A bracket in the equation

Four gift bags are packed alike. Each has some sweets and 3 chocolates. The four bags hold 44 things. Let s be the sweets in one bag. A bracket, as in 4(s + 3), groups what one bag holds. How many sweets are in one bag?

Two ways to work with a bracket

4(s + 3) means four bags. The bracket (s + 3) is one bag. Each bag has s sweets and 3 chocolates.

In Way 1, share both sides by 4. That gives s + 3 = 11, because 44 ÷ 4 = 11. Take 3 off both sides: s = 8, because 11 − 3 = 8.

In Way 2, count the sweets and the chocolates separately. Four bags hold 4s sweets and 12 chocolates, because 4 × 3 = 12. So 4s + 12 = 44. Take 12 off both sides: 4s = 32, because 44 − 12 = 32. Share by 4: s = 8, because 32 ÷ 4 = 8.

Both ways end at 8. Check in the first line: 4 × (8 + 3) = 44.

Rule: Share both sides by the number outside. It cannot be 0. Or multiply it into every part of the bracket. Either way the answer stays.