Proportional Problems 2 – RECIPES Mathematics Proportional Problems 2 – RECIPES

Lesson Objectives The aim of this powerpoint is to help you… Use logic Solve proportional problems

Recipe – Worked Example On the right we have a recipe for making a carrot cake for 12 people. Q1) If we used 180g of flour, how much of all the other ingredients would we need? Q2) If we used 5 eggs, how much of all the other ingredients would we need? Q3) How much of each ingredient would we need to bake enough cake for 18 people? Carrot Cake (for 12 people) 360g Flour 240g Caster Sugar 180g Butter 2 Eggs 2 Carrots (grated) Soften the butter and mix in the sugar. Once the sugar has been enveloped by the butter, mix the eggs into the mixture followed by the carrots and then the flour. Transfer your mixture into a greased baking tin and bake in a pre-heated oven at 160°C for 25-35 minutes until golden brown and set.

Worked Example – whole numbers Sometimes when we are answering these problems, one of the values has been multiplied or divided by a whole number so all the other values need to be multiplied or divided by the same number. Let’s compare the information in Q1 with the information given in the original recipe. Original recipe needs: 360g of flour Q1 needs: 180g of flour What has ‘360’ been divided by to become ‘180’? ÷ 2

Worked Example – whole numbers Now divide all the original amounts of the other ingredients by this number too and we get our answer… Ans. Caster Sugar 240 ÷ 2  120g Butter 180 ÷ 2  90g Eggs 2 ÷ 2  1 Carrots 2 ÷ 2  1

Worked Example – using two steps Sometimes when we are answering these problems, you cannot tell what the original value has been multiplied by. You will need to solve it in two steps rather than one. First you need to DIVIDE everything to get to a unitary point. Then you multiply everything to get to the final answer. Let’s do this for Q2 which asked how much of all the other ingredients would be needed to mix with 5 eggs… What does this mean? A unit is 1 of something!

Worked Example – using two steps 2 eggs 1 egg 5 eggs What do we have to divide by to get from 2 to 1? What do we have to multiply by to get from 1 to 5? Apply both of these to all the other ingredients… Flour: 360g Caster Sugar: 240g Butter: 180g Carrots: 2 ÷ 2 × 5 ÷ 2  180 × 5  Ans. 900g ÷ 2  120 × 5  Ans. 600g ÷ 2  90 × 5  Ans. 450g ÷ 2  1 × 5  Ans. 5

Worked Example – final part Q3 asked how much of each ingredient we would need in order to bake a cake for 18 people. The original recipe was for 12 people. What do we need to divide by to work out the ingredients for 1 person? Now multiply this up for 18 people Flour: 360g Caster Sugar: 240g Butter: 180g Carrots: 2 ÷ 12  30 × 18  Ans. 540g ÷ 12  20 × 18  Ans. 360g ÷ 12  15 × 18  Ans. 270g ÷ 12  1/6 × 18  Ans. 3

Individual Practice Please work through the worksheet called: PP2.xlsx When most of you have finished this worksheet, you will be asked to pass your worksheet on to the person on your left – you will mark each others. Before I read out the correct answer, you will be asked to volunteer what YOU think (not necessarily what is on the sheet you are marking) the answer is and give your reason. Next… Best Buy Problems