# FREE PACT Mathematics Questions and Answers

#### Which set of numbers shows four factors of 16?

Explanation:

Factors are the numbers that when multiplied together provide the result. Zero is not a factor of any number. Answer C provides multiples of 16.

#### Sean and Hillary are baking cookies for a bake sale. Sean baked 48 chocolate chip cookies, and Hillary baked 36 sugar cookies. If 50 cookies were sold altogether, how many were left over at the end of the bake sale?

Explanation:

First, write an equation to represent the word problem. This scenario can be represented by the equation 48 + 36 - 50 =
______. First, add the first two integers in the problem, 48 and 36. Write the problem vertically, making sure to line up the numbers according to place value. Start by adding the ones column to the right. Since 8 + 6 = 14, write 4 in the ones place as part of the answer and carry the 1 over to the tens place column. Next, add the tens column. Since 1 + 4 + 3 = 8, write 8 in the tens place as part of the answer. Therefore, 48 + 36 = 84.

From here, subtract the next integer from the original problem, 50, from 84. Write the problem vertically, making sure to line up the numbers according to place value. Start by subtracting the ones column on the right. Since 4 - 0 =4, write 4 in the ones column as part of the answer. From here, move to the tens column and subtract. Since 8 - 5 = 3, write 3 in the tens place as part of the answer, 48 + 36 - 50 = 34. There were 34 cookies left over after the bake sale.

#### The sum of three consecutive integers is 39. What is the smallest of these integers?

Explanation:

Let ๐ be the smallest integer, then ๐ + (๐ + 1) + (๐ + 2) = 39, 3๐ + 3 = 39, 3๐ = 36, ๐ = 12.

#### What is the value of 3x โ 7 when x = 5?

Explanation:

To find the value of 3๐ฅ โ 7 when ๐ฅ = 5, substitute ๐ฅ = 5 into the expression:

3 (5) โ 7

= 15 โ 7

= 15 โ 7

= 8

#### What is the area of a rectangle with a length of 8 cm and a width of 5 cm?

Explanation:

The area of a rectangle is calculated by multiplying its length by its width: 8 cm ร 5 cm = 40 cmยฒ.

#### Solve for x in the equation 2x + 5 = 17.

Explanation:

Subtract 5 from both sides to isolate 2๐ฅ, then divide both sides by 2: 2๐ฅ = 17 โ 5 = 12, ๐ฅ = 6.

#### In the base -5 number system, what is the sum of 303 and 2222?

Explanation:

The sum is written as:

2 2 2 2

+ 3 0 3

โโโโ

3 0 3 0

The sum of 2 and 3 equals 5, which must be represented as a 10. In the base-5 number system, a number cannot contain any 5's. The 1 of each 10 is carried to the next column to the left.

#### Mary's basketball team is losing tonight's game 42-15. Mary scores a three-point shot. How many more three-point shots will someone on her team have to score in order to tie the game?

Explanation:

To solve, first add Mary's shot to the score: 42-18. Subtract the figures to see how many points still need to be scored: 42 - 18 = 24. Divide by three, since three points are attained with each shot: 24 รท 3 = 8.

#### Put the following decimal numbers in order from least to greatest:

-1.32 0.014 0.31 0.308 -0.42 0

Explanation:

To order these numbers, first order the negative numbers from least to greatest. Remember, the largest negative number is the smallest.

-1.32, - 0.42

Then, 0 will separate the negative numbers from the positive numbers.

Finally, order the positive numbers from least to greatest.

0.014, 0.308, 0.31

The numbers ordered from least to greatest are: -1.32, - 0.42, 0, 0.014, 0.308, 0.31.

#### The perimeter of a square is 24 cm. What is the length of one side?

Explanation:

For a square, the perimeter is the sum of all four sides. Since all sides of a square are equal in length:

Perimeter = 4 ร Side Length

Given that the perimeter is 24 cm:
24 cm = 4 ร Side Length

24 cm = 4 ร Side Length

To find the length of one side, divide the perimeter by 4:

Side Length = 24 cm/4
Side Length = 6 cm

#### Which of the following is an example of the commutative property?

Explanation:

An operation is commutative if changing the order of the terms does not change the result. Addition and multiplication are commutative. Therefore, 8 + 12 = 12 + 8 is an example of the commutative property.