🥞 Scaling Up the Recipe: Ratio and Proportion

Pandi has found a lovely pancake recipe for 2 people. But 6 people are coming this evening! How do we scale the recipe up and keep the taste the same? The answer: ratio and proportion.

The recipe for 2 people is: 2 eggs, 1 cup of flour, 1 cup of milk. Let’s compare the eggs with the flour: 2 eggs for every 1 cup of flour. This is called a ratio, and we write it as 2 : 1.

Now let’s make a ratio table. If we double the number of people, 4 people need 4 eggs and 2 cups of flour. If we treble it, 6 people need 6 eggs and 3 cups of flour. We multiplied everything by the same number, so 2 : 1, 4 : 2 and 6 : 3 are the same ratio.

Paint works the same way. 2 drops of blue and 3 drops of yellow make a green. If we mix 4 blue with 6 yellow, the ratio is the same, so we get the same green. But if we mix 4 blue with 3 yellow, the ratio changes and the colour turns bluer.

Let’s show the number of people and the amount of flour on a graph. 0 people need 0 cups, 2 people need 1, 4 people need 2, 6 people need 3 cups. The points lie on a straight line, and the line goes through zero. The graph of two things in direct proportion always looks like this.

Now let’s go shopping. 2 kilograms of apples cost 36 dollars, and 5 kilograms cost 80 dollars. Which is cheaper? We look at the price of 1 kilogram in each bag, the unit price. 36 divided by 2 is 18 dollars a kilogram. 80 divided by 5 is 16 dollars a kilogram. The big bag is cheaper per kilogram!

Not everything is in proportion! Mina is 100 centimetres tall at age 4. When her age doubled to 8, her height did not become 200. It was 130. At 12 she is 150. Age and height are not in proportion.

Now let’s sort the cards. Apple weight and money paid: when one doubles, the other doubles too, so they are in proportion. People and flour needed: in proportion. Age and height: not in proportion.

Summary: A ratio compares two numbers. In a ratio table, we multiply every column by the same number. The graph of direct proportion is a straight line through zero. The unit price tells us which is cheaper. Some things, like age and height, are not in proportion. Now try it in Ratio Kitchen!