Learn about Equivalent Fractions and Mixed Numbers In this lesson, let’s learn how we determine if fractions and mixed numbers if they are indeed equivalent. So we need to find whether the fractions we need to pair are equivalent. First one is 8/10 and 12/15. Now if fractions are equivalent they can be brought down to the simplest form and they will both look the same. So if I want to take 8/10 and bring it down to the simplest form, what will I do? I will divide the top and bottom by two. That would give me 4/5 so that’s the simplest form. Let’s see if 12/15 if I bring to the simplest form gives me the same value. Here, I have to divide it by 3 4/5 both of these are brought down to the same simplest form which means they are indeed equivalent. Let’s try the next one; 3/7 and 4/9. These are already in simplest forms. So I can-- just by looking at them tell you that they're not equivalent but let’s do this. Let’s multiply the enumerator and denominator by nine to get them the same denominator which is 63. 3 x 9 is 27, 7 x 9, 63. Similarly, multiply here by seven to give me 28/63. So the two fractions are 27/63 and 28/63 which means they are not equivalent. I just showed you another way of doing it which is bring them to the same denominator and then compare the enumerators. Now, because these were already in simplest form I could have just looked at it and told you that they're not the same because the simplest forms are not the same. But just to double check it brings them to the same denominator. Let’s do the third one which involves mixed numbers. We've got 21/4 and 5 ¼ let’s do it two different ways. First let’s bring this down to mixed numbers. 21/4 is an improper fraction enumerator is greater than the denominator. So how do I bring this down to a mixed number? We divide 21 with 4, what do I get? 4 x 5 is 20 and the remainder is one. So the mixed number is the quotient which is five. The remainder which is one and the original denominator which is four, these two are the same so these are indeed equivalent. I could do something else. I could bring this down to an improper fraction. So what do you do? You take the denominator multiply it by the whole number, denominator times the whole number then you add the enumerator and divide it by the denominator. The denominator is 4 x 5 + 1, that’s 20 + 1, 21/4. This is the same as this so these are indeed equivalent.