Subtracting Fractions

Lesson Objective

In this lesson, we will learn about subtracting fractions and will be using some examples to explain how this subtraction works.

Study Tips

Tip #1

The lesson on adding fractions had already covered most of the basics needed. Feel free to go through that lesson first if you are not sure about it.

Math Video

Lesson Video

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Math Video Transcript

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In this lesson, we will learn about subtracting fractions.

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Now, the idea behind subtracting fraction is similar to adding fraction.

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To recall, let's add 3/5, with 1/5.

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Now, we know that, since the fractions have like denominators, we can just add the numerators together, and keep the denominator the same.

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Hence, we get 3 plus 1,/5.

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From this observation, we can see that, when we subtract the fractions, 3/5 with 1/5, we just need to subtract the numerators, and keep the denominators the same.

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Hence, we get 3 minus 1/5.

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Next, subtract 3 with 1. This gives 2. Finally, we get the fraction, 2/5.

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Alright, let's visually see how subtracting fractions work. We can see that, by subtracting these 3 green parts with this 1 green part, we get 2 green parts.  

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The 2 green parts represent the numerator 2, and all the 5 parts in this bar represent the denominator 5.

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Next example, let's subtract, 1/3, with 2/9.

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Notice that, these 2 fractions have unlike denominators. This means that, the size of these parts are not the same, as you can see here.

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Because of this, we can visually see that, we cannot subtract these two fractions as they are.

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Therefore, the only way to subtract these fractions, is to make all the parts to have the same size. This means that, these fractions must have like denominators.

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To do so, we need to use Equivalent Fractions.

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Now, using Equivalent Fractions, we can change this denominator to 9, by multiplying both the numerator and denominator of this fraction with 3.

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This gives the fraction, 3/9.

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Now, these fractions have like denominators. This means that, all the parts will have the same size. As you can see right here.

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With this, we can now subtract these two fractions just like the previous example. By doing so, we get, 3 minus 2/9.

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Minus 3 with 2. This gives 1. Finally, we have the fraction, 1/9.

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Next example, let's subtract, 1/3 with 1 1/2.

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Notice that, this fraction is a mixed fraction. To minimize mistakes, it is advisable to convert it to an improper fraction.

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Note that, when doing the conversion, we just need to focus on this mixed fraction, and ignore this minus sign. Now, we multiply 2 with 1. This gives 2.

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Next, we add 2 with 1. This gives 3, which becomes the improper fraction's numerator. Now, we have the improper fraction, 3/2.

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Notice that, we cannot subtract these 2 fractions because they have unlike denominators.

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Therefore, the only way to subtract these fractions, is to make them to have like denominators. We can do so, by using equivalent fractions.

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Here's how. We can make the denominators the same by multiplying the numerator and denominator of 1/3, with the other fraction's denominator 2, and by multiplying the numerator and denominator of 3/2, with the other fraction's denominator 3.

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Let's do so. Multiplying 1/3 with 2, and multiplying 3/2 with 3. This gives the equivalent fractions, 2/6, and 9/6 respectively. The denominators are now the same.

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Now, we subtract these two fractions. This gives 2 minus 9/6.  

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Subtracting 2 with 9, gives negative 7.

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Notice the negative sign here? We can rewrite it this way so that it looks neater. With this, we have the fraction, negative 7/6.

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Notice that, negative 7/6 is an improper fraction. So, rather than leaving the answer like this, it is recommended to change it to a mixed fraction, using long division.

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Now, when doing the conversion, we just need to focus on this fraction, and ignore this sign.

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Let's start. 7/6 is the same as 7 divides 6. Now, this division gives the quotient as 1. This quotient is actually the whole number for the mixed fraction.

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Next, we multiply 1 with 6. This gives 6. 7 minus 6 gives the remainder as 1.

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This remainder, 1, is actually the mixed fraction's numerator.

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So here, we have the final answer as, negative 1 1/6.

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That is all for this lesson. Try out the practice question to test your understanding.

Practice Questions & More

Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on subtracting fractions or pick your choice of question below.

Question 1 on subtracting fractions with like denominators
Question 2 on subtracting fractions with unlike denominators

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