Working with Fractions

A fraction names part of a whole: in 3/4, the denominator (4) tells you how many equal parts the whole is divided into, and the numerator (3) tells you how many parts you have.

Simplifying fractions

Divide the numerator and denominator by their greatest common factor (GCF).

Example: simplify 12/18. The GCF of 12 and 18 is 6 (the GCF calculator confirms it from any pair), so 12/18 = 2/3.

A fraction is fully simplified when the only common factor of numerator and denominator is 1.

Converting between mixed numbers and improper fractions

A mixed number like 2⅓ has a whole part and a fraction part (the mixed number calculator converts both directions automatically). To convert:

1. Multiply the whole number by the denominator: 2 × 3 = 6
2. Add the numerator: 6 + 1 = 7
3. Put that over the denominator: 7/3

To go back the other way, divide: 7 ÷ 3 = 2 remainder 1, so 7/3 = 2⅓.

Adding and subtracting fractions

Fractions must share a denominator before you can add or subtract.

1/4 + 1/6: the least common denominator of 4 and 6 is 12 — which is LCM(4, 6). The LCM calculator finds it for any pair when the denominators are harder.

1/4 = 3/12 and 1/6 = 2/12, so the sum is 5/12.

Multiplying and dividing fractions

Multiplication is the easiest operation — multiply straight across:

2/3 × 3/5 = 6/15 = 2/5

To divide, flip the second fraction and multiply:

2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

Fractions to decimals and back

To convert a fraction to a decimal, divide: 3/8 = 0.375 (or let the fraction calculator divide for you).

To convert a decimal to a fraction, use the place value: 0.75 is 75/100, which simplifies to 3/4. For messier values the decimal-to-fraction calculator does the expansion-and-reduce loop itself. Repeating decimals like 0.333… convert to 1/3.

Common pitfalls

• Adding denominators: 1/2 + 1/2 is 2/2 = 1, not 2/4.
• Comparing without a common denominator: 3/5 is larger than 4/7 even though 4 > 3.
• Simplifying only one part: whatever you divide the numerator by must also divide the denominator.