SSAT Elementary Level Math : Numbers and Operations

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

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Example Questions

Example Question #1 : Ratio And Proportion

Determine the ratio of 6 to 36.

Possible Answers:

\(\displaystyle 1:6\)

\(\displaystyle 3:12\)

\(\displaystyle 6:1\)

\(\displaystyle 6:6\)

Correct answer:

\(\displaystyle 1:6\)

Explanation:

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

1) 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.

\(\displaystyle 6\div6=1\)

\(\displaystyle 36\div6=6\) 

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

Therefore, the ratio of 6 to 36 is \(\displaystyle 1:6\).

Example Question #1 : Numbers And Operations

Determine the ratio of 12 to 32.

 

 

Possible Answers:

\(\displaystyle 4:12\)

\(\displaystyle 4:8\)

\(\displaystyle 3:8\)

\(\displaystyle 8:3\)

Correct answer:

\(\displaystyle 3:8\)

Explanation:

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

1) 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.

\(\displaystyle 12\div4=3\)

\(\displaystyle 32\div4=8\)

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

Therefore, the ratio of 12 to 32 is \(\displaystyle 3:8\).

Example Question #1 : Ratio And Proportion

Riley gives Maddie \(\displaystyle 7\) marbles, then gives Carl \(\displaystyle 3\) marbles. He repeats this process several times.

At the end of this process, Maddie has \(\displaystyle 84\) marbles. How many marbles does Carl have?

Possible Answers:

\(\displaystyle 12\) marbles

\(\displaystyle 30\) marbles

\(\displaystyle 33\) marbles

\(\displaystyle 42\) marbles

\(\displaystyle 36\) marbles

Correct answer:

\(\displaystyle 36\) 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.

\(\displaystyle 84\div7=12\), so the process occurred \(\displaystyle 12\) 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 \(\displaystyle 7:3\).

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.

\(\displaystyle 12 \times 3 = 36\) marbles.

Example Question #2 : Numbers And Operations

Which ratio is "20 to 60" written in simplest form?

Possible Answers:

\(\displaystyle 3:1\)

\(\displaystyle 1:2\)

\(\displaystyle 1:3\)

\(\displaystyle 1:4\)

\(\displaystyle 2:6\)

Correct answer:

\(\displaystyle 1:3\)

Explanation:

1)   Divide both terms of the ratio by the greatest common factor. In this case, the greatest common factor is 20, because 20 is the largest number that goes into both numbers evenly.

\(\displaystyle 20\div20=1\)

\(\displaystyle 60\div20=3\)

2)   Show the ratio with a colon (:). Remember to keep the numbers in the correct order!

Therefore, 20 to 60 is equivalent to 1 : 3.

 

Example Question #3 : Numbers And Operations

Determine the ratio of 12 to 48 in simplest form.

Possible Answers:

\(\displaystyle 4:1\)

\(\displaystyle 1:4\)

\(\displaystyle 1:5\)

\(\displaystyle 2:4\)

\(\displaystyle 1:3\)

Correct answer:

\(\displaystyle 1:4\)

Explanation:

1) Divide both terms of the ratio by the greatest common factor. In this case, the greatest common factor is 12, because 12 is the greatest number that goes into both numbers evenly.

\(\displaystyle 12\div12=1\)

\(\displaystyle 48\div12=4\)

2) Show the ratio with a colon (:), and remember to keep the numbers in the correct order.

Therefore, the ratio of 12 to 48 is \(\displaystyle 1:4\).

Example Question #4 : Numbers And Operations

Simplify the ratio: 400 students to 25 teachers

Possible Answers:

\(\displaystyle 24:1\)

\(\displaystyle 15:1\)

\(\displaystyle 20:1\)

\(\displaystyle 16:1\)

\(\displaystyle 18:1\)

Correct answer:

\(\displaystyle 16:1\)

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.

\(\displaystyle 400\div 25 = 16\)

\(\displaystyle 25\div 25 = 1\)

The ratio, simplified, is \(\displaystyle 16:1\).

Example Question #5 : Numbers And Operations

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?

Possible Answers:

\(\displaystyle 1:2\)

\(\displaystyle 2:2\)

\(\displaystyle 6:12\)

\(\displaystyle 2:1\)

\(\displaystyle 1:1\)

Correct answer:

\(\displaystyle 1:2\)

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:  

\(\displaystyle 6\div 6 = 1\)

\(\displaystyle 12 \div 6 = 2\)

For every girl, there are 2 boys in the class.  Therefore, the ratio is \(\displaystyle 1:2\) .

Example Question #6 : How To Find A Ratio

Which of the following is \(\displaystyle 12:4\) in a simplified form?

Possible Answers:

\(\displaystyle 4:1\)

\(\displaystyle 1:3\)

\(\displaystyle 12:1\)

\(\displaystyle 3\)

\(\displaystyle 3:1\)

Correct answer:

\(\displaystyle 3:1\)

Explanation:

In order to reduce \(\displaystyle 12:4\) 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 \(\displaystyle 3:1\), which is the correct answer. 

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

\(\displaystyle 12:4=3:1\)

Example Question #5 : Ratio And Proportion

Determine the ratio of \(\displaystyle 10\) to \(\displaystyle 100\).

Possible Answers:

\(\displaystyle 1:5\)

\(\displaystyle 1:1\)

\(\displaystyle 1:100\)

\(\displaystyle 10:1\)

\(\displaystyle 1:10\)

Correct answer:

\(\displaystyle 1:10\)

Explanation:

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

\(\displaystyle 1\))  Divide both terms of the ratio by the GCF (greatest common factor). In this case, the GCF is \(\displaystyle 10\) because \(\displaystyle 10\) is the greatest number that goes into both numbers evenly.

\(\displaystyle 10\div10=1\)

\(\displaystyle 100\div10=10\) 

\(\displaystyle 2\))  Show the ratio with a colon : and remember to keep the numbers in the same order!

Therefore, the ratio of \(\displaystyle 10\) to \(\displaystyle 100\) is \(\displaystyle 1:10\).

 

Example Question #6 : Ratio And Proportion

A car with a tank that holds \(\displaystyle 14\) gallons of gas gets \(\displaystyle 26\) 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?

Possible Answers:

\(\displaystyle 273 \textrm{ mi}\)

\(\displaystyle 364 \textrm{ mi}\)

\(\displaystyle 485 \frac{1}{3} \textrm{ mi}\)

\(\displaystyle 40 \textrm{ mi}\)

\(\displaystyle 30 \textrm{ mi}\)

Correct answer:

\(\displaystyle 273 \textrm{ mi}\)

Explanation:

Multiply \(\displaystyle 26\) miles per gallon by \(\displaystyle 14\) gallons to get the distance the car can travel on a full tank:

\(\displaystyle 14 \times 26 = 364\) miles.

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

\(\displaystyle 364 \times \frac{3}{4} = \frac{364 \times 3}{4}= \frac{1,092 }{4} = 1,092 \div 4 = 273\ miles\)

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