Operations with Decimals: Grade 5 Math Worksheet Answer Key – PDF Download

Grade 5 Decimal Worksheet Answer Key: problems 1–5

Problem 1: Add on a hundredths grid

Count the shaded squares: 27 + 46 = 73 hundredths. \(0.27 + 0.46 = 0.73\).

Answer: \(0.73\)

Problem 2: Add tenths and hundredths

1. Line up the decimal points and add place by place: \(0.6 + 0.7 = 1.3\) 1.3
2. Line up the decimal points and add place by place: \(0.45 + 0.38 = 0.83\) 0.83
3. Line up the decimal points and add place by place: \(1.25 + 0.9 = 2.15\) 2.15
4. Line up the decimal points and add place by place: \(3.07 + 2.68 = 5.75\) 5.75

Problem 3: Line up and add

1. Line up the decimal points and add place by place: \(12.5 + 3.75 = 16.25\) 16.25
2. Line up the decimal points and add place by place: \(8.06 + 14.9 = 22.96\) 22.96
3. Line up the decimal points and add place by place: \(25 + 4.38 = 29.38\) 29.38
4. Line up the decimal points and add place by place: \(19.99 + 0.01 = 20\) 20

Problem 4: Subtract tenths and hundredths

1. Line up the decimal points and subtract place by place: \(0.9 – 0.4 = 0.5\) 0.5
2. Line up the decimal points and subtract place by place: \(1 – 0.37 = 0.63\) 0.63
3. Line up the decimal points and subtract place by place: \(0.82 – 0.57 = 0.25\) 0.25
4. Line up the decimal points and subtract place by place: \(2.4 – 0.65 = 1.75\) 1.75

Problem 5: Line up and subtract

1. Line up the decimal points and subtract place by place: \(15.3 – 6.75 = 8.55\) 8.55
2. Line up the decimal points and subtract place by place: \(40 – 12.86 = 27.14\) 27.14
3. Line up the decimal points and subtract place by place: \(9.05 – 3.9 = 5.15\) 5.15
4. Line up the decimal points and subtract place by place: \(20.5 – 8.37 = 12.13\) 12.13

Grade 5 Decimal Worksheet Answer Key: problems 6–10

Problem 6: Subtract with jumps

The jumps are 0.25 and 1. Add them: \(0.25 + 1 = 1.25\). So \(4 – 2.75 = 1.25\). Check: \(2.75 + 1.25 = 4\).

Answer: \(1.25\)

Problem 7: Find the missing number

1. Subtract the known addend: \(7.15 – 3.4 = 3.75\). 3.75
2. Subtract the known addend: \(9.04 – 5.2 = 3.84\). 3.84
3. Add the amount that was taken away: \(4.45 + 2.6 = 7.05\). 7.05
4. Subtract the difference from the starting number: \(12 – 5.35 = 6.65\). 6.65

Problem 8: Multiply on a grid

The orange rows and blue columns overlap in 3 × 8 = 24 squares. Each square is one hundredth. \(0.3 \times 0.8 = 0.24\).

Answer: \(0.24\)

Problem 9: Multiply by a whole number

1. Multiply as whole numbers: \(3 \times 4 = 12\). The factors have 1 + 0 = 1 decimal places, so the product does too: \(0.3 \times 4 = 1.2\) 1.2
2. Multiply as whole numbers: \(25 \times 6 = 150\). The factors have 2 + 0 = 2 decimal places, so the product does too: \(0.25 \times 6 = 1.5\) 1.5
3. Multiply as whole numbers: \(14 \times 5 = 70\). The factors have 1 + 0 = 1 decimal places, so the product does too: \(1.4 \times 5 = 7\) 7
4. Multiply as whole numbers: \(235 \times 4 = 940\). The factors have 2 + 0 = 2 decimal places, so the product does too: \(2.35 \times 4 = 9.4\) 9.4

Problem 10: Multiply decimals

1. Multiply as whole numbers: \(5 \times 6 = 30\). The factors have 1 + 1 = 2 decimal places, so the product does too: \(0.5 \times 0.6 = 0.3\) 0.3
2. Multiply as whole numbers: \(12 \times 3 = 36\). The factors have 1 + 1 = 2 decimal places, so the product does too: \(1.2 \times 0.3 = 0.36\) 0.36
3. Multiply as whole numbers: \(9 \times 9 = 81\). The factors have 1 + 1 = 2 decimal places, so the product does too: \(0.9 \times 0.9 = 0.81\) 0.81
4. Multiply as whole numbers: \(46 \times 5 = 230\). The factors have 1 + 1 = 2 decimal places, so the product does too: \(4.6 \times 0.5 = 2.3\) 2.3

