P4 Operations with Decimals

Decimal operations are whole-number operations with place-value care. Align the points, keep exact hundredths, and extend a whole-number division with zeroes when the quotient needs decimal places.

Parents: let your child choose a prediction, then ask which place is being exchanged before each reveal.

By the end you will be able to add and subtract through two decimal places, multiply and divide by one-digit whole numbers, turn a whole-number quotient into a decimal, and round that answer to a stated accuracy.

Add and subtract through 2 decimal places

Write zero placeholders so the decimal points line up. In 5.06 + 1.87, 6 hundredths plus 7 hundredths make 13 hundredths; carry 1 tenth and write 3 hundredths. In 5.20 − 1.87, the hundredths need an exchange from the tenths, and the tenths then need an exchange from the ones.

🔬

Decimal operations: move through the places

🤔 Predict first: Which result matches 2.35 × 4?

9.408.409.04

Show the worked solution

Add 5.06 and 1.87

$$\begin{array}{r r r r}5&.&0&6\\+1&.&8&7\\\hline6&.&9&3\\\end{array}$$

$$\begin{array}{r r r r}\text{place}&\text{ones}&\text{tenths}&\text{hundredths}\\\text{carry}&&1&\\\text{first}&5&0&6\\+&1&8&7\\\hline\text{sum}&6&9&3\\\end{array}$$

$$6\text{ hundredths}+7\text{ hundredths}=13\text{ hundredths}:\text{ write 3 and carry 1 tenth}$$

$$0\text{ tenths}+8\text{ tenths}+1\text{ tenth}=9\text{ tenths}$$

$$5.06+1.87=6.93$$

Exchange in 5.20 − 1.87

$$\begin{array}{r r r r}5&.&2&0\\-1&.&8&7\\\hline3&.&3&3\\\end{array}$$

$$\begin{array}{r r r r}\text{place}&\text{ones}&\text{tenths}&\text{hundredths}\\\text{before}&5&2&0\\\text{exchange 1}&5&1&10\\\text{exchange 2}&4&11&10\\\hline\text{difference}&3&3&3\\\end{array}$$

$$0\text{ hundredths}\rightarrow10\text{ hundredths}:10-7=3$$

$$1\text{ tenth}\rightarrow11\text{ tenths}:11-8=3$$

$$4-1=3\text{ ones}$$

$$520-187=333$$

$$333\text{ hundredths}=3.33$$

Multiply a decimal by a one-digit whole number

For 2.35 × 4, think of 2.35 as 235 hundredths. Multiply the exact whole number of hundredths, then write the result back with two decimal places.

Show the worked solution

The exact whole-number product is 940 hundredths, so the trailing zero in 9.40 stays visible.

Scale to hundredths

$$2.35=235\text{ hundredths}$$

$$235\times4=940$$

$$940\text{ hundredths}=9.40$$

$$2.35\times4=9.40$$

Divide a decimal by a one-digit whole number

Divide the places in order and exchange a remainder into the next smaller place. For 7.20 ÷ 3, whole ones are shared first, then tenths and hundredths are kept as exact scaled units.

Divide 7.20 by 3

$$7\text{ ones}\div3=2\text{ ones, remainder }1\text{ one}$$

$$1\text{ one}=10\text{ tenths}; 10\text{ tenths}+2\text{ tenths}=12\text{ tenths}$$

$$12\text{ tenths}\div3=4\text{ tenths each}$$

$$0\text{ hundredths}\div3=0\text{ hundredths}$$

$$7.20\div3=2.40$$

$$240\text{ hundredths}\times3=720\text{ hundredths}$$

Divide a whole number into a decimal quotient

When a whole-number division has a remainder, extend the dividend with a decimal point and zeroes. For 7 ÷ 4, three leftover wholes become 30 tenths; two leftover tenths become 20 hundredths.

Extend 7 ÷ 4

$$7\div4=1\text{ remainder }3$$

$$3\text{ wholes}=30\text{ tenths}:30\div4=7\text{ tenths remainder }2$$

$$2\text{ tenths}=20\text{ hundredths}:20\div4=5\text{ hundredths}$$

$$7\div4=1.75$$

Round a computed answer

Sometimes the question asks for an answer to a stated place. Compute first, then inspect the next digit.

Show the worked solution

Since 5 ÷ 8 = 0.625, the thousandths digit is 5, so the hundredths digit rounds from 2 to 3.

Round the quotient

$$5\div8=0.625$$

$$0.625\text{ has 5 thousandths}$$

$$0.625\approx0.63\text{ (to 2 decimal places)}$$

Practise with worked steps

Practice 1. Calculate 5.06 + 1.87 and 5.20 − 1.87. Show the carry and both exchanges.

Show the complete subtraction solution

Decimal addition and subtraction

$$\begin{array}{r r r r}5&.&0&6\\+1&.&8&7\\\hline6&.&9&3\\\end{array}$$

$$\begin{array}{r r r r}\text{place}&\text{ones}&\text{tenths}&\text{hundredths}\\\text{carry}&&1&\\\text{first}&5&0&6\\+&1&8&7\\\hline\text{sum}&6&9&3\\\end{array}$$

$$5.06+1.87=6.93$$

$$\begin{array}{r r r r}\text{place}&\text{ones}&\text{tenths}&\text{hundredths}\\\text{before}&5&2&0\\\text{exchange 1}&5&1&10\\\text{exchange 2}&4&11&10\\\hline\text{difference}&3&3&3\\\end{array}$$

$$0\text{ hundredths}\rightarrow10\text{ hundredths}:10-7=3$$

$$1\text{ tenth}\rightarrow11\text{ tenths}:11-8=3$$

$$4-1=3\text{ ones}$$

$$520-187=333$$

$$333\text{ hundredths}=3.33$$

Practice 2. Calculate 2.35 × 4 and 7.20 ÷ 3. Keep two decimal places in both answers.

Show the scaled-unit solutions

Exact hundredths

$$235\times4=940$$

$$940\text{ hundredths}=9.40$$

$$7.20\div3=2.40$$

Practice 3. Calculate 7 ÷ 4, then round 5 ÷ 8 to 2 decimal places.

Show the quotient and rounding solutions

Whole division and rounding

$$7\div4=1.75$$

$$5\div8=0.625\approx0.63\text{ (to 2 decimal places)}$$

Watch out — easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. What is 5.06 + 1.87?

   6.936.037.93

2. What is 5.20 − 1.87?

   3.333.434.33

3. What is 2.35 × 4?

   9.409.0494.0

4. What is 7.20 ÷ 3?

   2.042.4024.0

5. What is 7 ÷ 4?

   1.751.572.75

6. What is 5 ÷ 8 rounded to 2 decimal places?

   0.620.630.65

See my score