### All PSAT Math Resources

## Example Questions

### Example Question #1 : Operations With Fractions

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

**Possible Answers:**

*y* = 1

*y *< 1

*y* = *x*

*y* > 1

*y *< *x*

**Correct answer:**

*y* > 1

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 #2 : How To Multiply 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:**

7/9

2/3

1/3

2/9

4/9

**Correct answer:**

2/9

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 #3 : How To Multiply 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:**

1359

351

251

151

906

**Correct answer:**

151

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 #4 : How To Multiply Fractions

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:**

1/48

35/48

23/24

13/48

1/24

**Correct answer:**

35/48

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 #4 : Operations With Fractions

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

**Possible Answers:**

2,640 ft/s

264 ft/s

44 ft/s

4,400 ft/s

440 ft/s

**Correct answer:**

44 ft/s

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

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

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

**Possible Answers:**

15

4

5

16

10

**Correct answer:**

15

Since of the children are girls, this totals to girls in the group.

boys.

### Example Question #21 : Operations With Fractions

**Possible Answers:**

**Correct answer:**

Remember, when you multiply fractions, you can directly multiply their denominators and their numerators; therefore, you can begin this problem by making it into one large fraction:

Now, you *could* multiply all of this out and then divide. However, you can cancel things immediately. The goes into the and the into the . Thus, you have:

### Example Question #22 : Operations With Fractions

Simplify:

**Possible Answers:**

**Correct answer:**

First, begin by remembering that is the same as :

Next, recall that you multiply fractions by multiplying the numerators and denominators by each other. It is very simple. This would give you:

Now, you can cancel the and the :

Next, you can reduce the and the :

You can also reduce the resulting and the :

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