Grade 5 Decimal Worksheet Answer Key: problems 11–15

Problem 11: Place the decimal point

1. \(2.5 \times 1.6 = 4\): the factors have 1 + 1 = 2 decimal places, so 400 becomes 4. 4
2. \(0.25 \times 16 = 4\): the factors have 2 + 0 = 2 decimal places, so 400 becomes 4. 4
3. \(2.5 \times 0.16 = 0.4\): the factors have 1 + 2 = 3 decimal places, so 400 becomes 0.4. 0.4

Problem 12: Estimate, then multiply

1. Estimate: \(5 \times 3 = 15\). Exact: \(49 \times 31 = 1519\), two decimal places, so \(4.9 \times 3.1 = 15.19\). 15.19
2. Estimate: \(6 \times 3 = 18\). Exact: \(61 \times 29 = 1769\), two decimal places, so \(6.1 \times 2.9 = 17.69\). 17.69

Problem 13: Divide by a whole number

1. Divide as with whole numbers and keep the decimal point in place: \(4.8 : 4 = 1.2\) 1.2
2. Divide as with whole numbers and keep the decimal point in place: \(0.96 : 8 = 0.12\) 0.12
3. Divide as with whole numbers and keep the decimal point in place: \(7.5 : 5 = 1.5\) 1.5
4. Divide as with whole numbers and keep the decimal point in place: \(13.2 : 6 = 2.2\) 2.2

Problem 14: Divide with strips

Eight tenths make 4 groups of two tenths. \(0.8 : 0.2 = 4\). Check: \(4 \times 0.2 = 0.8\).

Answer: \(4\)

Problem 15: Divide by a decimal

1. Multiply both numbers by 10 so the divisor is a whole number: \(36 : 9 = 4\). So \(3.6 : 0.9 = 4\) 4
2. Multiply both numbers by 10 so the divisor is a whole number: \(45 : 5 = 9\). So \(4.5 : 0.5 = 9\) 9
3. Multiply both numbers by 100 so the divisor is a whole number: \(720 : 6 = 120\). So \(7.2 : 0.06 = 120\) 120
4. Multiply both numbers by 100 so the divisor is a whole number: \(84 : 12 = 7\). So \(0.84 : 0.12 = 7\) 7

Grade 5 Decimal Worksheet Answer Key: problems 16–20

Problem 16: Divide to hundredths

1. Divide as with whole numbers and keep the decimal point in place: \(9 : 4 = 2.25\) 2.25
2. Divide as with whole numbers and keep the decimal point in place: \(5.1 : 6 = 0.85\) 0.85
3. Multiply both numbers by 10 so the divisor is a whole number: \(126 : 4 = 31.5\). So \(12.6 : 0.4 = 31.5\) 31.5
4. Multiply both numbers by 10 so the divisor is a whole number: \(147 : 7 = 21\). So \(14.7 : 0.7 = 21\) 21

Problem 17: Back-to-school supplies

1. \(\$3.45 + \$1.89 + \$2.50 = \$7.84\). $7.84
2. \(\$10.00 – \$7.84 = \$2.16\). $2.16

Problem 18: Training miles

1. \(2.4 + 3.15 + 1.85 = 7.4\). 7.4 miles
2. \(10 – 7.4 = 2.6\). 2.6 miles

Problem 19: Farmers market

Apples: \(3.5 \times \$1.80 = \$6.30\). Grapes: \(2.25 \times \$2.40 = \$5.40\). Total: \(\$6.30 + \$5.40 = \$11.70\).

Answer: $11.70

Problem 20: Ribbon pieces

Multiply both numbers by 100: \(1875 : 75 = 25\). Check: \(25 \times 0.75 = 18.75\).

Answer: 25 pieces

Grade 5 Decimal Worksheet Answer Key: problems 21–23

Problem 21: Birthday money

Spent: \(\$18.75 + \$12.40 = \$31.15\). Left: \(\$50.00 – \$31.15 = \$18.85\).

Answer: $18.85

Problem 22: Gas prices

1. \(41.58 : 12.6\): multiply both by 10 to get \(415.8 : 126\), or check that \(12.6 \times 3.3 = 41.58\). $3.30 per gallon
2. \(8.5 \times \$3.30 = \$28.05\). $28.05

Problem 23: Relay team

Total: \(25.8 + 26.45 + 24.9 + 27.15 = 104.3\) seconds. Difference: \(104.3 – 100 = 4.3\).

Answer: 4.3 seconds over the goal

How to use this grade 5 decimal worksheet answer key

Read this grade 5 decimal worksheet answer key after trying each problem yourself, and redo any problem you missed.

See every chapter on the Grade 5 math page.