# Percentages Problems in Two Steps

*Keywords:*

AO elaboration and other teaching resources

Estimate and find percentages of whole number and decimal amounts.

Number Framework Stage 8

Students find mark-up problems easier to do by calculating the amount of mark-up as the first step, then adding this to the original as the second step. This delays the problem of percentages over 100%.

### Using Number Properties

Problem: “Matt buys shirts to sell in his clothing store. He pays $24.85 for each shirt. What does he charge his customers?”

Discuss why the mark-up is 0.79 x 24.85 and write this on the board. *(Answer: 79% of 24.85 = 0.79 *x *24.85.)*

Why should this answer not be rounded yet? *(Answer: As a general rule, calculations should be rounded after the last calculation **to avoid errors.)*

Discuss why the price to the customer is 19.6315 + 24.85 and write it on the board. Discuss how to enter this on a calculator. *(Answer: 19.6315 is already showing on the calculator so adding 24.85 does not **require re-entering 19.6315.)*

Discuss rounding the answer sensibly. *(Answer: 44.4815 = 44.48 to the nearest cent – fractions of a cent are not allowed.)*

Problem: “At the vegetable shop, the owner Mrs Brown buys 450 tomatoes for resale. Before they can be sold, 14% of the tomatoes spoil. How many tomatoes does Mrs Brown sell?”

Discuss why 0.14 x 450 is the number of spoiled tomatoes and why Mrs Brown sells 387 tomatoes. *(Answer: 0.14 *x *450 = 63, 450 – 63 = 387.)*

Examples : Worksheet (Material Master 8–20).

### Understanding Number Properties:

Make up a mark-up or a discount problem and solve it. Explain the steps you took.