6th Math Unit 2 Review (Positive Rational Numbers)

Mark is having a birthday party. He bought 8 pizzas to be shared equally among 40 people. Which two equivalent representations could be used to determine how much pizza each guest will receive?

• 8 ÷ 40 = 40/8

• 8 ÷ 40 = 8/40

• 40 ÷ 8 = 40/8

• 40 ÷ 8 = 8/40

Answer explanation

The correct choice is 8 ÷ 40 = 8/40. This shows that dividing the total pizzas (8) by the number of people (40) gives the same result as the fraction of pizzas per person (8/40).

Ann cut her king-size chocolate bar into 12 equal parts. She ate 7 parts. Which equation shows two equivalent ways to represent how much chocolate is left from Ann’s chocolate bar?

• 5 ÷ 12 = 5/12

• 7 ÷ 12 = 7/12

• 12 ÷ 5 = 12/5

• 12 ÷ 7 = 12/7

Answer explanation

Ann has 12 parts and eats 7, leaving her with 5 parts. The equation 5 ÷ 12 = 5/12 shows the fraction of the chocolate bar left, representing the same amount in two equivalent forms.

Which two expressions represent 7/21?

• 7/21 and 7 ÷ 21

• 21/7 and 21 ÷ 7

• 21/7 and 7 ÷ 21

• 7/21 and 21 ÷ 7

Answer explanation

The expression 7/21 is equivalent to 7 divided by 21, which is represented as 7 ÷ 21. Therefore, the correct choice is 7/21 and 7 ÷ 21.

Willie and two of his friends earn money mowing lawns in their neighborhood. On Saturday, they mowed two lawns and were paid $28. If Willie and his friends split the earnings equally, which expression does NOT equal how much Willie will receive from working on Saturday?

• 28/3

• 28 ÷ 3

• 3/28

Answer explanation

Willie and his friends earned $28, which they split equally among three people. The correct expression for Willie's share is 28 ÷ 3 or 28/3. The expression 3/28 does not represent his share, as it implies a different calculation.

• 3/5 x 9/7

• 5/9 × 7/3

• 7/9 ÷ 5/3

• 9/5 × 7/3

Answer explanation

To divide fractions, multiply by the reciprocal. Thus, 3/5 ÷ 7/9 is equivalent to 3/5 x 9/7. Therefore, the correct choice is 3/5 x 9/7.

• 4

• 1/4

• 25

• 1/25

Answer explanation

To solve for the missing value, we can rewrite the equation as 5/7 × 0.25 = 5/7 ÷ x. This simplifies to 0.25 = 1/x. Thus, x = 1/0.25 = 4. Therefore, Luke should place 4 in the box.

Answer explanation

To find the number of holes, we divide the total length by the distance between holes. The expression can be rewritten as \(4\frac{1}{2} \div \frac{3}{8} = \frac{9}{2} \times \frac{8}{3}\), confirming the correct choice.

• The product is greater than 5.

Answer explanation

To find the product of \( \frac{3}{4} \) and \( \frac{16}{5} \), calculate \( \frac{3 \times 16}{4 \times 5} = \frac{48}{20} = \frac{12}{5} \). Since \( \frac{12}{5} = 2.4 \), it is between \( \frac{16}{5} \) and 5.

Sheryl’s magnolia tree grows 1.68 feet per year. Her oak tree grows 2.5 times faster than her magnolia tree. Based on this information, which statement is true?

• Sheryl’s oak tree grows 4.18 feet per year, because 1.68 + 2.5 = 4.18.

• Sheryl’s oak tree grows 1.93 feet per year, because 1.68 + 2.5 = 1.93.

• Sheryl’s oak tree grows 11.76 feet per year, because 1.68 x 2.5 = 11.76.

• Sheryl’s oak tree grows 4.173 feet per year, because 1.68 x 2.5 = 4.2.

Answer explanation

Sheryl’s oak tree grows 1.68 x 2.5 = 4.2 feet per year. The correct choice states this calculation, confirming that the oak tree grows 4.173 feet per year, which is a rounded version of 4.2.

What is the percent of the shaded region in the figure? 

• 60%

• 12%

• 40%

• 8%

Answer explanation

To find the percent of the shaded region, divide the area of the shaded part by the total area and multiply by 100. If the shaded area is 60% of the total, the correct answer is 60%.