SAT Math : Operations with Fractions

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #1 : How To Multiply Fractions

If xy = 1 and 0 < x < 1, then which of the following must be true?

Possible Answers:

x

y > 1

y = 1

< 1

y = x

Correct answer:

y > 1

Explanation:

If x is between 0 and 1, it must be a proper fraction (e.g., ½ or ¼). Solving the first equation for y, y = 1/x. When you divide 1 by a proper fraction between 0 and 1, the result is the reciprocal of that fraction, which will always be greater than 1.

To test this out, pick any fraction. Say x = ½. This makes y = 2.

Example Question #1 : Operations With Fractions

Before going to school, Joey ran 1/3 of his daily total miles. In gym class, Joey did 2/3 of the remainder. What part of his daily total miles was left for after school?

Possible Answers:

2/9

1/3

4/9

2/3

7/9

Correct answer:

2/9

Explanation:

Before school, Joey did 1/3 of the total miles. In school, Joey did 2/3 of the remaining 2/3, or 4/9 of the running. When added to his in school run, his before school run of 3/9 brings his completed miles to 7/9 of his dialy total. Thus, only 2/9 of the total miles are left for after school.

Example Question #1 : Operations With Fractions

Sally bought five computers for her office that cost $300, $405, $485, $520, and $555 respectively. She made a down payment of 2/5 the total cost and paid the rest in nine equal payments over the next nine months. Assuming no tax and no interest, what is the value of each of the nine payments?

Possible Answers:

251

1359

151

906

351

Correct answer:

151

Explanation:

The total cost of the 5 computers is 2265.

2/5 of 2265 = 906, which is what Sally pays up front.

2265 – 906 = 1359, which is what Sally still owes.

1359/9 = 151, which is the value of each of the 9 equal payments.

Example Question #121 : Arithmetic

The price of a computer is reduced by 1/8.  The new price is then reduced by 1/6.  What fraction of the original price is the current price?

Possible Answers:

13/48

23/24

1/24

35/48

1/48

Correct answer:

35/48

Explanation:

Let the original price = p.

After the first reduction, the price is (7/8)p

After the second reduction, the price is (5/6)(7/8)p = (35/48)p

Example Question #1 : How To Multiply Fractions

If a car travels at 30 mph, how many feet per second does travel?

Possible Answers:

2,640 ft/s

44 ft/s

4,400 ft/s

264 ft/s

440 ft/s

Correct answer:

44 ft/s

Explanation:

30 miles / 1 hour  *  5280 ft / 1 mile * 3600 seconds / 1 hour = 44 ft/sec

Example Question #1 : How To Multiply Fractions

In a group of 20 children, 25% are girls.  How many boys are there?

Possible Answers:

15

16

5

4

10

Correct answer:

15

Explanation:

Since \dpi{100} \small \frac{1}{4} of the children are girls, this totals to \dpi{100} \small 20 \times \frac{1}{4} = 5 girls in the group.

\dpi{100} \small 20-5=15 boys.

Example Question #2 : Operations With Fractions

Simplify:

  Sat_math_167_03

 

 

Possible Answers:

a2/c2

ad/bc

ac/bd

a/b/c/d

It is already in simplest terms

Correct answer:

ad/bc

Explanation:

Division is the same as multiplying by the reciprocal.  Thus, a/b ÷ c/d = a/b x d/c = ad/bc

 

 

Example Question #1 : How To Divide Fractions

If p is a positive integer, and 4 is the remainder when p-8 is divided by 5, which of the following could be the value of p?

Possible Answers:

17

19

18

20

Correct answer:

17

Explanation:

Remember that if x has a remainder of 4 when divided by 5, x minus 4 must be divisible by 5. We are therefore looking for a number p such that p - 8 - 4 is divisible by 5. The only answer choice that fits this description is 17. 

Example Question #3 : Operations With Fractions

If \dpi{100} \small x=\frac{2}{3} and \dpi{100} \small y= \frac {3}{4}, then what is the value of \dpi{100} \small \frac {x}{y}?

Possible Answers:

\dpi{100} \small \frac{8}{9}

\dpi{100} \small \frac{9}{8}

\dpi{100} \small \frac{1}{2}

\dpi{100} \small \frac{5}{7}

\dpi{100} \small 2

Correct answer:

\dpi{100} \small \frac{8}{9}

Explanation:

Dividing by a number (in this case \dpi{100} \small \frac {3}{4}) is equivalent to multiplying by its reciprocal (in this case \dpi{100} \small \frac {4}{3}).  Therefore:

\dpi{100} \small \frac {2}{3}\div \frac{3}{4} = \frac{2}{3}\times \frac{4}{3} = \frac{8}{9}

Example Question #1 : How To Divide Fractions

Evaluate the following:

Possible Answers:

None of the available answers

\frac{400}{507}

\frac{507}{400}

\frac{25}{507}

\frac{4}{5}

Correct answer:

\frac{400}{507}

Explanation:

First we will evaluate the terms in the parentheses:

Next, we will square the first fraction:

\frac{100}{169}\div \frac{3}{4}

We can evaluate the division as such:

\frac{100}{169}\times\frac{4}{3}=\frac{400}{507}

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