Finding Equivalent Fractions

Hello. My name is Ms. Bishop. And I will be helping you with equivalent fractions. Equivalent fractions are fractions that name the same value. We can see this by using models. Here, we have 2/6. 2 shaded out of a group of 6. 1, 2, 3, 4, 5, 6. What we can do there is we can create other groups-- equal groups. We have three equal groups of 2. And so by creating three equal groups now, now we say, well, there is one group that's shaded in out of the 1, 2, 3. So we have an equivalent fraction. 2/6 is the same as 1/3.

Let's try that again. Here, we have 4/8. We have 4 shaded out of a group of 8. Well, again, we can create another equal group. We have an equal group of 4 here and an equal group of 4 here. So now I have 1, 2 groups, and one of those groups is shaded. So I have 1 out of 2. So 4/8 is equivalent to 1/2.

Let's look at that with fractions strips. Here, we have a fraction of 1. And here we have 1/4. We have 1, 2 1/4. Now, we want the same value, or the same amount, so here we have 1/8. And what we do is we line them up and then we count. We have 1/8, 2/8, 3/8, 4/8. So 2/4 is equivalent to 4/8. We see it names the same amount, has the same value. Here, we have 12. So we can do the same thing. Lining it up, we have 1, 2, 3, 4, 5, 6/12. So 2/4, 4/8, and 6/12 are all equivalent fractions. They all name the same value.

You can see that also with a number line. Here, we have a number line broken into equal groups of 10. We have 1/10 here. And here, we have a number line broken into equal groups of 5/5. So here, we have them lined up. So if we look at 4/10-- here is 4/10 here-- we want to find the 1/5 that names the same value. Well, if we go straight down, we see that 2/5 names that same amount. They are equal. So 4/10 and 2/5 are equivalent fractions.

Now, I'd like you to look at the number line and tell me what is equivalent to 4/5. When you have your answer, press continue. OK, so here we have 4/5. And we want to find the 1/10 that names that same value, that is an equal amount. And if you follow it up, you see that 8/10 is equivalent to 4/5. Now, we can use a model or fraction strips or a number line, but we can also multiply or divide to find those equivalent fractions.

And what we do there is we multiply and divide the numerator and denominator by the same number. Let's look at that. Here, we have 3/7. So what we can do there is we want to multiply or divide by the same number. So we can multiply by, let's say, 2. If I multiply the top by 2, I multiply the bottom by 2-- the numerator and the denominator. So now I have 3 times 2 is 6 and 7 times 2 is 14. So 3/7 is equivalent to 6/14.

Let's try that again. This time, let's try to divide. Again, dividing by the same number. So let's divide by 2, because 2 can go into 8 and 2 can go into 10. 8 divided by 2 is 4. 10 divided by 2 is 5. So we now create an equivalent fraction. 8/10 is equivalent to 4/5. And we found that up at the top with the number line. But this is a quicker and easier way for us to find equivalent fractions. We can also use this to help us find simplest form.

Now, simplest form just means that the numerator and denominator only have a common factor of 1. So let's see what that means. Here, we have 5/15. Well, that's not in simplest form, because we can find a number to divide equally into the numerator and the denominator. And that number would be 5. I can divide 5 into 5 and I can divide 5 into 15. If I do that, 5 divided by 5 is 1, and 5 divided by 15 is 3. So these two fractions are equivalent, but 1/3 here is giving us the simplest form. We can't divide any more than we just did. 1/3 is the simplest form.

Let's try that one more time. What if we had 6/10? OK, well, we can find a number that goes into both of those. Let's see. Well, 2 goes into 6. Let's divide by 2. And 2 goes into 10. 6 divided by 2 is 3 and 10 divided by 2 is 5. Now, can we find a number that can be divided into 3 and 5? No, so 3/5 is the simplest form. And of course, 6/10 and 3/5 are equivalent fractions.

OK, so now that we learned all about equivalent fractions, I'd like you to show me two equivalent fractions for the number 9/18-- 9/18. Is it a, b, or c? That's right. Your answer is b. 3/6 and 18/36. If we look at the first one, 3/6, we see that 9/18-- if we divide both numbers by 3, the same number-- we get the equivalent fraction of 3/6. And the same thing with 9/18. If we multiply both the numerator and denominator by 2, we get 18/36. OK, very good. Well, you are ready now to do more with equivalent fractions. So have fun and work well.