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Doubling a recipe

Ratio, rates and money · level 1, lesson 3 of 5

A question to start

Grandpa's banana cake needs 2 cups of flour and 1 cup of sugar. Today it is a big birthday party, so you want to bake 2 cakes that taste just like Grandpa's.

Your friend says: "Easy! Use 4 cups of flour. And keep 1 cup of sugar, because sugar is not flour."

Will your friend's cakes taste the same as Grandpa's? Or will something go wrong?

Think about it for a moment, then read on. By the end of this lesson you will know what to do with every ingredient when you make more, and you will be able to explain why to your friend.

The idea

What a recipe is

A recipe is a list of what goes into a food, and how much of each. The things on the list are called ingredients. Here is a simple recipe for one small cake.

Ingredient For 1 cake
Flour 2 cups
Sugar 1 cup
Eggs 3 eggs
Milk 1 cup

A recipe is a "for every" list. It says: for every cake, use 2 cups of flour, 1 cup of sugar, 3 eggs and 1 cup of milk. One cake is one group.

Doubling means making the recipe twice

To double something means to have two of it. To double a recipe means to make the recipe twice.

Imagine two bowls side by side. Into each bowl, you put one full recipe.

bowl 1: one recipebowl 2: one recipe together: 4 flour, 2 sugar, 6 eggs, 2 milk (orange = flour, blue = sugar, green = eggs, white = milk)

Now pour both bowls into one giant bowl. What is in the giant bowl?

  • Flour: 2 cups and 2 cups make 4 cups.
  • Sugar: 1 cup and 1 cup make 2 cups.
  • Eggs: 3 eggs and 3 eggs make 6 eggs.
  • Milk: 1 cup and 1 cup make 2 cups.
Ingredient For 1 cake For 2 cakes
Flour 2 cups 4 cups
Sugar 1 cup 2 cups
Eggs 3 eggs 6 eggs
Milk 1 cup 2 cups

Every ingredient doubled. Not just the flour. Every single one.

Why every ingredient must double

Here is the reason, and it is a good one.

Each bowl on its own makes a perfect cake, because each bowl has exactly Grandpa's recipe. When you pour the two bowls together, nothing new gets added and nothing gets taken away. The giant bowl is just two perfect cakes' worth of batter. Cut the giant bowl's batter into two cake pans, and each pan gets a perfect cake.

So the doubled recipe must be exactly what two bowls hold. And two bowls hold double of everything.

What goes wrong if you forget one

Now back to your friend, who used 4 cups of flour but only 1 cup of sugar.

Think of the giant bowl again. To make it match two of Grandpa's bowls, it needs 2 cups of sugar. Your friend's bowl only has 1 cup. So the sugar is spread over twice as much batter. Each bite has only half the sugar it should have. The cakes will taste much less sweet. They will not taste like Grandpa's.

The same thing happens with anything you forget to double:

  • Forget to double the eggs, and the cake may not hold together.
  • Forget to double the milk, and the batter will be too dry and thick.

The ingredients are a team. When one grows, they all have to grow together.

Same taste, bigger amount

When two mixtures taste the same, we say they are mixed in the same way. Double the recipe and the cake tastes the same, there is just more of it. Later in this topic you will learn the grown-up word for "mixed in the same way". It is ratio. But you already know the idea: keep the groups the same and just make more groups.

Tripling and more

You can make the recipe 3 times too. That is called tripling. Use three bowls, or count by groups like in the lesson "For every".

Ingredient 1 cake 2 cakes 3 cakes
Flour (cups) 2 4 6
Sugar (cups) 1 2 3
Eggs 3 6 9
Milk (cups) 1 2 3

Look down the flour row: 2, 4, 6, counting by twos. The eggs row: 3, 6, 9, counting by threes. Every row counts by its own number, the number for one cake.

Worked examples

Example 1. Pancakes for two batches. One batch of pancakes needs 1 cup of flour, 1 egg and 2 cups of milk. How much do you need for 2 batches?

