Source: Official Guide Revised GRE 1st Ed. Part 8; Section 5; #10

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# The ratio of 1/3 to 3/8 is equal

The ratio of 1/3 to 3/8 is equal to the ratio of 1 to 8, 8 to1, 8 to 3, 8 to 9, 9 to 8

### 2 Explanations

1

Jay Villanueva Jr

Is this the same as simply cross multiplying?

Aug 7, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Jay,

Yes, we do get the same result if we cross multiply. What the explanation video shows is what we really do when we cross multiply, which is multiply both sides by each denominator. The denominators are simplified to 1 and we are left with integers on each side of the equation :)

Hope this helps!

Malak Kudaimi

I'm not quite sure I understand the explanation. If you cross multiply, don't you get 3 * 3 = 9 and 1 * 8 = 8, getting a ratio of 9:8?

Hi Malak,

As Cydney explains below, because we have a ratio, we're actually dividing. When we divide two fractions, it's the same as flipping one fraction over and then multiplying them:
(1/3) / (3/8) = (1/3) * (8/3) = 8/9

Malak Kudaimi

I remember learning in the lesson on ratios that when you have to ratios set equal to each other, the best way to solve the problem is cross-multiplying, so I don't really understanding why we're dividing in the first place.

Sam Kinsman, Magoosh Tutor

Hi Malak - you're right that if we set ratios equal to each other, we can cross multiply. However, in this question, the ratios are not set equal to each other. Instead, we have a ratio of fractions: 1/3 to 3/8, or (1/3) : (3/8). Since we haven't set these two fractions equal to each other, we cannot cross multiply. I hope that helps!

2 Chris Lele, Magoosh Tutor

Oct 11, 2012 • Comment

Why aren't we dividing 1/3 / 3/8 instead?

Cydney Seigerman, Magoosh Tutor

Hi Anaelia,

While Chris presents one approach to this question, we could also divide 1/3 / 3/8, as you mentioned. When dividing fractions, we flip the second fraction and multiply:

1/3 / 3/8 = 1/3 * 8/3 = 8/9

As you can see, we get the same final ratio using either the approach in the explanation or dividing like I show above :)

Hope this helps!