### All HSPT Math Resources

## Example Questions

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

One Australian dollar is equal to about 86 cents. To the nearest whole, for how many Australian dollars can a tourist to Australia expect to exchange $600 in American money?

**Possible Answers:**

**Correct answer:**

One Australian dollar is equivalent to 86 cents, or $0.86, in American money, so divide $600 dollars by this conversion factor. $600 is equivalent to

Australian dollars.

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

On average, 1 in 9 peanuts that are harvested will only have one pod instead of two pods. Of those one-pod peanuts, three quarters of them will be smaller than the average peanut.

If 900 peanuts are harvested, how many will be one-pod peanuts that are smaller than average in size?

**Possible Answers:**

**Correct answer:**

If there are 900 peanuts and 1 in 9 will be one-podded, that means that 100 will be one-podded.

Three quarters of these 100 one-podded peanuts will be of smaller than average size. Three quarters of of 100 is 75. Therefore, 75 is the correct answer.

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

A small bakery sells two flavors of muffins: chocolate and banana.

At the end of the day, there are 13 muffins left.

There are chocolate muffins and banana muffins.

If

how many banana muffins are left?

**Possible Answers:**

**Correct answer:**

The first step is to solve for x.

If there are 1x chocolate muffins and 2y banana muffins, for a total of 13 muffins then:

Since the number of banana muffins remaining is 2y, there are 12 banana muffins left.

### Example Question #2 : How To Solve Arithmetic Word Problems

of a class of 36 students are boys. If 2 girls and 4 boys were to drop the class, what percentage of the class would be girls?

**Possible Answers:**

75%

70%

65%

55%

60%

**Correct answer:**

60%

First determine how many boys and girls are currently in the class.

boys in the class, which means that there are 20 girls.

When the 6 students drop the new class size will be 30, which will be made up of girls and boys.

### Example Question #12 : Algebraic Concepts

How many seconds are in of one minute?

**Possible Answers:**

30

4

5

15

**Correct answer:**

4

To find of one minute in terms of seconds, you need to first convert one minute to its value in seconds, which is 60 seconds.

Now, you just need to find the value for of 60, which you determine by multiplying the two values:

You can simplify the above fraction by division, which will you give you your correct answer in seconds:

Your answer is **4 **seconds.

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

Multiply:

**Possible Answers:**

**Correct answer:**

Since we are multiply fractions, multiply the numerator with numerator, and denominator with denominator. Simplify if possible.

### Example Question #41 : Arithmetic

Divide:

**Possible Answers:**

**Correct answer:**

Rewrite the expression using a division sign.

Convert the sign to a multiplication sign, and take the inverse of the second term.

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

A tree feet high casts a shadow 20 feet long at the same time a tree 30 feet high casts a shadow how many feet long? Give your answer in terms of .

**Possible Answers:**

**Correct answer:**

The ratio of the height of an object to the length of the shadow it casts at a point in time is the same for all objects, so, if we let the length of the shadow cast by the second tree be :

Set the cross-products equal to each other and solve for

, the correct choice.

### Example Question #21 : Fractions

The length and width of a given make of car are 4.5 and 1.8 meters, respectively.

A scale model of this make of car will be feet long. In terms of , how wide will this scale model be?

**Possible Answers:**

**Correct answer:**

The ratio of the width of the scale model to its length is the same as the comparable ratio for the actual car, so we can set up this equation:

### Example Question #2 : How To Multiply And Divide Fractions

Edna needs cups of sugar to make 24 of her world-famous Oatmeal Chocolate Dynamite Cookies.

She has cups of sugar on hand. If the other ingredients are sufficiently plentiful, then in terms of , how many cookies can she make? (Note: the number of cookies need not be a multiple of 24.)

**Possible Answers:**

**Correct answer:**

An easier way to look at the number of cookies Edna can make with her sugar is as follows:

cups of sugar go into making 24 cookies, so

cups of sugar go into making cookies.

1 cup of sugar, therefore, goes into making cookies.

cups go into making , or , cookies. This is the correct response.

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