Question

lessons 2.3-2.4 review & refresh (continued)

1. a gray rock weighs 2.62 ounces. a black rock weighs 2.618 ounces. a red rock weighs 2.588 ounces. list the rocks in order from the lightest to the heaviest.
2. you have 0.402 liter of milk, 0.42 liter of juice, and 0.248 liter of water. list the drinks in order from the least amount to the greatest amount.

complete the equation. identify the property shown.

1. ____ × 12 = 0
2. (3 + 6) + 5 = ____ + (6 + 5)

complete each statement.

1. ____ is 100 times as great as 0.475.
2. ____ is \\(\frac{1}{100}\\) of 32.4.

tell whether each equation is true or false.

1. 54 ÷ 6 + 3 \\(\stackrel{?}{=}\\) 54 ÷ (6 + 3)
2. 36 ÷ 6 + 6 \\(\stackrel{?}{=}\\) 2 + (5 × 2)
3. 4 + 5 × 6 \\(\stackrel{?}{=}\\) 6 × 5 + 4
4. 60 ÷ (7 − 2) + 3 \\(\stackrel{?}{=}\\) (50 − 5) ÷ (1 + 2)

Explanation:

Step1: Compare rock weights

$2.588 < 2.618 < 2.62$

Step2: Order rocks light to heavy

Red rock < Black rock < Gray rock

Step3: Compare drink volumes

$0.248 < 0.402 < 0.42$

Step4: Order drinks least to greatest

Water < Milk < Juice

Step5: Solve for missing factor

$0 \times 12 = 0$; Property: Zero Property of Multiplication

Step6: Match associative property

$(3 + 6) + 5 = 3 + (6 + 5)$; Property: Associative Property of Addition

Step7: Calculate 100×0.475

$100 \times 0.475 = 47.5$

Step8: Calculate 32.4÷100

$\frac{32.4}{100} = 0.324$

Step9: Evaluate left side of #17

$54 \div 6 + 3 = 9 + 3 = 12$

Step10: Evaluate right side of #17

$54 \div (6 + 3) = 54 \div 9 = 6$

Step11: Compare #17 results

$12
eq 6$, so False

Step12: Evaluate left side of #18

$36 \div 6 + 6 = 6 + 6 = 12$

Step13: Evaluate right side of #18

$2 + (5 \times 2) = 2 + 10 = 12$

Step14: Compare #18 results

$12 = 12$, so True

Step15: Evaluate left side of #19

$4 + 5 \times 6 = 4 + 30 = 34$

Step16: Evaluate right side of #19

$6 \times 5 + 4 = 30 + 4 = 34$

Step17: Compare #19 results

$34 = 34$, so True

Step18: Evaluate left side of #20

$60 \div (7 - 2) + 3 = 60 \div 5 + 3 = 12 + 3 = 15$

Step19: Evaluate right side of #20

$(50 - 5) \div (1 + 2) = 45 \div 3 = 15$

Step20: Compare #20 results

$15 = 15$, so True

Answer:

1. Red rock, Black rock, Gray rock
2. Water, Milk, Juice
3. $0$; Zero Property of Multiplication
4. $3$; Associative Property of Addition
5. $47.5$
6. $0.324$
7. False
8. True
9. True
10. True