How to Use the Math Branching Method

The math branching method is valuable for solving math questions because it’s easier to use. Model drawing can be tedious and time-consuming. Therefore, the math branching method will be much easier to teach your child.

We use the math branching method when the question has keywords like “fraction of the remainder” or “fraction of a fraction.”

These keywords can be confusing for students, but this method shows a chronological flow of information, making the topic easier for students to understand.

In this tutorial, we’re using two examples from 2021 papers to show you how you can use the math branching method to solve “fraction of the remainder” or “fraction of a fraction” questions.

But before you read on, you might want to download this entire revision notes in PDF format to print it out for your child, or to read it later.

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Example 1

This question is taken from the CHIJ ST. Nicholas Girls’ School Prelim paper 2 and is worth 3 marks.

Identifying a fraction of a fraction

The keyword in this question is “ $\frac{2}{9}$ of the candles” because it indicates a fraction of a fraction. Since the candles make up $\frac{3}{8}$ of the total items, of the candles will effectively mean “ $\frac{2}{9}$ of $\frac{3}{8}$ ,” which is a fraction of a fraction.

The key concept of this question is that the fraction of the total number of items sold is $\frac{7}{12}$ because $\frac{5}{12}$ of the items were left in the end. So, 1 whole - $\frac{5}{12}$ would give us $\frac{7}{12}$ .

Once you’ve identified the type of question and understood the key concept, you can now use the math branching method to express the number of items sold as a fraction of the total.

Branching the provided information

When using the math branching method, the beginning part of the branch is always the original number of items.

The question does not state how many candles and pins were there at first, so you simply write “items” and start branching from there.

$\frac{3}{8}$ of the items were candles. Since 3 units were candles, then 5 units were pins.

If $\frac{2}{9}$ candles were sold, then $\frac{7}{9}$ were left.

Explanation: Since 2 out of 9 units were sold, that means 7 out of 9 were left.

From the information given, we know that 84 pins were sold. However, we do not know the actual number of pins left. So, we can leave that branch blank. The number of items sold represents $\frac{7}{12}$ of the total.

Express the number of candles sold as a fraction of the total number of items

The term “of” in “ $\frac{2}{9}$ of $\frac{3}{8}$ ” means “multiply (×).” So, you’ll need to multiply $\frac{2}{9}$ by $\frac{3}{8}$ , as shown in the worksheet:

This means that $\frac{1}{12}$ of the total + 84 is actually $\frac{7}{12}$ of the total.

From here, work out what fraction of the total makes up 84 items. This is calculated as follows:

The above calculation tells us that the 84 pins make up half of the total items. That means the total number of items is 84 × 2 = 168.

The question asked for the number of pins Reese makes at first.

Now, $\frac{5}{8}$ of the items were pins, and the total number of items is 168. That means of 168 items were pins. $\frac{5}{8}$ of 168 can be calculated as shown below:

This means Reese made 105 pins at first, and that is the final answer to this question.

Example 2

This question is taken from the Red Swastika School Prelim Paper 2 and is also worth 3 marks.

The keywords in the question are “ $\frac{1}{4}$ of the remainder,” meaning this is a fraction of a fraction. So, we can use the math branching method.

The key concept of this question is that since $\frac{1}{4}$ of the remainder are pears, then $\frac{3}{4}$ would be the number of apples.

The goal now is to use the math branching method to express the number of apples as a fraction of the total. From there, we can find the fraction of just the green apples.

Branching the provided information

Since $\frac{3}{8}$ of the total number of fruits were oranges, the remainder would be $\frac{5}{8}$ .

There’s a special case here because the apples are further split into green and red apples. There are twice as many green apples as red apples. Below, we’ve presented 2u as green apples and 1u as red apples.

Expressing the number of apples as a fraction of the total

To complete this step, we multiply the fractions involved.

There is no cancellation needed for this multiplication because both fractions are already in their simplest form.

The question says there are twice as many green apples as red apples. So, 2 units of green apples and 1 unit of red apples give us 3 units (3u) in total. This means 3u would be $\frac{15}{32}$ of the total.

The question asked for the fraction of the green apples, which make up 2 units. First, find 1 unit: 1 unit is $\frac{5}{32}$ of total.

So, 2 units would be $\frac{10}{32}$ of total.

This means $\frac{10}{32}$ of the total fruits are green apples. Remember that all fractions must be expressed in the simplest form, unless otherwise stated.

Our final fraction is $\frac{5}{16}$ , meaning $\frac{5}{16}$ of the total fruits are green apples. That is the final answer to this question.

I hope this tutorial was easy to follow and gives you a better idea of what how to use the math branching method.

If you have any questions or suggestions, leave them in the comments below. You can also watch the full Math Branching Method video tutorial here:

Before you go, you might want to download this entire revision notes in PDF format to print it out for your child, or to read it later.

This will be delivered to your email inbox.

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