# PSAT Math : Operations with Fractions

## Example Questions

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### Example Question #1 : Operations With Fractions

Define an operation  as follows:

For all real ,

.

Evaluate .

Explanation:

### Example Question #2 : Operations With Fractions

Define an operation  as follows:

For all real ,

.

Evaluate .

Explanation:

### Example Question #3 : Operations With Fractions

Define an operation  as follows:

For all real ,

Evaluate .

Explanation:

### Example Question #4 : Operations With Fractions

Define an operation  as follows:

For all real ,

.

Evaluate .

Explanation:

### Example Question #5 : Operations With Fractions

Define an operation  as follows:

For all real ,

Evaluate

Explanation:

### Example Question #6 : Operations With Fractions

Define an operation  as follows:

For all real ,

.

Evaluate .

The correct answer is not among the other responses.

The correct answer is not among the other responses.

Explanation:

This answer is not among the choices given.

### Example Question #7 : Operations With Fractions

Subtract and simplify the fractions:

Explanation:

First we need to give them common denominators. Remember, whatever you do to the denominator you must do to the numerator:

From here, we do algebraic operations to subtract and simplify.

### Example Question #8 : Operations With Fractions

Simplify:

a/b/c/d

ac/bd

a2/c2

It is already in simplest terms

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 : Operations With 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?

17

20

18

19

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 #10 : Operations With Fractions

If  and , then what is the value of ?