SSAT Middle Level Math : Numbers and Operations

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Questions

Example Question #671 : Ssat Middle Level Quantitative (Math)

Express this ratio in simplest form: 

Possible Answers:

Correct answer:

Explanation:

A ratio involving decimals can be simplified as follows:

First, move the decimal point over a common number of places in each number so that both numbers become whole. In this case, it would be two places:

 (Note the addition of a zero at the end of the first number.)

Now, rewrite as a fraction and divide both numbers by :

The ratio, simplified, is .

Example Question #12 : Numbers And Operations

In Mrs. Jones' class, the ratio of boys to girls is 3:2.  If there are 8 girls in the class, how many total students are in the class?

Possible Answers:

Correct answer:

Explanation:

Using the ratio, we find that there are 12 boys in the class  .  

Summing 12 and 8 gives the total number of 20 students.  

Example Question #13 : Numbers And Operations

A 16-ounce bottle of Charlie's Fizzy Fizz Root Beer costs 89 cents. Give the price per ounce to the nearest tenth of a cent.

Possible Answers:

Correct answer:

Explanation:

Divide 89 by 16:

The soda costs about 5.6 cents per ounce.

Example Question #11 : Numbers And Operations

A batting average is defined as the ratio of hits to turns at bat. It is expressed as a decimal rounded to the nearest thousand.

In 2013, Yadier Molina's batting average was 0.319. If he maintains this same batting average over the 2014 baseball season, how many turns at bat should he expect to need to achieve 50 hits? (Nearest whole number)

Possible Answers:

Correct answer:

Explanation:

Since a batting average is a ratio of hits to turns at bat,

Let  be the number of turns at bat Molina needs to get 50 hits. Then:

Solve for :

Molina should need 157 turns at bat,

Example Question #11 : Numbers And Operations

Carlos owns a hamburger and hot-dog stand. When the fridge in the stand is  full, there are 16 hamburgers and hot dogs total. If the ratio of hamburgers to hot dogs is always 5:3, how many hot dogs are in the cart when it is full?

Possible Answers:

Correct answer:

Explanation:

When solving a ratio problem, first add each part of the ratio:

So, one part in this ratio is equal to 8. The number of hamburgers and hot dogs in the fridge is currently only  the amount it can hold. To figure out how much it can hold total, we can multiply by the denominator of the fraction since the numerator is 1.

64 is the total amount of hamburgers and hot dogs that can be held in the fridge. Divide 8 into 64 in order to figure out how many parts fit into this number.

This number tells us how many times we need to multiply the ratio by in order to figure out how many hamburgers or hot dogs can be in the fridge at once. Since we are trying to figure out how many hot dogs are in the fridge when it is full, we use the second number, 3. We use the number 3 because, since the ratio is hamburgers to hotdogs, the second number represents the number of hot dogs.

This gives you your answer. There are 24 hot dogs in the fridge when it is full.

Example Question #672 : Ssat Middle Level Quantitative (Math)

There are  girls and  boys in Miss Bailey's class. What is the ratio of girls to boys?

Possible Answers:

Correct answer:

Explanation:

The ratio of girls to boys in Miss Bailey's class is , which can be reduced to  when both the numerator and denominator are divided by .

Example Question #11 : How To Find A Ratio

In a library, there are  children's books and  young adult books. What is the ratio of young adult books to children's books?

Possible Answers:

Correct answer:

Explanation:

The ratio of young adult books to children's books is  to , or , which can be reduced to .

Example Question #11 : Numbers And Operations

There are  male and  female employees at a company. What is the ratio of females to males?

Possible Answers:

Correct answer:

Explanation:

The ratio of females to males is  to , or , which can be reduced to .

Example Question #19 : Numbers And Operations

One dollar is equal to about 116.76 Japanese yen. For how many yen should a tourist to Japan be able to exchange $2,500 at that rate (nearest whole yen)?

Possible Answers:

Correct answer:

Explanation:

One dollar is equal to 116.76 yen, so multiply $2,500 by this conversion rate to get

 yen.

Example Question #12 : Numbers And Operations

Sharon is having a birthday party. So far, she has invited twenty of her friends from school, nine of whom are girls. She wants to make the ratio of boys to girls at the party two to one. If she decides to add her two cousins, both girls, to the guest list, and no other girls, how many more boys does she need to invite?

Possible Answers:

Correct answer:

Explanation:

So far, Sharon has invited twenty friends from school - eleven boys and nine girls. Including Sharon's cousins and Sharon herself, there are eleven boys and twelve girls. 

For there to be a two-to-one boy-to-girl ratio, Sharon must have twice as many boys as girls. She will need  boys total, so she will need to invite  more boys.

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