By Alicia Bodine • Updated Aug 30 2022
Fractions illustrate how a whole can be divided into equal parts. The denominator tells how many pieces make up the whole, and the numerator tells how many of those pieces you’re working with. Mastering fractions is essential for higher‑level math, science, and everyday budgeting.
When fractions share the same denominator, simply add or subtract the numerators and keep the denominator unchanged. For example, 1/5 + 2/5 = 3/5.
If the denominators differ, determine the LCD, then convert each fraction. For instance, 2/4 and 1/3 share an LCD of 12. Convert 2/4 to 6/12 and 1/3 to 4/12 before adding or subtracting: 6/12 + 4/12 = 10/12.
To multiply, multiply the numerators together and the denominators together. Example: 2/5 × 3/10 = 6/50.
Reduce to lowest terms by dividing numerator and denominator by their greatest common factor (GCF). 6/50 simplifies to 3/25 because 2 is the GCF of 6 and 50.
Convert the division problem into multiplication by flipping the divisor: 2/3 ÷ 1/9 → 2/3 × 9/1 = 18/3.
When the numerator exceeds the denominator, express the result as a mixed number. 18/3 becomes 6, and 20/3 becomes 6 2/3.
Multiply the whole number by the denominator, add the numerator, and keep the original denominator. Example: 2 3/4 → (2×4)+3 = 11; thus 11/4.
Consistent practice turns fraction work into a skill. Use free online worksheets to reinforce each step.
