There are many situations, such as with recipes, where quantities need to be scaled up or down.

- If two quantities are in proportion, then
**multiplying**one by a**scale factor**means the other will be**multiplied**by the**same scale factor**

- E.g. if 4 muffins require 100 grams of flour then 12 muffins require 300 grams of flour (by multiplying both quantities by a scale factor of 3)
- The working can also be written in equivalent
**ratios**- 4 muffins : 100 grams becomes 12 muffins : 300 grams

- The unitary method is when the proportion relating to just 1 unit of a quantity is found. This can be used to find any proportional amount
- This is done when two quantities in proportion are
**divided**by the same**scale factor**

- This is helpful to find
**1 unit**of a quantity - E.g. if 6 identical bicycles weigh 108 kg, then 1 bicycle weighs 108 ÷ 6 = 18 kg (by dividing both quantities by a scale factor of 6)
- This means 11 bicycles weigh 11 × 18 = 198 kg etc

- This is helpful to find

- If two quantities are
**inversely proportional**, then as one increases the other**decreases** **Multiplying**one quantity by a**scale factor**will**divide**the other quantity by the**same scale factor**(and vice versa)- E.g. if 200 builders can build a stadium in 12 months, then
**doubling**the number of builders to 400 will**halve**the time it takes to 6 months

Read the question to see if your answer needs to be a whole number

- For example, the number of servings in a recipe should be a whole number
- You might have to decide which way to round when working with actual objects
- this might not always be the same way that you would normally round a number
- e.g. if you end up needing 1.2 bags of flour you'd have to round up and buy 2 bags to have enough!
- or if you have enough flour to make 12.9 pancakes, that's still only enough to make 12 whole pancakes

The ingredients for 12 cookies are as follows:

90 g butter

130 g chocolate

180 g flour

150 g sugar

1 egg

(a) If Tanya makes 50 cookies, how much sugar does she need?

12 cookies require 150 g of sugar

Find how much sugar is needed to make 1 cookie (by dividing 150 by 12)

150 ÷ 12 = 12.5 grams of sugar for 1 cookie

Find how much sugar is needed for 50 cookies (by multiplying 12.5 by 50)

12.5 × 50 = 625

**625 grams of sugar**

(b) If Giles buys a 500 gram bag of flour to make cookies, how many whole cookies can he make?

__Method 1__

12 cookies require 180 g of flour

Find out how much flour is in 1 cookie (by dividing 180 by 12)

180 ÷ 12 = 15 grams of flour for 1 cookie

Find how many lots of 15 grams are in 500 grams of flour (by dividing 500 by 15)

500 ÷ 15 = 33.33… cookies

Write down how many whole cookies can be made

There is not enough for 34 whole cookies

**33 cookies**

__Method 2__

12 cookies have 180 grams of flour

Find how many lots of 12 cookies the 500-gram bag of flour contains (by dividing 500 by 180)

500 ÷ 180 = 2.77… lots of 12 cookies

Calculate how many cookies are in 2.77… lots of 12 cookies (by multiplying 2.77… by 12)

2.77… × 12 = 33.33… cookies

Write down how many whole cookies can be made

There is not enough for 34 whole cookies

**33 cookies**

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