In this lesson, we will learn about subtracting fractions and will be using some examples to explain how this subtraction works.
About This Lesson
The basic ideas behind subtracting fractions are the same as
. So, once you know how to add fractions, it is very easy to subtract fractions.
In this lesson, we will learn how to subtract two fractions that involve:
proper fractions with like denominators
proper fractions with unlike denominators
proper and mixed fractions with unlike denominators
below will explain more.
The lesson on
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 Transcript
00:00:03.030 In this lesson, we will learn about subtracting fractions. 00:00:07.110 Now, the idea behind subtracting fraction is similar to adding fraction. 00:00:13.070 To recall, let's add 3/5, with 1/5. 00:00:18.180 Now, we know that, since the fractions have like denominators, we can just add the numerators together, and keep the denominator the same. 00:00:28.200 Hence, we get 3 plus 1,/5. 00:00:33.150 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. 00:00:47.110 Hence, we get 3 minus 1/5. 00:00:52.110 Next, subtract 3 with 1. This gives 2. Finally, we get the fraction, 2/5. 00:01:02.240 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. 00:01:15.220 The 2 green parts represent the numerator 2, and all the 5 parts in this bar represent the denominator 5. 00:01:26.110 Next example, let's subtract, 1/3, with 2/9. 00:01:32.070 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. 00:01:44.060 Because of this, we can visually see that, we cannot subtract these two fractions as they are. 00:01:51.120 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. 00:02:03.090 To do so, we need to use Equivalent Fractions. 00:02:08.080 Now, using Equivalent Fractions, we can change this denominator to 9, by multiplying both the numerator and denominator of this fraction with 3. 00:02:18.090 This gives the fraction, 3/9. 00:02:22.230 Now, these fractions have like denominators. This means that, all the parts will have the same size. As you can see right here. 00:02:34.240 With this, we can now subtract these two fractions just like the previous example. By doing so, we get, 3 minus 2/9. 00:02:46.240 Minus 3 with 2. This gives 1. Finally, we have the fraction, 1/9. 00:02:57.130 Next example, let's subtract, 1/3 with 1 1/2. 00:03:04.020 Notice that, this fraction is a mixed fraction. To minimize mistakes, it is advisable to convert it to an improper fraction. 00:03:13.000 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. 00:03:28.200 Next, we add 2 with 1. This gives 3, which becomes the improper fraction's numerator. Now, we have the improper fraction, 3/2. 00:03:43.000 Notice that, we cannot subtract these 2 fractions because they have unlike denominators. 00:03:49.190 Therefore, the only way to subtract these fractions, is to make them to have like denominators. We can do so, by using equivalent fractions. 00:04:01.240 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. 00:04:20.020 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. 00:04:33.180 Now, we subtract these two fractions. This gives 2 minus 9/6. 00:04:46.070 Subtracting 2 with 9, gives negative 7. 00:04:50.210 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. 00:05:01.200 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. 00:05:14.080 Now, when doing the conversion, we just need to focus on this fraction, and ignore this sign. 00:05:22.040 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. 00:05:37.130 Next, we multiply 1 with 6. This gives 6. 7 minus 6 gives the remainder as 1. 00:05:47.200 This remainder, 1, is actually the mixed fraction's numerator. 00:05:54.240 So here, we have the final answer as, negative 1 1/6. 00:06:03.160 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.
on subtracting fractions with like denominators
on subtracting fractions with unlike denominators
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