fractions - Equivalent fractions

Equivalent fractions

16 viewed last edited 4 years ago

fractions mathematics

Sherlyn Casco Noperi (Student, 7^th Grade)

I didn't try anything cause I don't know how to do it.

Equivalent fractions of 10/15=?/3

Mahesh Godavarti (last edited 4 years ago) (Expert, Founder @Qalaxia)

Hi Sherlyn, we have to understand what fractions are. First, I will give you the quick answer then I will explain the meaning behind it in a comment. First, notice that 10 = 5 X 2, 15 = 5 X 3. Therefore, 10/15 = (5 X 2)/(5 X 3) = 2/3 (Removing 5 as a common factor between numerator and denominator)

Mahesh Godavarti (last edited 4 years ago)

Think of what fractions are. Let's say there are 15 apples in a bag and you take out 10 of them. Then you have taken 10 / 15 fraction of apples. But, now let's say apples in the bag are bundled together in a mini-bag. Let each mini-bag contain 5 apples. Let there be 3 such mini-bags. If we pick out 2 mini-bags, then the fraction of mini-bags that we picked is 2/3 (we picked 2 mini-bags out of 3). But, note that this is the same as picking 10 apples out of 15 apples. Therefore, whether we think of it as picking 10 apples out of 15 apples or 2 mini-bags out of 3 mini-bags, it is basically the same thing! Therefore, 10/15 = 2/3

Vivekanand Vellanki (last edited 4 years ago) (Expert, Founder @Qalaxia)

You seem to be asking for an equivalent fraction in simplest form. 10/15 is equivalent to 2/3; it is also equivalent to 4/6; or 20/30, etc. Mahesh's answer shows how to find the equivalent fraction in simplest form. To do this, you need to do the following: 1) find the common factors between the numerator and the denominator. In this case, 5 is the common factor 2) Write the numerator and denominator as multiples of the common factor. 10/15 = 2*5/3*5 3) Now, eliminate the common factor to get 10/15 = 2/3 Continue this process until there are no more common factors

Sangeetha Pulapaka (last edited 4 years ago) (Expert, Educator @Qalaxia)

The question you have is how to find the missing number when the two fractions are equivalent. Equivalent fractions are fractions which look different but have the same value. All we need to know to find the missing number in two fractions which are are equivalent is the multiplication table or the division table. \frac{10}{15}= \frac{?}{3} Look at the denominators of both the fractions given. When you divide 15 by which number do you get a 3? You divide 15 by 5 you get 3. To make sure that the value of the fraction does not change when the denominator is divided by 5, the numerator should also be divided by 5. So dividing the numerator 10 by 5 we get the missing number as 2. How to check if this answer is right or wrong? Do the multiplication table of 2 which is 2\times 5 = 10 Do the multiplication table of 3 which is 3\times 5 = 15. Since we get the same fraction this means that the missing number is 2.