Decimal Operations Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Decimal Operations.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Decimal operations — addition, subtraction, multiplication, and division — follow the same rules as whole-number arithmetic but require careful attention to decimal point placement and alignment.

Decimal operations follow the same rules as whole numbers, but you must track the decimal point carefully—like keeping track of dollars and cents.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Decimal arithmetic follows whole-number rules but tracks the decimal point through every step.

Common stuck point: The procedure for decimal operations is the easy part; the trap is aligning the last digits instead of the decimal points when adding. Asking "Am I computing with decimal numbers where the point must be tracked?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I computing with decimal numbers where the point must be tracked?

Worked Examples

Example 1

easy
Add 12.74+5.6+0.0812.74 + 5.6 + 0.08.

Answer

18.4218.42

First step

1
Write each number so decimal points are aligned, padding with zeros as needed: 12.7412.74, 5.605.60, 0.080.08.

Full solution

  1. 2
    Add column by column from right: hundredths 4+0+8=124+0+8=12, write 22 carry 11; tenths 7+6+0+1=147+6+0+1=14, write 44 carry 11; ones 2+5+0+1=82+5+0+1=8; tens 11.
  2. 3
    Result: 18.4218.42.
Aligning decimal points ensures digits with the same place value are added together. Padding shorter decimals with trailing zeros (e.g., writing 5.6 as 5.60) prevents column-alignment errors.

Example 2

medium
Multiply 0.45×0.80.45 \times 0.8 and explain how to place the decimal point.

Example 3

medium
Calculate 4.25×3.64.25 \times 3.6.

Example 4

medium
Multiply 1.25×0.41.25\times 0.4 and explain the decimal placement.

Example 5

medium
Divide 4.5÷0.54.5\div 0.5.

Example 6

medium
Add 12.3+0.45+712.3+0.45+7.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Subtract 14.5−6.8314.5 - 6.83.

Example 2

hard
A 3-metre length of rope is cut into pieces, each 0.150.15 m long. How many complete pieces can be cut, and how much rope is left over?

Example 3

easy
Add 0.3+0.40.3+0.4.

Example 4

easy
Subtract 0.9−0.50.9-0.5.

Example 5

easy
Add 1.2+3.51.2+3.5.

Example 6

easy
Multiply 0.2×0.30.2\times 0.3.

Example 7

easy
Subtract 5.6−2.15.6-2.1.

Example 8

easy
Multiply 0.4×50.4\times 5.

Example 9

easy
Add 0.25+0.50.25+0.5.

Example 10

easy
Divide 0.8÷40.8\div 4.

Example 11

medium
Multiply 1.5×0.41.5\times 0.4.

Example 12

medium
Divide 4.5÷0.54.5\div 0.5.

Example 13

medium
Add 2.75+1.4+0.052.75+1.4+0.05.

Example 14

medium
Multiply 0.06×0.50.06\times 0.5.

Example 15

medium
Subtract 7−2.357-2.35.

Example 16

medium
A pen costs $1.25\$1.25. How much do 6 pens cost?

Example 17

medium
Divide 1.44÷1.21.44\div 1.2.

Example 18

medium
Multiply 2.5×1.22.5\times 1.2.

Example 19

medium
Divide 3.6÷0.93.6\div 0.9.

Example 20

challenge
You buy items for $3.49\$3.49, $1.25\$1.25, and $2.99\$2.99 and pay with $10\$10. How much change?

Example 21

challenge
Estimate then compute 0.25×0.250.25\times 0.25. Why is the answer less than each factor?

Example 22

challenge
A 2.5 kg bag of rice costs $4.50\$4.50. What is the price per kilogram?

Example 23

easy
Add 3.7+2.453.7+2.45.

Example 24

easy
Subtract 8.3−4.758.3-4.75.

Example 25

easy
What is 5.6÷105.6\div 10?

Example 26

medium
Compute 9.6÷0.49.6\div 0.4.

Example 27

medium
A box weighs 0.850.85 kg. What do 8 boxes weigh?

Example 28

easy
Add 0.05+0.60.05+0.6.

Example 29

medium
A pen costs \$1.25. How much do 12 pens cost?

Example 30

medium
Compute 6.3−1.076.3-1.07.

Example 31

easy
What is 0.5+0.5+0.50.5+0.5+0.5?

Example 32

medium
You buy items for \$3.75 and \$2.40 and pay with a \$10 bill. How much change?

Example 33

hard
Multiply 2.05×3.42.05\times 3.4.

Example 34

medium
Divide 7.2÷67.2\div 6.

Example 35

hard
A car drives 0.60.6 km per minute. How far in 7.57.5 minutes?

Example 36

medium
Compute 1−0.371-0.37.

Example 37

easy
What is 0.25×40.25\times 4?

Example 38

hard
Divide 0.84÷0.070.84\div 0.07.

Example 39

medium
Round 4.6734.673 to the nearest hundredth.

Example 40

hard
A water jug holds 4.54.5 L. How many 0.250.25 L glasses can it fill?

Example 41

challenge
Compute (1.2)2+(0.5)2(1.2)^2+(0.5)^2.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

decimalsadditionsubtractionmultiplicationdivision