Operations with Fractions & Decimals
Master adding, subtracting and multiplying fractions, and perform decimal operations with confidence.
Adding & Subtracting Fractions: Same Denominator
When the denominators are the same, simply add or subtract the numerators and keep the denominator.
Visual: 2/5 + 1/5
2/5 (two fifths)
1/5 (one fifth)
3/5 (three fifths)
2/5 + 1/5 = 3/5
Adding & Subtracting Fractions: Different Denominators
When the denominators are different, you must first find a common denominator before adding or subtracting.
Example: 1/3 + 1/4
Step 1: Find the lowest common denominator (LCD) of 3 and 4. LCD = 12
Step 2: Convert each fraction: 1/3 = 4/12 and 1/4 = 3/12
Step 3: Add the numerators: 4/12 + 3/12 = 7/12
Visual: Fraction Strips with Common Denominator
1/3 = 4/12
1/4 = 3/12
Total = 7/12
Multiplying Fractions
To multiply fractions: multiply the numerators together and multiply the denominators together.
a/b × c/d = a × c/b × d
Example: 2/3 × 3/4
Step 1: Multiply numerators: 2 × 3 = 6
Step 2: Multiply denominators: 3 × 4 = 12
Step 3: Simplify: 6/12 = 1/2
Answer: 2/3 × 3/4 = 1/2
Decimal Operations
When adding or subtracting decimals, line up the decimal points. When multiplying, count the total decimal places in both numbers.
Adding: 3.45 + 2.7
3.45 + 2.70 ------ 6.15
Add a zero to 2.7 to make 2.70, then add column by column.
Subtracting: 5.3 - 1.86
5.30 - 1.86 ------ 3.44
Add a zero to 5.3 to make 5.30, then subtract column by column.
Key Vocabulary
Common Denominator
A shared denominator that allows fractions to be added or subtracted.
Simplify
To reduce a fraction to its lowest terms by dividing numerator and denominator by their HCF.
Equivalent Fractions
Fractions that have the same value but different numerators and denominators (e.g. 1/2 = 2/4).
Decimal Place
The position of a digit after the decimal point (tenths, hundredths, thousandths).
Worked Examples
Calculate 3/8 + 1/8
Step 1: Same denominator, so add the numerators: 3 + 1 = 4
Step 2: Keep the denominator: 4/8
Step 3: Simplify: 4/8 = 1/2
Calculate 2/3 - 1/6
Step 1: Find LCD of 3 and 6: LCD = 6
Step 2: Convert: 2/3 = 4/6
Step 3: Subtract: 4/6 - 1/6 = 3/6
Answer: 3/6 = 1/2
Calculate 3/5 × 2/3
Step 1: Multiply numerators: 3 × 2 = 6
Step 2: Multiply denominators: 5 × 3 = 15
Answer: 6/15 = 2/5
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is 2/7 + 3/7?
Question 2
What is 1/2 + 1/3?
Question 3
What is 1/4 × 2/3?
Question 4
What is 4.56 + 2.3?
Question 5
What is 5/6 - 1/3?
Key Concepts Summary
- ●Same denominator: add/subtract the numerators, keep the denominator.
- ●Different denominators: find the LCD first, convert, then add/subtract.
- ●Multiplying fractions: multiply numerators, multiply denominators, then simplify.
- ●Always simplify your answer if possible.
- ●For decimals, line up the decimal points before adding or subtracting.