Question

12 × 2² - 18.4 + 0.6 5² - 0.2 × 8 + 12 × ½ 19 + 1⁵ + ½ + 5

1. nikki’s backyard is in the shape of a rectangle. the length is 27 feet. the width is one - third the length plus 4 feet. write and evaluate an expression to find the area of nikki’s backyard.
2. make sense and persevere write a numerical expression, with at least three operations, that has the same value as (12 - 9)² × (4 + 3). justify your answer.
3. critique reasoning ivy’s basketball team scored 38 points in the first game of the season. in the next two games they scored a total of 77 points. for every point scored, $0.50 is put in a jar to use for a party after the season. ivy says that you can use the expression 38 + 77 × 0.5 to find how much money is in the jar after the third game. is she correct? explain.
4. a printing error in a math book removed the brackets and parentheses from a numerical expression. rewrite the expression 3² + 7 × 4 + 5 with parentheses so that it is equivalent to 69.

Explanation:

Problem 10

Step1: Define width variable

Length $l = 27$ ft. Width $w = \frac{1}{3}l + 4$

Step2: Calculate width value

$w = \frac{1}{3} \times 27 + 4 = 9 + 4 = 13$ ft

Step3: Calculate area of rectangle

Area $A = l \times w$
$A = 27 \times 13 = 351$

First calculate the value of $(12 - 9)^2 \times (4 + 3)$: $(3)^2 \times 7 = 9 \times 7 = 63$. We need a numerical expression with at least three operations that equals 63. For example, we can use multiplication, addition, and subtraction: multiply two numbers, add a value, then subtract another to reach 63.

Total points after three games are the sum of points from all three games: $38 + 77 = 115$ points. The correct expression for total money is total points multiplied by $0.50$, which is $(38 + 77) \times 0.50$. Ivy's expression $38 + 77 \times 0.5$ calculates 38 plus half of 77, which is not the total points times 0.50.

Answer:

The area of Nikki's backyard is 351 square feet.

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Problem 11