5th Grade Multiplying and Dividing Decimals Worksheet Solutions (PDF)

5th Grade math worksheet solutions: Multiplying and Dividing Decimals – Maths PDF

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This multiply divide decimals answers for 5th Grade covers multiplying and dividing decimals (Common Core 5.NBT.B.7), with a free PDF to print.

This answer key gives a full worked solution for each of the 20 decimal problems. Each solution shows the whole-number step, the decimal-point step, and the final answer in bold. Compare the steps with your own work to find where a mistake started.

Grade 5 · Common Core State Standards: 5.NBT.B.7

Multiply divide decimals answers: exercises 1 to 10

Exercise 1 – Tenths times a whole number

Ignore the decimal points and multiply: $7 \times 6 = 42$.

The factors have 1 and 0 decimal places, so the product has 1 + 0 = 1 decimal place: $4.2$.

$4.2$

Exercise 2 – Hundredths times a whole number

Ignore the decimal points and multiply: $6 \times 7 = 42$.

The factors have 2 and 0 decimal places, so the product has 2 + 0 = 2 decimal places: $0.42$.

$0.42$

Exercise 3 – Product from a model

The overlap holds 18 squares, so the product is 0.18.

6 columns shaded blue show 0.6. 3 rows shaded orange show 0.3.

The overlap is $6 \times 3 = 18$ squares, and each square is 0.01.

$0.6 \times 0.3 = 0.18$

Exercise 4 – Decimal times tenths

Ignore the decimal points and multiply: $42 \times 5 = 210$.

The factors have 1 and 1 decimal places, so the product has 1 + 1 = 2 decimal places: $2.10$.

Dropping the extra zero gives $2.1$.

$2.1$

Exercise 5 – Two decimal factors

Ignore the decimal points and multiply: $36 \times 24 = 864$.

The factors have 1 and 1 decimal places, so the product has 1 + 1 = 2 decimal places: $8.64$.

$8.64$

Exercise 6 – Hundredths and tenths

Ignore the decimal points and multiply: $25 \times 4 = 100$.

The factors have 2 and 1 decimal places, so the product has 2 + 1 = 3 decimal places: $0.100$.

Dropping the extra zero gives $0.1$.

$0.1$

Exercise 7 – Zeros in the product

Ignore the decimal points and multiply: $5 \times 2 = 10$.

The factors have 2 and 1 decimal places, so the product has 2 + 1 = 3 decimal places: $0.010$.

Dropping the extra zero gives $0.01$.

$0.01$

Exercise 8 – Divide tenths by a whole number

Each part is 1.2.

Divide as with whole numbers: $48 \div 4 = 12$.

Put the decimal point so the quotient has 1 decimal place: $1.2$.

$1.2$

Exercise 9 – Divide hundredths by a whole number

Divide as with whole numbers: $756 \div 6 = 126$.

Put the decimal point so the quotient has 2 decimal places: $1.26$.

$1.26$

Exercise 10 – Quotient less than 1

Divide as with whole numbers: $72 \div 9 = 8$.

Put the decimal point so the quotient has 2 decimal places: $0.08$.

$0.08$

Exercises 11 and up

Exercise 11 – Keep dividing with zeros

Write 9.3 as 9.30 so the division can end.

Divide as with whole numbers: $930 \div 5 = 186$.

Put the decimal point so the quotient has 2 decimal places: $1.86$.

$1.86$

Exercise 12 – Divide by tenths

Both numbers are multiplied by 10.

Multiply both numbers by 10 so the divisor is a whole number: $6.3 \times 10 = 63$ and $0.9 \times 10 = 9$.

Now divide: $63 \div 9 = 7$.

$7$

Exercise 13 – Divide by hundredths

Multiply both numbers by 100 so the divisor is a whole number: $1.44 \times 100 = 144$ and $0.12 \times 100 = 12$.

Now divide: $144 \div 12 = 12$.

$12$

Exercise 14 – Decimal divided by decimal

Multiply both numbers by 10 so the divisor is a whole number: $0.72 \times 10 = 7.2$ and $0.4 \times 10 = 4$.

Now divide: $7.2 \div 4 = 1.8$.

$1.8$

Exercise 15 – Apples at the market

Multiply the weight by the price per pound: $3.5 \times 1.8$.

Ignore the decimal points and multiply: $35 \times 18 = 630$.

The factors have 1 and 1 decimal places, so the product has 1 + 1 = 2 decimal places: $6.30$.

Dropping the extra zero gives $6.3$.

The product 6.3 means $6.30.

The apples cost $6.30.

Exercise 16 – Ribbon for bows

Ribbon used: $0.65 \times 12$.

$65 \times 12 = 780$, and 2 decimal places gives $7.80 = 7.8$.

Ribbon left: $10 – 7.8 = 2.2$.

2.2 yards are left.

Exercise 17 – Unit price

Divide the total cost by the number of pounds: $14.40 \div 1.8$.

Multiply both numbers by 10 so the divisor is a whole number: $14.40 \times 10 = 144$ and $1.8 \times 10 = 18$.

Now divide: $144 \div 18 = 8$.

Trail mix costs $8 per pound, or $8.00.

Exercise 18 – Movie tickets

Total cost: $8.75 \times 4$.

$875 \times 4 = 3{,}500$, and 2 decimal places gives $35.00$.

She pays $40. Change: $40 – 35 = 5$.

Priya gets $5.00 in change.

Exercise 19 – Trail markers

Divide the trail length by the length of one section: $5.4 \div 0.45$.

Multiply both numbers by 100 so the divisor is a whole number: $5.4 \times 100 = 540$ and $0.45 \times 100 = 45$.

Now divide: $540 \div 45 = 12$.

The trail has 12 equal sections.

Exercise 20 – Garden soil

Area: $3.6 \times 2.5$.

$36 \times 25 = 900$, and 2 decimal places gives $9.00 = 9$ square feet.

Cost: $9 \times 0.75$.

$9 \times 75 = 675$, and 2 decimal places gives $6.75$.

The area is 9 square feet and the soil costs $6.75.

Key facts behind this multiply divide decimals answers

Key facts

The product of two decimals has as many decimal places as both factors together.
A hundredths grid shows 0.3 times 0.4 as 12 squares, which is 0.12.
When dividing by a whole number, keep the decimal point in line.
Multiplying both numbers by 10, 100, or 1,000 does not change a quotient.
Estimate first to check where the decimal point belongs.

How to use this multiply divide decimals answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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