Fractions & Decimals

The four operations on fractions — and how to move between fractions and decimals — with every rule you need.

QUICK ANSWER

Adding fractions: find common denominator → add numerators. ½ + ⅓ = 3/6 + 2/6 = 5/6. Multiplying: multiply straight across. ½ × ¾ = 3/8. Dividing: flip the second fraction and multiply. ½ ÷ ¼ = ½ × 4/1 = 2. Fraction to decimal: numerator ÷ denominator. ¾ = 0.75.

Step-by-Step: Adding Fractions with Different Denominators

1
Find a common denominator

Find the lowest common multiple (LCM) of the two denominators. For 1/3 + 1/4, the LCM of 3 and 4 is 12.

2
Convert each fraction

Rewrite each fraction over the common denominator. 1/3 = 4/12 and 1/4 = 3/12.

3
Add the numerators

Add the top numbers and keep the common denominator. 4/12 + 3/12 = 7/12.

4
Simplify if possible

Reduce the result to lowest terms by dividing by the greatest common divisor. 7/12 is already in lowest terms, so the answer is 7/12.

The Four Operations

Addition

Find common denominator, add numerators

1/3 + 1/4 = 4/12 + 3/12 = 7/12

Formula: (ad+bc)/bd

Subtraction

Find common denominator, subtract numerators

3/4 − 1/3 = 9/12 − 4/12 = 5/12

Formula: (ad−bc)/bd

Multiplication

Multiply numerator × numerator, denominator × denominator

2/3 × 3/4 = 6/12 = 1/2

Cross-simplify first when possible

Division

Flip the second fraction (reciprocal) then multiply

3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8 = 1⅛

Keep, Change, Flip (KCF)

Converting Between Fractions and Decimals

Fraction → Decimal

Divide the numerator by the denominator.

  • 3/4 = 3 ÷ 4 = 0.75
  • 2/5 = 2 ÷ 5 = 0.4
  • 1/3 = 1 ÷ 3 = 0.3333… (repeating)
  • 7/8 = 7 ÷ 8 = 0.875

Decimal → Fraction

Count decimal places. Write as that power of 10, then simplify.

  • 0.75 = 75/100 = 3/4
  • 0.4 = 4/10 = 2/5
  • 0.125 = 125/1000 = 1/8
Fraction Decimal Percentage
1/2 0.5 50%
1/3 0.333… 33.3%
2/3 0.666… 66.7%
1/4 0.25 25%
3/4 0.75 75%
1/5 0.2 20%
1/8 0.125 12.5%
1/10 0.1 10%

Decimal Notation Around the World

The decimal point is not universal — it is a cultural convention:

  • US, UK, Australia, China: period = decimal point. 3.14
  • Germany, France, Spain, Italy, Brazil: comma = decimal point. 3,14
  • Switzerland: period for decimals, apostrophe for thousands. 1'234.56
  • India: period for decimals, but comma grouping is 2-2-3. 1,23,456.78

This is the most common source of international calculation errors — a price of "1.500" means $1,500 in Germany but $1.50 in the US.

Frequently Asked Questions

How do you add fractions with different denominators? ▾
Find a common denominator, convert each fraction, then add the numerators. Example: 1/3 + 1/4. LCM of 3 and 4 = 12. Convert: 4/12 + 3/12 = 7/12. Formula: a/b + c/d = (ad + bc) / bd. Example: 1/3 + 1/4 = (4+3)/12 = 7/12.
How do you convert a fraction to a decimal? ▾
Divide the numerator by the denominator. Examples: 3/4 = 3 ÷ 4 = 0.75. 1/3 = 1 ÷ 3 = 0.333... (repeating). 7/8 = 7 ÷ 8 = 0.875. To convert a decimal back to a fraction: write the decimal over 1, multiply both by 10^(decimal places), simplify. 0.75 = 75/100 = 3/4.
How do you multiply fractions? ▾
Multiply numerator × numerator and denominator × denominator. Simplify the result. Example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. Tip: cross-simplify first. 2/3 × 3/4 → cancel a 3: 2/1 × 1/4 = 2/4 = 1/2.
How do you divide fractions? ▾
Flip the second fraction (its reciprocal) and multiply. Example: 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8 = 1⅛. A simple way to remember the rule is Keep, Change, Flip (KCF): keep the first fraction, change ÷ to ×, and flip the second fraction.
Why do some countries use a comma as the decimal point? ▾
The decimal separator is a cultural convention, not a mathematical rule. The US, UK, Australia, and China use a period (3.14), while Germany, France, Spain, Italy, and Brazil use a comma (3,14). This is one of the most common sources of international calculation errors — "1.500" means 1,500 in Germany but 1.5 in the US.

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