Dividing Fractions, Set 4
Dividing fractions follows a clear process: when you divide by a fraction, you multiply by its reciprocal (that's just a fancy way of saying you flip the second fraction upside down).
The rule for dividing fractions can be expressed as: A/B ÷ C/D = A/B × D/C.
Here's the step-by-step process for dividing fractions:
- Keep the first fraction as it is.
- Change the division sign to multiplication.
- Take the reciprocal of the second fraction (flip it upside down).
- Multiply the fractions.
- Simplify if possible.
Let's look at some examples:
Example 1: 3/4 ÷ 1/2
- First, we keep 3/4 as it is.
- Then we change division to multiplication and flip the second fraction: 3/4 × 2/1
- Now we multiply: (3 × 2)/(4 × 1) = 6/4 = 3/2 or 1½
Example 2: 5/6 ÷ 2/3
- Following our steps: 5/6 × 3/2
- Multiplying: (5 × 3)/(6 × 2) = 15/12 = 5/4 or 1¼
Example 3 (with a mixed number): 2¾ ÷ 1/3
- First, we need to convert the mixed number to an improper fraction: 2¾ = 11/4
- Now we apply our division rule: 11/4 ÷ 1/3 = 11/4 × 3/1
- Multiplying: (11 × 3)/(4 × 1) = 33/4 = 8¼
The reason this method works is because dividing by a number is the same as multiplying by its reciprocal. When you divide by 2, it's the same as multiplying by 1/2. Similarly, when you divide by 1/2, it's the same as multiplying by 2. This is why flipping the second fraction works so well for division.