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

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

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

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: $0.08$.

$0.08$

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.

All Grade 5 chapters: Grade 5 math.

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