PSAT Math : How to divide fractions

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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Example Question #1 : Operations With Fractions

Simplify:

  Sat_math_167_03

 

 

Possible Answers:

ac/bd

a/b/c/d

It is already in simplest terms

a2/c2

ad/bc

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 #2 : 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:

18

17

20

19

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 : How To Divide 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 2

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

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

\dpi{100} \small \frac{1}{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 : Operations With Fractions

Evaluate the following:

Possible Answers:

\frac{25}{507}

\frac{4}{5}

\frac{400}{507}

None of the available answers

\frac{507}{400}

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}

Example Question #111 : Arithmetic

Simplify: 

Possible Answers:

Correct answer:

Explanation:

Start by rewriting this fraction as a division problem:

When dividing fractions, you multiply by the reciprocal of the second fraction, so you can rewrite your problem like this:

Multiply across the numerators and then across the denominators to get . The x's cancel, and you can reduce the fraction to be .

Example Question #112 : Arithmetic

Define an operation  as follows:

For all real numbers ,

.

Evaluate .

Possible Answers:

Correct answer:

Explanation:

, or, equivalently,

Example Question #113 : Arithmetic

Define an operation  as follows:

For all real numbers ,

.

Evaluate .

Possible Answers:

Correct answer:

Explanation:

,

or, equivalently, 

 

Example Question #114 : Arithmetic

Define an operation  as follows:

For all real numbers ,

.

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Example Question #115 : Arithmetic

Define an operation  as follows:

For all real numbers ,

.

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Example Question #116 : Arithmetic

Define an operation  as follows:

For all real numbers ,

.

Evaluate .

Possible Answers:

The correct answer is not among the other responses.

Correct answer:

Explanation:

or, equivalently,

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