problems include multiplying a whole number by a decimal (e.g., 6.3, 8.5, 6.2, 5.7) and by fractions expressed over the same denominator, such as 7×11/12 and 8×7/8. Solutions demonstrate the expanded form and the summed total.

LanguageEnglish

CategoryExam

FormatPDF

Pages3

Reading Time8 min

AccessFree to download

Distributive Property Practice

Decimal Products

Fraction and Mixed Number Products

Using the Distributive Property with Decimals and Mixed Numbers Name: | Break apart each number and fill in the blanks to solve.
1) 5 × 6.3 = (5 × ) + (5 × ) = + =
2) 12 × 711⁄ 12 = (12 × ) + (12 ×~~ ~~12~~ ~~) =+ = 3) 12 × 45⁄ 12 = (12 × ) + (12 ×~~ ~~12~~ ~~) =+ = 4) 7 × 8.5 = (7 × ) + (7 × ) = + =
5) 8 × 47⁄ 8 = (8 × ) + (8 ×~~ ~~8~~ ~~) = + = 6) 7 × 6.2 = (7 × ) + (7 × ) = + =
7) 5 × 5.7 = (5 × ) + (5 × ) = + =
8) 12 × 91⁄ 12 = (12 × ) + (12 ×~~ ~~12~~ ~~) =+ = 9) 4 × 8.6 = (4 × ) + (4 × ) = + =
10) 12 × 65⁄ 6 = (12 × ) + (12 ×~~ ~~6~~ ~~) =+ = 11) 3 × 21⁄ 3 = (3 × ) + (3 ×~~ ~~3~~ ~~) = + =
12) 2 × 3.2 = (2 × ) + (2 × ) = + = | Answers | | --- | --- | | | 1.
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12. | Math [www.CommonCoreSheets.com](www.CommonCoreSheets.com) 10 1-10 92 11-12 8 83 0 75 67 58 50 42 33 25 17 Using the Distributive Property with Decimals and Mixed Numbers Name: Answer Key | Break apart each number and fill in the blanks to solve.
1) 5 × 6.3 = (5 × 6 ) + (5 × 0.3 ) = 30 + 1.5 = 31.5 | | | | | | | | | | Answers | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | | | | | | | | | | 1. 31.5 | | | | | 2) | 12 × 711⁄ 12 = (12 × 7 ) + (12 ×~~ ~~1112~~ ~~) = 84 + 11 = 95 | | | | | | | | | 2. 95
3. 53 | | | | | 3) | 12 × 45⁄ 12 = (12 × 4 ) + (12 ×~~ ~~152~~ ~~) = 48 + 5 = 53 | | | | | | | | | 4. 59.5 | | | | | 4) | 7 × 8.5 = (7 × 8 ) + (7 × 0.5 ) = 56 + 3.5 = 59.5 | | | | | | | | | 5. 39
6. 43.4 | | | | | 5) | 8 × 47⁄ 8 = (8 × 4 ) + (8 ×~~ ~~78~~ ~~) = 32 + 7 = 39 | | | | | | | | | 7. 28.5
8. 109 | | | | | 6) | 7 × 6.2 = (7 × 6 ) + (7 × 0.2 ) = 42 + 1.4 = 43.4 | | | | | | | | | 9. 34.4 | | | | | 7) | 5 × 5.7 = (5 × 5 ) + (5 × 0.7 ) = 25 + 3.5 = 28.5 | | | | | | | | | 10. 82
11. 7 | | | | | 8) | 12 × 91⁄ 12 = (12 × 9 ) + (12 ×~~ ~~112~~ ~~) = 108 + 1 = 109 | | | | | | | | | 12. 6.4 | | | | | 9) | 4 × 8.6 = (4 × 8 ) + (4 × 0.6 ) = 32 + 2.4 = 34.4 | | | | | | | | | | | | | | 10) | 12 × 65⁄ 6 = (12 × 6 ) + (12 ×~~ ~~56~~ ~~) = 72 + 10 = 82 | | | | | | | | | | | | | | 11) | 3 × 21⁄ 3 = (3 × 2 ) + (3 ×~~ ~~13~~ ~~) = 6 + 1 = 7 | | | | | | | | | | | | | | 12) | 2 × 3.2 = (2 × 3 ) + (2 × 0.2 ) = 6 + 0.4 = 6.4 | | | | | | | | | | | | | | | Math
[www.CommonCoreSheets.com](www.CommonCoreSheets.com) | 10 | 1-10
11-12 | 92 | 83 | 75 | 67 | 58 | 50 | 42 | 33 | 25 | 17 | | | | | | 8 | 0 | | | | | | | | | Using the Distributive Property with Decimals and Mixed Numbers Name: | Break apart each number and fill in the blanks to solve.
1) 5 × 6.3 = (5 × ) + (5 × ) =+ =
2) 12 × 711⁄ 12 = (12 × ) + (12 ×~~ ~~12~~ ~~) =+ =
3) 12 × 45⁄ 12 = (12 × ) + (12 ×~~ ~~12~~ ~~) =+ =
4) 7 × 8.5 = (7 × ) + (7 × ) =+ =
5) 8 × 47⁄ 8 = (8 × ) + (8 ×~~ ~~8~~ ~~) = + =
6) 7 × 6.2 = (7 × ) + (7 × ) =+ =
7) 5 × 5.7 = (5 × ) + (5 × ) =+ =
8) 12 × 91⁄ 12 = (12 × ) + (12 ×~~ ~~12~~ ~~) =+ = | | | | | Answers | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | | | | | 1.
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8. | | | | | | 1-8 | 88 | 75 | 63 | 50 | | 38 | 25 | 13 | 0 | Math Modified [www.CommonCoreSheets.com](www.CommonCoreSheets.com) 10

FAQs

How do you use the distributive property with decimals in these problems?

Split the decimal into a whole-number part and a decimal part (for example, 6.3 into 6 and 0.3). Multiply each part separately and then add the results.

How are fractions and mixed numbers handled in the worksheets?

Rewrite the fractional or mixed component so it can be split into parts over the denominator, then multiply each part separately and add the partial products.

What is the expected method to fill in the blanks?

Fill in the factors created by breaking the original number into parts, compute each partial product, and then sum them to match the final answer for each problem.

Sep 30, 2026

Uploaded by Bulrr