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Fractions

Mixed Number Calculator

Add, subtract, multiply and divide mixed numbers with every step shown — converting to improper fractions, finding common denominators, and converting the answer back. Also converts between mixed numbers and improper fractions.

Mixed number calculator

Number A
+
Number B

Enter the whole number and fraction parts separately. Use 0 for the whole number if you have a plain fraction.

Step by step calculations

Key Terms & Abbreviations

LCD Lowest Common Denominator The smallest common multiple of the bottom numbers, used to add or subtract fractions.
LCM Lowest Common Multiple The smallest positive integer that is divisible by both denominators.
GCD / HCF Greatest Common Divisor The largest factor that divides top and bottom numbers, used to simplify fractions.
KCF Keep, Change, Flip The division rule: Keep 1st fraction, Change ÷ to ×, Flip 2nd fraction.

Mixed Number Calculator Explained

Core concepts, classroom applications, and plain-English explanations for all audiences.

Where mixed numbers actually appear

A recipe needs 2½ cups of flour — not 2 cups, not 3 cups. A carpenter measures a shelf at 3⅜ inches. You've been driving for 1¾ hours. Mixed numbers appear whenever a quantity falls between two whole numbers and a fraction is the natural way to express the remainder.

Worked example

"Add 1½ + 2¾."

Step 1: Convert to improper fractions

1½ = (1×2 + 1)/2 = 3/2

2¾ = (2×4 + 3)/4 = 11/4

Step 2: Common denominator (LCD = 4)

3/2 = 6/4

Step 3: Add: 6/4 + 11/4 = 17/4

Step 4: Convert back: 17 ÷ 4 = 4 remainder 1

Result: 4¼

Always convert to improper fractions first — adding whole parts and fraction parts separately can go wrong when you need to carry.

Common mistake to avoid

  • ✗ Adding whole parts and fraction parts separately: 1½ + 2¾ ≠ 3 + (½ + ¾). The fraction parts still need a common denominator — and if they sum to more than 1, you'd need to carry into the whole number anyway. Converting to improper fractions first sidesteps all of this.
Good to know

Working with mixed numbers

⇄
Mixed numbers and improper fractions
A mixed number (e.g. 2⅓) combines a whole part and a fraction. An improper fraction (e.g. 7/3) has a numerator larger than its denominator — they represent the same value. Converting to improper fractions is the key step before doing any operation.
2 1/3 → (2×3)+1 = 7 → 7/3

7/3 → 7÷3 = 2 rem 1 → 2 1/3
+−
Adding and subtracting
Convert both to improper fractions. Find the Lowest Common Denominator (LCD) — the smallest number both denominators divide into. Rewrite both fractions over the LCD, then add or subtract the numerators. Simplify and convert the result back to a mixed number.
1 1/2 + 2 3/4
= 3/2 + 11/4
LCD(2,4) = 4
= 6/4 + 11/4 = 17/4
= 4 1/4
×
Multiplying
Convert both to improper fractions, then multiply straight across: numerator × numerator over denominator × denominator. Simplify the result. You can also simplify diagonally before multiplying (cross-cancelling) to keep the numbers smaller — the calculator shows both approaches.
2 1/2 × 1 3/4
= 5/2 × 7/4
= (5×7) / (2×4)
= 35/8 = 4 3/8
÷
Dividing — keep, change, flip
Convert to improper fractions. Then use "Keep, Change, Flip" (KCF): keep the first fraction, change ÷ to ×, flip the second fraction (take its reciprocal). Multiply across, simplify and convert back. Dividing by a fraction is the same as multiplying by its reciprocal.
3 1/2 ÷ 1 1/4
= 7/2 ÷ 5/4
Keep: 7/2 Change: × Flip: 4/5
= 7/2 × 4/5 = 28/10
= 14/5 = 2 4/5