  1. Two batches means making the recipe twice.
  2. Flour: 1 cup and 1 cup make 2 cups.
  3. Eggs: 1 egg and 1 egg make 2 eggs.
  4. Milk: 2 cups and 2 cups make 4 cups.
  5. Check: did every ingredient double? 1 became 2, 1 became 2, 2 became 4. Yes.

Example 2. Fruit salad for three. One bowl of fruit salad has 2 apples, 1 banana and 5 strawberries. How much fruit do you need for 3 bowls?

  1. Three bowls means the recipe 3 times. Count by groups for each fruit.
  2. Apples: 2, 4, 6. So 6 apples.
  3. Bananas: 1, 2, 3. So 3 bananas.
  4. Strawberries: 5, 10, 15. So 15 strawberries.

Example 3. Spotting the mistake. Lily wants to double this playdough recipe: 2 cups of flour, 1 cup of salt, 1 cup of water. She uses 4 cups of flour, 2 cups of salt and 1 cup of water. What will happen?

  1. Doubling means every ingredient doubles.
  2. Flour: 2 doubles to 4. Lily used 4. Good.
  3. Salt: 1 doubles to 2. Lily used 2. Good.
  4. Water: 1 doubles to 2. Lily used only 1. Not good.
  5. So Lily's playdough has only half the water it needs. It will be too dry and crumbly. She should add 1 more cup of water.

Example 4. Going back. Dad made a double batch of cookies and used 6 cups of oats. How many cups of oats are in the normal recipe?

  1. A double batch is two normal batches put together.
  2. So 6 cups of oats is two equal amounts. Share 6 into 2 equal parts: 3 and 3.
  3. The normal recipe uses 3 cups of oats.
  4. Check: 3 and 3 make 6. Yes.

Try it

  1. Juice for one glass: 1 scoop of powder and 1 glass of water. How much for 2 glasses?
  2. One sandwich needs 2 slices of bread and 1 slice of cheese. How much bread and cheese for 2 sandwiches?
  3. One smoothie needs 1 banana and 3 strawberries. How many bananas and strawberries for 3 smoothies?
  4. A bird feeder mix uses 2 cups of seeds and 1 cup of nuts. Ben doubles it and uses 4 cups of seeds and 4 cups of nuts. Is that right? What will the mix be like?
  5. A cake recipe uses 3 eggs. Mum made a double batch. How many eggs did she use?
  6. A double batch of muffins used 4 cups of flour. How much flour does one batch use?
  7. Mia says: "To double the recipe, I add 1 more of everything." The recipe is 2 cups of flour and 1 cup of milk. Use her way and the right way. Do they give the same answer?
Answers
  1. 2 scoops and 2 glasses of water. Make the recipe twice: 1 and 1 make 2, for each ingredient.
  2. 4 slices of bread and 2 slices of cheese. Bread: 2 and 2 make 4. Cheese: 1 and 1 make 2.
  3. 3 bananas and 9 strawberries. Bananas: 1, 2, 3. Strawberries: count by threes, 3, 6, 9.
  4. No. The seeds doubled correctly (2 to 4). But the nuts should double from 1 cup to 2 cups, and Ben used 4 cups. That is too many nuts: the mix will be much more nutty than the real one.
  5. 6 eggs. A double batch is the recipe twice: 3 and 3 make 6.
  6. 2 cups. The double batch is two equal batches. Share 4 into 2 equal parts: 2 and 2.
  7. No, they are different. Mia's way: flour 2 and 1 more is 3 cups, milk 1 and 1 more is 2 cups. The right way: flour 2 and 2 make 4 cups, milk 1 and 1 make 2 cups. The milk happens to come out right, but the flour does not. Adding 1 to everything is not doubling. Doubling means adding the whole amount again.

Common mistake

Doubling only the "main" ingredient. People often double the flour, the biggest amount, and forget the rest. Every ingredient must double, even the little ones like a spoon of salt.

Adding the same amount to everything. "One more cup of everything" is not doubling. To double, each ingredient gets its own amount again: 2 cups of flour gets 2 more, 1 cup of milk gets 1 more.

Where it leads