Fractions and Decimals • Topic 3 of 7

Mixed Numbers

A mixed number combines a whole number and a proper fraction, such as 2 3/4, which means 2 + 3/4. Mixed numbers are easy to read and estimate but awkward to compute with, so for multiplication, division and many additions you first convert to an improper fraction. To convert, multiply the whole number by the denominator, add the numerator, and keep the same denominator. Going back, divide the numerator by the denominator: the quotient is the whole part and the remainder over the denominator is the fraction. Always simplify the fractional part at the end.

✅ Solved examples

1. Add 1 1/4 + 2 1/4.
Add the whole parts (1 + 2 = 3) and the fractions (1/4 + 1/4 = 2/4 = 1/2), giving 3 1/2.
2. Convert 4 2/3 to an improper fraction.
4·3 + 2 = 14, over 3, so 14/3.
3. Convert 19/6 to a mixed number.
19 ÷ 6 = 3 remainder 1, so 3 1/6.
4. Subtract 3 3/5 − 1 1/5.
Whole parts: 3 − 1 = 2; fractions: 3/5 − 1/5 = 2/5. Result 2 2/5.

✏️ Practice — try these, take hints as needed

1. Add 2 1/3 + 1 1/3.
Add the whole numbers.
Add the fractions: 1/3 + 1/3 = 2/3.
Combine.
3 2/3.
2. Convert 5 3/4 to an improper fraction.
5 · 4 = 20.
Add 3.
Put 23 over 4.
23/4.
3. Convert 22/5 to a mixed number.
22 ÷ 5 = 4 remainder 2.
Whole part 4.
Remainder over 5.
4 2/5.
4. Subtract 4 5/8 − 2 1/8.
Whole parts: 4 − 2 = 2.
Fractions: 5/8 − 1/8 = 4/8.
Simplify 4/8.
2 1/2.
5. Multiply 1 1/2 × 2 (convert first).
1 1/2 = 3/2.
Multiply 3/2 by 2.
6/2 = 3.
3.

📝 Topic test — 8 questions

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