### All HSPT Math Resources

## Example Questions

### Example Question #1 : How To Add And Subtract Fractions

The time is now 11:17 AM. What time will it be in three hours and twenty-four minutes?

**Possible Answers:**

**Correct answer:**

The time is 11:17 AM. In 24 minutes, the minutes will read , so it wil be 11:41 AM. Let's then add three hours to it.

The time will be 2:41 PM.

### Example Question #1 : How To Find The Solution To An Equation

For a party, Marco buys 4 boxes of cookies, each containing 10 cookies. Marco gives each of his guests 3 cookies, and then he eats 6 cookies himself. He now has 4 cookies left. How many guests did Marco give cookies to?

**Possible Answers:**

**Correct answer:**

He begins with 40 and ends with 4, so 36 cookies total were eaten. Since he ate 6 himself, that means that his guests ate 30. Since each guest ate 3 cookies, guests.

### Example Question #1 : Fractions

Adam has 3 siblings. When his mother bakes a cake, each of the 4 children is given ¼ of the cake. Adam only finished 1/3 of his share of cake. If the original cake had 12 slices, how many slices did Adam eat?

**Possible Answers:**

3

1

4

6

2

**Correct answer:**

1

Each of the children gets 1/4 of the cake. Taking 1/4 of 12 shows that each child gets 3 slices. If Adam finishes 1/3 of his share, then he has eaten one out of the 3 slices.

### Example Question #1 : How To Find A Complex Fraction

Steven purchased of vegetables on Monday and of vegetables on Tuesday. What was the total weight, in pounds, of vegetables purchased by Steven?

**Possible Answers:**

**Correct answer:**

To solve this answer, we have to first make the mixed numbers improper fractions so that we can then find a common denominator. To make a mixed number into an improper fraction, you multiply the denominator by the whole number and add the result to the numerator. So, for the presented data:

and

Now, to find out how many total pounds of vegetables Steven purchased, we need to add these two improper fractions together:

To add these fractions, they need to have a common denominator. We can adjust each fraction to have a common denominator of by multiplying by and by :

To multiply fractions, just multiply across:

We can now add the numerators together; the denominator will stay the same:

Since all of the answer choices are mixed numbers, we now need to change our improper fraction answer into a mixed number answer. We can do this by dividing the numerator by the denominator and leaving the remainder as the numerator:

This means that our final answer is .

### Example Question #1 : How To Add And Subtract Fractions

**Possible Answers:**

**Correct answer:**

To solve, convert all mixed numbers to improper fractions:

Because the denominators are not the same you have to find the Least Common Multiple, which is the Least Common Denominator of 3 and 6, which is 6. Then convert both fractions, if needed, to equivalent fractions with 6 as the denominator.

These are equivalent because the numerator and the denominator have been multiplied by 2 to get the equivalent fraction.

The answer is negative because the numerator with the greatest absolute value is -38 and that is a negative number.

### Example Question #1 : How To Add And Subtract Fractions

**Possible Answers:**

**Correct answer:**

The subtraction of a negative changes the subtraction sign to a positive.

Find the LCD of 3 and 4 and convert to equivalent fractions, with the LCD as the denominator for both fractions.

The LCD is 12.

The numerator and the denominator were multiplied by 4.

The numerator and the denominator were multiplied by 3.

Because the absolute value of 9 is greater than the absolute value of -4, the answer is positive.

### Example Question #4 : How To Add And Subtract Fractions

Evaluate if and .

**Possible Answers:**

**Correct answer:**

Evaluate if and .

First, convert any mixed numbers to improper fractions.

In order to solve, find the common denominator of 8 and 6. This is found by listing the multiples and picking the LCM or the least common multiple. This becomes the LCD or Least Common Denominator.

Multiples of 8 are 8, 16, 24.

Multiples of 6 are 6, 12,18, and 24.

The LCM or the LCD will be 24.

Create equivalent fractions for both with 24 as the denominator,

Both numerator and denominator were multiplied by 3.

Both numerator and denominator were multiplied by 4.

When adding two negatives, the result is negative.

### Example Question #1 : How To Add And Subtract Fractions

**Possible Answers:**

**Correct answer:**

Change all whole numbers and mixed numbers to improper fractions.

When there is a whole number, just place the number 1 underneath the fraction bar as the denominator.

Because the denominators are different, create equivalent fractions by using the Least Common Denominator. The LCD of 8 and 1 is 8.

does not have to be changed, because the denominator is already the LCD, which is 8.

Now that the denominators are the same, subtract.

### Example Question #1 : How To Add And Subtract Fractions

Evaluate if and .

**Possible Answers:**

**Correct answer:**

Evaluate if and

The subtraction of a negative changes the operation from subtraction to addition.

Find the Least Common Multiple of 7 and 5.

Multiples of 7 are 7, 14, 21, 28, 35.

Multiples of 5 are 5, 10, 15, 20 ,25, and 35.

You can also just multiply the denominators.

The LCM or the LCD of 7 and 5 is 35.

Create equivalent fractions with 35 as the denominator.

Both the numerator and denominator were multiplied by 5.

Both the numerator and denominator were multiplied by 7.

Now that the denominators are the same, just add the numerators.

### Example Question #2 : Fractions

**Possible Answers:**

**Correct answer:**

Convert all mixed numbers to improper fractions.

Because all of the denominators are not the same find the LCM. This will become the LCD or Least Common Denominator.

Multiples of 8 are 8,16,24,32.

Multiples of 16 are 16, 32, 48.

Multiples of 4 are 4, 8, 12, 16.

The Least Common Multiple of 8,16 and 4 is 16. The LCD is 16.

The numerator and denominator were both multiplied by 2.

The numerator and the denominator were both multiplied by 4.

Now, that all of the fractions have the same denominator, add the numerators.