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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.