### All PSAT Math Resources

## Example Questions

### Example Question #1 : How To Find The Reciprocal Of A Fraction

What is the reciprocal of the following fraction: 18/27

**Possible Answers:**

-18/27

27/18

9

9/27

**Correct answer:**

27/18

A fraction multiplied by its reciprocal will equal 1. To find the reciprocal of a fraction, switch the denominator and numerator. The reciprocal of 18/27 is 27/18.

### Example Question #1 : How To Find The Lowest / Least Common Denominator

3/5 + 4/7 – 1/3 =

**Possible Answers:**

3/37

88/105

4/3

72/89

7/9

**Correct answer:**

88/105

We need to find a common denominator to add and subtract these fractions. Let's do the addition first. The lowest common denominator of 5 and 7 is 5 * 7 = 35, so 3/5 + 4/7 = 21/35 + 20/35 = 41/35.

Now to the subtraction. The lowest common denominator of 35 and 3 is 35 * 3 = 105, so altogether, 3/5 + 4/7 – 1/3 = 41/35 – 1/3 = 123/105 – 35/105 = 88/105. This does not simplify and is therefore the correct answer.

### Example Question #1 : How To Find The Lowest / Least Common Denominator

3/5 + 4/7 – 1/3 =

**Possible Answers:**

3/37

72/89

88/105

7/9

4/3

**Correct answer:**

88/105

We need to find a common denominator to add and subtract these fractions. Let's do the addition first. The lowest common denominator of 5 and 7 is 5 * 7 = 35, so 3/5 + 4/7 = 21/35 + 20/35 = 41/35.

Now to the subtraction. The lowest common denominator of 35 and 3 is 35 * 3 = 105, so altogether, 3/5 + 4/7 – 1/3 = 41/35 – 1/3 = 123/105 – 35/105 = 88/105. This does not simplify and is therefore the correct answer.

### Example Question #1 : General Fractions

**Possible Answers:**

**Correct answer:**

### Example Question #1 : General Fractions

Simplify:

**Possible Answers:**

**Correct answer:**

First, find the common denominator of the fractions in order to add them together. Looking at the first two fractions, we can see that the common denominator is 15 because 3 times five is 15. We can now change both fractions to have a denominator of 15 so that we can add them together:

Now, find a common denominator for the remaining fractions. This can be done by listing multiples of 15 and 20 and finding the lowest common multiple:

15: 15, 30, 45,** 60**, 75

20: 20, 40, **60**, 80

60 is the lowest common multiple, so it is our least common denominator.

### Example Question #1 : How To Find A Solution To A Compound Fraction

Simplify:

**Possible Answers:**

**Correct answer:**

### Example Question #1 : General Fractions

Simplify:

**Possible Answers:**

**Correct answer:**

### Example Question #141 : Arithmetic

Simplify:

**Possible Answers:**

**Correct answer:**

### Example Question #1 : How To Find A Solution To A Compound Fraction

Simplify:

**Possible Answers:**

None of the other responses gives the correct answer.

**Correct answer:**

### Example Question #1 : General Fractions

Simplify:

**Possible Answers:**

**Correct answer:**

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