7th Grade Graded Quiz #5

Sandy has $200 in her bank account.

If she writes 6 checks for exactly $19.98, what "expression" describes the change in her bank account?

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Answer explanation

Sandy has $200 in her bank account.
If she writes 6 checks for exactly $19.98, what "expression" describes the change in her bank account?

This problem is asking you to create an expression so you are trying to turn a word problem into a math equation.

The correct answer to represent this situation is
$6\left(-19.98\right)$

Sandy has $200 in her bank account. If she writes 6 checks for exactly $19.98, what is her account balance after the checks are cashed?

Answer explanation

Sandy has $200 in her bank account. If she writes 6 checks for exactly $19.98, what is her account balance after the checks are cashed?

Using the expression from the last problem $6\left(-19.98\right)$ to find out how much she spent you take that amount and subtract it from the total to find how much she has left. $200-119.88=80.12$

Explain, in words, how to find the product of $-4\left(-1.5\right)$ using a number line. Where do you end up?

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Answer explanation

Explain, in words, how to find the product of $-4\left(-1.5\right)$ using a number line. Where do you end up?

Your answer should have sounded similar to this.

Start at 0, then move  $1.5$  units to the left (because  $1.5$  is negative)  $4$  times. You are now on  $-6$ . Then find the opposite of  $-6$ , which is  $6$  

Greg sets his watch for the correct time on Wednesday. Exactly one week later, he finds that his watch has lost  $3\frac{1}{4}$ minutes. What is the overall change in time after 8 weeks?

Answer explanation

Greg sets his watch for the correct time on Wednesday. Exactly one week later, he finds that his watch has lost  $3\frac{1}{4}$ minutes. What is the overall change in time after 8 weeks?

First, you must convert  $3\frac{1}{4}$  to an improper fraction so  $3\frac{1}{4}=\frac{13}{4}$  .
Second, you multiply your improper fraction by 8 weeks  $\frac{13}{4}\times8=\frac{104}{4}$  .
Finally, YOU ALWAYS SIMPLIFY  $\frac{104}{4}=26$  

A submarine dives below the surface, heading downward in three moves. If each move downward was 325 feet, where is the submarine after it is finished diving?

Answer explanation

A submarine dives below the surface, heading downward in three moves. If each move downward was 325 feet, where is the submarine after it is finished diving?

Since the submarine is moving "downward" by 325 feet each time that number is negative. So, all you do is multiply this by 3 times since the submarine went down 3 times.

$-325\times3=-975$

For Home Economics class, Sandra has 5 cups of flour. She made 3 batches of cookies that each used 1.5 cups of flour. Write and solve an expression to find the amount of flour Sandra has left after making the 3 batches of cookies.

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Answer explanation

For Home Economics class, Sandra has 5 cups of flour. She made 3 batches of cookies that each used 1.5 cups of flour. Write and solve an expression to find the amount of flour Sandra has left after making the 3 batches of cookies.

You start out with 5 cups so we will place that number first. $5$
Next, we place a subtraction sign because this problem is asking us to find a "difference". $5-$
Finally, we see that "each" batch of cookies used 1.5 cups of flour so that is multiplication. $5-3\left(1.5\right)$
So your answer should have been

$5-3\left(1.5\right)=0.5$

In class, Matthew stated, “I think that a negative is like an opposite. That is why multiplying a negative times a negative equals a positive. The opposite of negative is positive, so it is just like multiplying the opposite of a negative twice, which is two positives.” Do you agree or disagree with this statement? What would you say in response to him?

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Answer explanation

In class, Matthew stated, “I think that a negative is like an opposite. That is why multiplying a negative times a negative equals a positive. The opposite of negative is positive, so it is just like multiplying the opposite of a negative twice, which is two positives.” Do you agree or disagree with this statement? What would you say in response to him?

By Matthew’s definition, all negatives would be positive because of his opposite assumption, which is incorrect. The opposite refers to the distance from $0$ . $-7$ is the opposite of $7$ , but it is not the same thing as $7$ .

Kaitlin is on a long car trip. Every time she stops to buy gas, she loses 15 minutes of travel time. If she has to stop 5 times, how many minutes late will she be getting to her destination?

Answer explanation

Kaitlin is on a long car trip. Every time she stops to buy gas, she loses 15 minutes of travel time. If she has to stop 5 times, how many minutes late will she be getting to her destination?
$15\times5=75$

The table shows the scoring system for quarterbacks in Jeremy’s fantasy football league. In one game, Jeremy’s quarterback had 2 touchdown passes, 16 complete passes, 7 incomplete passes, and 2 interceptions. How many total points did Jeremy’s quarterback score?

Answer explanation

The table shows the scoring system for quarterbacks in Jeremy’s fantasy football league. In one game, Jeremy’s quarterback had 2 touchdown passes,

$2\left(6\right)$

16 complete passes,

$16\left(0.5\right)$

7 incomplete passes,

$7\left(-0.5\right)$

and 2 interceptions.

$2\left(-1.5\right)$

How many total points did Jeremy’s quarterback score?
$2\left(6\right)+16\left(0.5\right)+7\left(-0.5\right)+2\left(-1.5\right)=13.5$

The ground temperature at Brigham Airport is 12 °C. The temperature decreases by 6.8 °C for every increase of 1 kilometer above the ground. What is the temperature outside a plane flying at an altitude of 5 kilometers?

Answer explanation

The ground temperature at Brigham Airport is 12 °C. The temperature decreases by 6.8 °C for every increase of 1 kilometer above the ground. What is the temperature outside a plane flying at an altitude of 5 kilometers?

For this problem you take the current temperature 12 °C and add the change in temperature. Since the temperature "decreases" as the plane goes up the 6.8 °C is negative. Since, the temperature "decreases" for "every" 1 kilometer the plane rises you multiply $-6.8$ by $5$ . So your equation should look like

$12+5\left(-6.8\right)=-22$ .