Divide fractions
How many times does a small fraction fit into another fraction? That's what division is all about! The secret is a simple trick: 'Keep, Change, Flip'. Master this, and you can divide any fraction.
Concept
Dividing by a fraction is the same as multiplying by its reciprocal. The easiest way to remember this is with the phrase "Keep, Change, Flip". **The "Keep, Change, Flip" Method** 1. **Keep** the first fraction the same. 2. **Change** the division sign to a multiplication sign. 3. **Flip** the second fraction upside down. This flipped fraction is called the **reciprocal**. 4. **Multiply** the two fractions straight across (top x top, bottom x bottom). 5. **Simplify** your answer if needed. **Example: 2/3 ÷ 1/4** 1. **Keep** 2/3. 2. **Change** ÷ to x. 3. **Flip** 1/4 to get 4/1. 4. **Multiply:** 2/3 x 4/1 = (2x4)/(3x1) = 8/3. 5. **Simplify** (as a mixed number): 8/3 = 2 2/3. **Visualizing Fraction Division** What does 2/3 ÷ 1/4 = 8/3 mean? It's asking: "How many 1/4-sized pieces can fit into a 2/3-sized piece?" The answer is 2 and 2/3 pieces. It's a tricky concept to visualize, which is why "Keep, Change, Flip" is such a useful tool. **Another Example: 3/4 ÷ 1/2** 1. **Keep** 3/4. 2. **Change** ÷ to x. 3. **Flip** 1/2 to 2/1. 4. **Multiply:** 3/4 x 2/1 = 6/4. 5. **Simplify:** 6/4 = 3/2 = 1 ½. **Cross-Canceling Before You Multiply** You can still use this shortcut! After you flip the second fraction, see if you can simplify any numerator with any denominator. **Example: 3/4 ÷ 9/10** 1. Rewrite as a multiplication problem: 3/4 x 10/9 2. Cross-cancel: * 3 and 9 can both be divided by 3 (become 1 and 3). * 4 and 10 can both be divided by 2 (become 2 and 5). 3. New problem: 1/2 x 5/3 4. Multiply: 1x5=5, 2x3=6. 5. Answer: 5/6. **Key Idea:** When you divide by a proper fraction (less than 1), your answer will be bigger than the number you started with. This is because you are figuring out how many small pieces can fit into it.
Try it
Practice: Divide fractions.