To calculate the fraction, choose the operation: Add/Subtract: rewrite with a common denominator (LCD), add or subtract the numerators, and keep the denominator unchanged. Multiply: multiply numerators across and denominators across. Divide: multiply by the reciprocal of the second fraction (Keep-Change-Flip). Fraction of a Number: divide the quantity by the denominator and multiply by the numerator.
Example: 2/3 + 1/4 = 8/12 + 3/12 = 11/12. To find 3/4 of 80: (80 ÷ 4) × 3 = 60.
Our free online fraction calculator helps students, teachers, and parents calculate fraction equations and word problems with verified step-by-step solutions. Use the calculator to add, subtract, multiply, and divide proper fractions, improper fractions, and mixed numbers. The calculator automatically computes the Least Common Denominator (LCD), simplifies fractions to lowest terms using the Greatest Common Factor (GCF), and converts answers to mixed numbers and decimals.
Every fraction consists of two parts: the top number (numerator), which indicates the number of parts you have, and the bottom number (denominator), which indicates the total equal parts that make up a whole. Below is the step-by-step mathematical guide for each arithmetic operation:
Formula: a/c + b/c = (a + b)/c | a/b + c/d = (a·d + b·c) / (b·d)
Formula: a/c - b/c = (a - b)/c | a/b - c/d = (a·d - b·c) / (b·d)
Formula: (a/b) × (c/d) = (a × c) / (b × d)
Formula: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a × d) / (b × c)
Another common search intent for “calculate the fraction” is finding a fractional portion of a whole number (for example, finding 3/4 of 80 or 2/5 of 150):
Two Simple Steps:
1. Divide the quantity by the denominator: 80 ÷ 4 = 20 (this finds 1/4 of the number).
2. Multiply by the numerator: 20 × 3 = 60 (this gives 3/4 of the number).
When calculating fractions that involve mixed numbers (such as 2 3/4 or 1 1/2), always convert them into improper fractions before multiplying or dividing:
Problem: Calculate 2/3 + 1/4.
Step 1: Find the LCD of 3 and 4. The least common multiple is 12.
Step 2: Rewrite fractions with denominator 12: 2/3 = (2×4)/(3×4) = 8/12, and 1/4 = (1×3)/(4×3) = 3/12.
Step 3: Add numerators: 8/12 + 3/12 = 11/12.
Problem: Calculate 5/6 - 3/8.
Step 1: Find the LCD of 6 and 8. Multiples of 6: 6, 12, 18, 24. Multiples of 8: 8, 16, 24. The LCD is 24.
Step 2: Scale fractions: 5/6 = 20/24, and 3/8 = 9/24.
Step 3: Subtract numerators: (20 - 9)/24 = 11/24.
Problem: Calculate 4/9 × 3/8.
Step 1: Cross-cancel: 4 and 8 share a factor of 4 (4÷4 = 1, 8÷4 = 2). 3 and 9 share a factor of 3 (3÷3 = 1, 9÷3 = 3).
Step 2: Multiply simplified terms: (1 × 1) / (3 × 2) = 1/6.
Problem: Calculate 5/8 ÷ 3/4.
Step 1: Keep-Change-Flip: 5/8 × 4/3.
Step 2: Cross-cancel 4 and 8 by 4: (5 × 1) / (2 × 3) = 5/6.
Problem: Calculate the value and quantity of 5/8 of 200.
Step 1: Divide 200 by the denominator 8: 200 ÷ 8 = 25.
Step 2: Multiply by numerator 5: 25 × 5 = 125.
Problem: In algebra, solve the equation x/4 + 1/3 = 7/12 to find the unknown numerator value.
Step 1: Subtract the second fraction 1/3 from both sides: x/4 = 7/12 − 1/3.
Step 2: Rewrite with common denominator 12: 1/3 = 4/12. Then 7/12 − 4/12 = 3/12 = 1/4.
Step 3: Equate x/4 = 1/4, multiplying both sides by 4 to solve: x = 1.
Problem: A recipe has a ratio of 2 parts sugar to 3 parts flour. What fraction of the total mixture is sugar?
Step 1: Calculate the total ratio quantity: 2 + 3 = 5 total parts.
Step 2: Set up the part-over-whole fraction: 2/5 (or 0.40 / 40% of the mixture).
| Operation | Rule / Method | Formula | Worked Example |
|---|---|---|---|
| Addition (+) | Find LCD, add numerators | a/b + c/d = (ad + bc)/bd | 1/2 + 1/3 = 5/6 |
| Subtraction (−) | Find LCD, subtract numerators | a/b - c/d = (ad - bc)/bd | 3/4 - 1/3 = 5/12 |
| Multiplication (×) | Multiply numerators & denominators | (a/b) × (c/d) = (ac)/(bd) | 2/3 × 3/5 = 2/5 |
| Division (÷) | Keep-Change-Flip (reciprocal) | (a/b) ÷ (c/d) = (ad)/(bc) | 1/2 ÷ 1/4 = 2 |
| Fraction of a Number | Divide by bottom, multiply by top | (a/b) × N = (N ÷ b) × a | 3/4 of 40 = 30 |
| Simplification | Divide numerator & denominator by GCF | (a ÷ g) / (b ÷ g) | 12/16 = 3/4 (GCF=4) |
To calculate a fraction: For addition and subtraction, rewrite both fractions with a common denominator (LCD), add or subtract the numerators, and keep the denominator the same. For multiplication, multiply the numerators together and denominators together. For division, multiply by the reciprocal of the second fraction (Keep-Change-Flip). Finally, reduce the fraction to lowest terms.
No. Common denominators are only required for addition and subtraction. When multiplying fractions, multiply straight across (numerator × numerator and denominator × denominator). When dividing fractions, invert the second fraction and multiply.
To calculate a fraction of a number (such as 3/5 of 100), divide the whole number by the denominator (100 ÷ 5 = 20), then multiply the result by the numerator (20 × 3 = 60). Alternatively, multiply the number by the numerator and divide by the denominator: (100 × 3) ÷ 5 = 60.
Convert all mixed numbers into improper fractions before calculating. For example, to calculate 2 1/3 + 1 1/2: convert to 7/3 + 3/2. Find the LCD (6): 14/6 + 9/6 = 23/6. Convert the improper fraction back to a mixed number: 3 5/6.
Divide the numerator by the denominator using long division or a calculator. For example, 3/4 = 3 ÷ 4 = 0.75, and 1/3 = 1 ÷ 3 = 0.3333... (recurring decimal).
Division is the inverse operation of multiplication. Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal. For example, dividing by 1/2 is the same as asking how many halves fit into a quantity, which is identical to multiplying by 2.