Increasing ratios

## Increasing

The price of a Science book increased from Sh 300 to Sh 320.

The ratio of the new price to the old is 320:300 = 32:30

Therefore, the new price has increased in the ratio 32:30 which should be of the 32/30 old price.

## Decreasing

The price of a loaf of bread dropped from Sh 30 to Sh 25, then the ratio of the new price to old price is 25:30 = 5:6

This shows that the price of a loaf of bread decreased in the ratio 5:6

The new price should be expressed as 5/6 of the old price.

The Recipe we have made serves four people.

But what if we have 5 people coming over for a curry dinner?

How can we adjust our recipe for 4 people, so that it can feed 5 people?

We need to use the Mathematics of Ratios !

We need to increase our Recipe in the Ratio of 5 : 4

This makes perfect sense, because Ratios are often used for comparing.

The Ratio of 5 : 4 means we are now feeding 5 people as compared to the recipe’s 4 people.

Remembering that all Ratios can be written as Fractions, we can increase our Recipe by 5 : 4 by

simply multiplying all of the Ingredients by 5/4 or one and one quarter.

Let’s consider the Chicken Curry Spice Mix Quantities.

For Four People we need the following Spice amounts

1 heaped teaspoon of fennel seeds

2 teaspoons of crushed ground black peppercorns

1 heaped teaspoon of dried red chilli flakes

1/4 heaped teaspoon of ground cardamom seeds

1 flat teaspoon of ground Nutmeg

For Five People we need to multiply all these amounts by 5 / 4

5/4 x 1 = One and one quarter heaped teaspoon of fennel seeds

5/4 x 2 = 10/4 = two and a half teaspoons of black peppercorns

5/4 x 1 = One and one quarter heaped teaspoon of chilli flakes

5/4 x 1/4 = 5/16 heaped teaspoon of ground cardamom seeds **

5/4 x 1 = One and one quarter flat teaspoon of ground Nutmeg

** 5/16 teaspoon of ground cardamom seeds is going to be very hard to measure, and is only 1/16 of a teaspoon extra compared to the original recipe. For this reason we would probably just leave the Cardamom as 1 heaped quarter teapsoon.

As well as the ratio mathematics, we also need to use some common sense when scaling up and down recipes!

So Problem Solved! Five people will be able to come over for dinner and enjoy our delicious chicken curry.

Note that we can also Decrease Ratios.

For example if only three people were coming to dinner, we could decrease down our recipe in the Ratio 3 : 4 by multiply all our recipe quantities by 3/4.

Look at the worked example below on increasing a ratio

Look at the worked example below on decreasing a ratio

### Sources

• 37945885-7644-4e56-8c94-353d17fd5f56 by elimu used under CC_BY-SA
• 21c037c4-6183-4fbd-83a0-0387abf2b877 by elimu used under CC_BY-SA
• reduce_and_increase_ratio by Unknown used under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
• Ratio_img3 by elimu used under CC_BY-SA
• e565097a-8dcc-44d9-ba65-7aad9788d461 by elimu used under CC_BY-SA