Fractions - showing that they are equivalent

In summary, the conversation discusses proving the equivalence of two fractions, a = c/d * b and a = c/(c+d) * (a+b). The approach suggested is to start with the second equation and simplify it by substituting the first expression for a. This would result in the first equation, showing their equivalence. The reverse can also be done to show how to go from the first to the second equation.
  • #1
aaaa202
1,169
2
fractions -- showing that they are equivalent

I have the fraction:

a = c/d * b

And from that I want to show that:

a = c/(c+d) * (a+b)

At least the two equations should be equivalent if I did everything right. How do I go from first to the second?
 
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  • #2


its probably easier to go from the second to the first. And then you can just do those steps in reverse if you want to show how to go from the first to the second. You see what I mean? So, if you want to do it this way, then looking at the second equation, how would you try to get it in a more simple form?
 
  • #3


aaaa202 said:
How do I go from first to the second?
Try going from the second to the first. Just substitute your first expression for a and simplify.
 

FAQ: Fractions - showing that they are equivalent

How do you show that two fractions are equivalent?

To show that two fractions are equivalent, you need to find the lowest common denominator (LCD) between the two fractions. Then, multiply both the numerator and denominator of each fraction by the same number until they have the same denominator. The resulting fractions will be equivalent.

What is the easiest way to compare two fractions?

The easiest way to compare two fractions is to convert them to decimals. Then, you can easily compare the decimals to determine which fraction is larger or smaller.

Can fractions with different denominators be equivalent?

Yes, fractions with different denominators can be equivalent. As long as they have the same value, they are considered equivalent. This means that the numerator and denominator of one fraction can be multiplied by the same number to get the other fraction.

Why is it important to understand equivalent fractions?

Understanding equivalent fractions is important because it allows us to simplify and compare fractions easily. It also helps us in performing operations with fractions, such as addition, subtraction, multiplication, and division.

How can real-life situations involve equivalent fractions?

Real-life situations that involve measurements or parts of a whole can involve equivalent fractions. For example, a recipe may call for 1/2 cup of flour, but you only have a 1/4 cup measuring cup. By understanding equivalent fractions, you can easily determine that you need to use 2 of the 1/4 cup measuring cups to get the same amount of flour as 1/2 cup.

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