### All PSAT Math Resources

## Example Questions

### Example Question #1 : Operations With Fractions

Simplify:

**Possible Answers:**

a/b/c/d

It is already in simplest terms

ad/bc

a^{2}/c^{2}

ac/bd

**Correct answer:**

ad/bc

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

### Example Question #5 : 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?

**Possible Answers:**

19

17

18

20

**Correct answer:**

17

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 #6 : Operations With Fractions

If and , then what is the value of ?

**Possible Answers:**

**Correct answer:**

Dividing by a number (in this case ) is equivalent to multiplying by its reciprocal (in this case ). Therefore:

### Example Question #1 : Operations With Fractions

Evaluate the following:

**Possible Answers:**

None of the available answers

**Correct answer:**

First we will evaluate the terms in the parentheses:

Next, we will square the first fraction:

We can evaluate the division as such:

### Example Question #1 : How To Divide Fractions

Simplify:

**Possible Answers:**

**Correct answer:**

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 #111 : Arithmetic

Define an operation as follows:

For all real numbers ,

.

Evaluate .

**Possible Answers:**

**Correct answer:**

, or, equivalently,

### Example Question #3 : How To Divide Fractions

Define an operation as follows:

For all real numbers ,

.

Evaluate .

**Possible Answers:**

**Correct answer:**

,

or, equivalently,

### Example Question #4 : How To Divide Fractions

Define an operation as follows:

For all real numbers ,

.

Evaluate .

**Possible Answers:**

**Correct answer:**

### Example Question #5 : How To Divide Fractions

Define an operation as follows:

For all real numbers ,

.

Evaluate .

**Possible Answers:**

**Correct answer:**

### Example Question #111 : Fractions

Define an operation as follows:

For all real numbers ,

.

Evaluate .

**Possible Answers:**

The correct answer is not among the other responses.

**Correct answer:**

or, equivalently,

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