Dividing a fraction by a whole number

Three fifths of a chocolate bar is shared equally among 2 friends. How much of a bar does each friend get? Let's draw it. Here's a whole chocolate bar. The bottom number is 5, so it's cut into 5 equal parts. 3 of those parts are shaded. That's three fifths of a bar. We're sharing it among 2 friends. Dividing by 2 is the same as multiplying by one half. So we cut each part into 2, straight across the bar. That doubles the bottom number. The 5 parts become 10, and the top number stays 3. That one cut has split the shaded part into 2 equal rows, one for each friend. Each friend gets one row. That's 3 pieces out of 10. So three fifths shared among 2 is three tenths of a bar.

Your turn. Here's two thirds of a cereal bar, shared equally among 4 friends. How much of a cereal bar does each friend get? Try it first. Pause if you like. Let's finish it. Dividing by 4 is the same as multiplying by one quarter. So we cut each part into 4. That multiplies the bottom number by 4. The 3 parts become 12, and the top stays 2. Each friend gets one row. That's 2 pieces out of 12. On the expression, the top 2 and the bottom 4 share a factor of 2. So cross both out, and write 1 above the 2 and 2 below the 4. 1 times 1 on top, and 3 times 2 on the bottom, so each friend gets one sixth of a cereal bar. So, here's the rule. To divide a fraction by a whole number, multiply the bottom number by it. The top number stays the same. Dividing by a whole number is the same as multiplying by one over that number.