Divide whole numbers by unit fractions
When you divide a whole number by a fraction, you're asking: 'How many pieces of this fraction can I fit into the whole?' The answer might surprise you—it gets bigger! 😮
Concept
Dividing a whole number by a unit fraction is asking a simple question: "How many of these fractional pieces fit into the whole item(s)?" **Understanding the Question** **Problem: 4 ÷ 1/3** * This does NOT mean "split 4 into 3 parts." * It DOES mean: "How many **1/3-sized pieces** can you get from **4 wholes**?" **Visualizing the Answer** 1. Imagine you have **4 whole pizzas**. 2. You slice each pizza into **thirds** (1/3s). 3. How many slices do you have in total? * Pizza 1 gives you 3 slices. * Pizza 2 gives you 3 slices. * Pizza 3 gives you 3 slices. * Pizza 4 gives you 3 slices. * Total slices = 4 x 3 = 12. So, **4 ÷ 1/3 = 12**. **The "Keep, Change, Flip" Method** This is the famous shortcut for dividing fractions: 1. **Keep** the first number (the whole number). 2. **Change** the division sign to a multiplication sign. 3. **Flip** the second number (the fraction). This is called finding the reciprocal. **Example: 6 ÷ 1/4** 1. **Keep** the 6. (Write it as 6/1) 2. **Change** ÷ to x. 3. **Flip** 1/4 to become 4/1. * New problem: **6/1 x 4/1** * Multiply straight across: 6 x 4 = 24, and 1 x 1 = 1. * Answer: 24/1 = **24**. Does this make sense? Yes! If you have 6 candy bars and cut each one into fourths, you will have 24 pieces. **Key Idea:** Dividing by a fraction is the same as multiplying by its reciprocal. This is why dividing by a small fraction gives you a big answer! You are seeing how many small pieces fit into a big item.
Try it
Practice dividing by unit fractions! **Conceptual Questions:** 1. How many 1/2-sized pieces are in 1 whole? 2. How many 1/4-sized pieces are in 1 whole? 3. How many 1/3-sized pieces are in 2 wholes? **Use "Keep, Change, Flip":** 4. 5 ÷ 1/2 = ? 5. 3 ÷ 1/4 = ? 6. 7 ÷ 1/3 = ? 7. 10 ÷ 1/5 = ? **Word Problems:** 8. A 5-mile race has water stops every 1/2 mile. How many water stops are there in total? 9. You have 3 large candy bars. You cut them into pieces that are each 1/4 of a bar. How many pieces do you have? 10. A carpenter has a board that is 8 feet long. He needs to cut it into sections that are 1/3 of a foot long. How many sections can he cut? **Challenge Problems:** 11. 12 ÷ 1/6 = ? 12. If 15 ÷ 1/x = 45, what is x? 13. Which is greater: 10 ÷ 1/2 or 10 x 2? Why?