Algebra Word Problem

by Abby Hope
(Henderson, NC)

The product of two fractions is 1/9. The larger fraction divided by the smaller fraction is 4. What is the sum of the two fractions? Express your answer as a common fraction.

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Sep 29, 2010
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by: Karin

Hi Abbey,

This is a great problem!

Let's first identify the variables. You know that you are dealing with 2 numbers and one is larger than the other.

Let x = the larger number
Let y = the smaller number

Now we can write two equations:

The product of the two numbers is 1/9. Product means multiply.

xy = 1/9

The larger number divided by the smaller number is 4.

x/y = 4

So, we have: xy = 1/9 and x/y = 4

Since we have two equations, we actually have a system of equations. We need to solve the system.

I am going to use the substitution method.

Step 1: Solve one of the equations for a variable. I will solve x/y = 4 for x.

Multiply both sides by y.

y(x/y)= 4y

x = 4y

Now, we'll substitute 4y for x into the equation:
xy = 1/9

4y(y) = 1/9

4y^2 = 1/9

Now divide by 4 on both sides.

4y^2/4 = 1/9 / 4
y^2 = 1/36

Now take the square root of both sides and you end up with:

y = 1/6

Now substitute 1/6 for y into the equation x = 4y

x = 4y
x = 4(1/6)
x = 4/6
x = 2/3

So, the two numbers are 1/6, & 2/3.

Now let's check before we finish the problem:

xy = 1/9
(1/6)(2/3) = 1/9
2/18 = 1/9
1/9 = 1/9

AND

x/y = 4

2/3 / 1/6 = 4
2/3 * 6/1 = 4
12/3 = 4
4 = 4

Yes, our answers are correct. So, now the question asked for the sum of the numbers, so we must add the numbers together.

1/6 + 2/3 = 5/6

The correct answer is 5/6

Hope this helps,
Karin
xy = 1/9
(1/6)(2/3) =

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