SSAT Elementary Level Quantitative - How to find a ratio

Simplify the following ratio:

Explanation

In order to simplify the ratio, you need to find the greatest common factor of the two numbers. The greatest common factor of is . If you reduce both numbers by then it would be .

Determine the ratio of to .

Explanation

Ratios represent how one number is related to another. These steps will help you determine the ratio of the numbers shown:

) Divide both terms of the ratio by the GCF (greatest common factor). In this case, the GCF is because is the greatest number that goes into both numbers evenly.

$10\div10=1$

$100\div10=10$

) Show the ratio with a colon : and remember to keep the numbers in the same order!

Therefore, the ratio of to is .

Simplify the ratio: 400 students to 25 teachers

Explanation

A ratio can be simplified by dividing both numbers by their greatest common factor. Since 400 is divisible by 25, the GCF is 25.

$400\div 25 = 16$

$25\div 25 = 1$

The ratio, simplified, is .

Riley gives Maddie marbles, then gives Carl marbles. He repeats this process several times.

At the end of this process, Maddie has marbles. How many marbles does Carl have?

marbles

Explanation

Divide the number of marbles Maddie has by the number she received per turn to find the number of times the process occurred.

$84\div7=12$ , so the process occurred times.

Set up a ratio of the number of marbles given to Maddie to the number of marbles given to Carl on each turn. This ratio would be .

We can find the number of marbles Carl has by multiplying the number of times the process occurred by the number of marbles he received each turn.

$12 \times 3 = 36$ marbles.

A car with a tank that holds gallons of gas gets miles to the gallon. If the car's gas gauge reads that the tank is three-fourths full, how many miles can it travel before it needs to be refueled?

$273 \textrm{ mi}$

$364 \textrm{ mi}$

$485 \frac{1}{3} \textrm{ mi}$

$40 \textrm{ mi}$

$30 \textrm{ mi}$

Explanation

Multiply miles per gallon by gallons to get the distance the car can travel on a full tank:

$14 \times 26 = 364$ miles.

Multiply this by three-fourths to get the distance it can travel on three-fourths of a tank.

$364 \times \frac{3}{4} = \frac{364 \times 3}{4}= \frac{1,092 }{4} = 1,092 \div 4 = 273\ miles$

Determine the ratio of 6 to 36.

Explanation

Ratios represent how one number is related to another. These steps will help you determine the ratio of the numbers shown:

Divide both terms of the ratio by the GCF (greatest common factor). In this case, the GCF is 6 because 6 is the greatest number that goes into both numbers evenly.

$6\div6=1$

$36\div6=6$

Show the ratio with a colon : and remember to keep the numbers in the same order!

Therefore, the ratio of 6 to 36 is .

If there are 6 girls in a class and 12 boys in a class, what is the ratio of girls to boys in the class, in simplest form?

Explanation

To find a ratio, divide the two numbers given until they are reduced to their lowest common factor, then put them into a ratio with a colon in between. Remember to order them in the way the question is asked!

6 (girls) and 12 (boys) can both be divided by 6:

$6\div 6 = 1$

$12 \div 6 = 2$

For every girl, there are 2 boys in the class. Therefore, the ratio is .

Which of the following is in a simplified form?

Explanation

In order to reduce to its simpler form, the key is to divide each side by the same number. Dividing each side by 4 gives us a reduced ratio of , which is the correct answer.

$12:4=(12\div4):(4\div4)$

Determine the ratio of 12 to 32.

Explanation

Ratios represent how one number is related to another. These steps will help you determine the ratio of the numbers shown:

Divide both terms of the ratio by the GCF (greatest common factor). In this case, the GCF is 4 because 4 is the greatest number that goes into both numbers evenly.

$12\div4=3$