math · 34 minutes · Official OETT Aligned
Fractions
Work with parts of a whole
What to know
- numerator: top number
- denominator: bottom number
- matching bottom numbers
- flipping a fraction to divide
Before adding or subtracting fractions, make sure the pieces are the same size.
The core rule
To add or subtract, match the bottom numbers. To multiply, multiply across. To divide, flip the second fraction and multiply.
The top number, or numerator, tells how many parts you have. The bottom number, or denominator, tells how many equal parts make a whole. For 3/4 + 1/8, change 3/4 to 6/8, then add to get 7/8. Flipping a fraction gives its reciprocal: the flipped fraction 8/3 is 8/3.
Worked examples
Example 1: easy
3/4 + 1/8 = 7/8.
- Convert 3/4 to eighths by multiplying top and bottom numbers by 2: 6/8.
- Add equal parts: 6/8 + 1/8 = 7/8.
Both fractions now count the same size pieces: eighths.
Example 2: medium
2/3 × 9/10 = 3/5.
- Multiply top and bottom numbers: (2 × 9)/(3 × 10) = 18/30.
- Reduce by 6 to obtain 3/5.
Dividing the top and bottom by the same number keeps the value unchanged.
Example 3: hard
2 1/4 ÷ 3/8 = 6.
- Convert 2 1/4 to 9/4, then multiply by the flipped fraction 8/3: 9/4 × 8/3.
- Cancel 8/4 = 2 and 9/3 = 3, giving 3 × 2 = 6.
To divide by a fraction, flip the second fraction and multiply.
Common mistakes
Add the top numbers and the bottom numbers.
First make the bottom numbers match. Then add only the top numbers and keep the common bottom number.
Put it into practice
Use guided explanations, check your answers, and try a new variation.