Multiplying Fractions
Lesson Objective
In this lesson, we will learn the basics behind multiplying fractions and will be using some examples to explain how this multiplication works.
About This Lesson
It is easier to multiply fractions as compared to adding or subtracting fractions. This is because we don't have to worry about the denominators.
In this lesson, we will learn how to multiply two fractions that:
are proper fractions
a proper fraction and a mixed fraction.
The
study tips
and
math video
below will explain more.
Study Tips
Tip #1
When multiplying fractions, the denominators don't have to be the same.
Tip #2 - How to Multiply Fractions
Below are steps to multiply two fractions:
Multiply the numerators:
Multiply the denominators:
Simplify the fraction if possible:
Tip #3 - Multiplying Mixed Fractions
The steps below show how we can multiply mixed fractions. Let's use the following example:
Convert the mixed fractions to improper fractions:
After the conversions, we have:
Now, multiply the fractions as usual. Simplify if possible:
Watch the math video below for more explanation.
Math Video
Lesson Video
Math Video Transcript
00:00:02.100 In this lesson, we will learn the basics behind multiplying fractions. 00:00:07.180 Now, compared to adding or subtracting fractions, it is easier to multiply fractions. 00:00:14.130 This is because when we multiply fractions, we don’t have to make the denominators the same. 00:00:21.030 For example, let's multiply, 2/3 with 4/5. 00:00:29.020 To do so, we just need to multiply the numerators together. 00:00:34.190 Therefore, we multiply 2 with 4. This gives 8. 00:00:40.100 Next, we multiply the denominators together. 00:00:44.130 Therefore, we multiply 3 with 5. This gives 15. 00:00:51.020 So finally, we can see that this fraction multiplication gives 8/15. 00:00:57.180 Now, let's visually examine how this multiplying fractions work. 00:01:03.000 We can represent 2/3, with this rectangle. Similarly, we represent 4/5, with this rectangle. 00:01:13.130 When we multiply these fractions, visually, it means that we are combining these rectangles. 00:01:20.210 When the green and purple rectangles overlap, they give blue rectangles. 00:01:26.090 Here, we can see that, these 8 blue rectangles are represented by the numerator 8. 00:01:32.150 Also, notice that there are total of 15 rectangles, which are represented by the denominator 15. 00:01:43.240 Alright, let's take a look at more examples on multiplying fractions. 00:01:50.100 Let's multiply, 7/8, with 2/5. 00:01:57.120 First we multiply the numerators. So, we multiply 7 with 2. This gives 14. 00:02:12.030 Next, multiply the denominators. So, we multiply 8 with 5. This gives 40. 00:02:18.220 Now, we have the fraction, 14/40. 00:02:23.210 Notice that, we can simplify this fraction. To do so, we divide the numerator and denominator with 2. 00:02:32.070 This gives the simplified fraction, 7/20. 00:02:38.120 Next example, let's multiply 1/3, with 3 1/2. 00:02:45.080 Notice the mixed fraction here? 00:02:48.050 It is important to change it to an improper fraction before multiplying. 00:02:53.180 To do so, first, we multiply 2 with 3. This gives 6. 00:03:01.100 Next, we add 6 with 1. This gives 7. This 7 becomes the improper fraction's numerator. 00:03:11.150 Hence, we have the improper fraction, 7/2. 00:03:16.170 We can now multiply these fractions. 00:03:20.230 First, multiply the numerators. So, we multiply 1 with 7. This gives 7. 00:03:31.000 Next, we multiply the denominators. So, we multiply 3 with 2. This gives 6. 00:03:41.230 Notice that, 7/6 is an improper fraction. Now, rather than leaving the answer like this, it is recommended to change it to a mixed fraction, by using long division. 00:03:53.240 Here's how. 7/6 is the same as, 7 divides 6. Now, this division gives the quotient 1. This quotient is actually the whole number for the mixed fraction. 00:04:11.160 Next, we multiply 1 with 6. This gives 6. 7 minus 6 gives the remainder as 1. 00:04:21.230 This remainder, 1, is actually the mixed fraction's numerator. 00:04:29.030 So here, we have the answer in mixed fraction, 1 1/6. 00:04:35.240 That is all for this lesson. Try out the practice question to further your understanding. --End of Multiplying Fractions Transcript--
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 Multiplying Fractions
or pick your choice of question below.
Question 1
on multiplying two proper fractions
Question 2
on multiplying a mixed fraction with a proper fraction
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