Which of these situations illustrates two quantities that combine to make 0?(1 point)
Responses
Mariah lost ten pounds and then gained 6 pounds.
Mariah lost ten pounds and then gained 6 pounds.
A business whose expenses are more than their profit.
A business whose expenses are more than their profit.
Sarah gets 10 dollars for her allowance and then spends 10 dollars at the movies.
Sarah gets 10 dollars for her allowance and then spends 10 dollars at the movies.
Marcus scores 900 points playing a video game and then loses over half of those points.
Marcus scores 900 points playing a video game and then loses over half of those points.
On a number line, what is the distance between -67 and 14?(1 point)
Responses
53
53
81
81
-81
-81
-53
81
Madison has $650 in her account. She makes a $350 withdrawal, deposits $100, and then gets charged a $20 fee. How much does she have in her account?(1 point)
Responses
$440
$440
$330
$330
$380
$380
$490
$490
Question 2
6. On Friday morning the temperature was 67°F. The temperature dropped 6°F and then rose 10°F. How much does the temperature need to rise or fall to return to the initial temperature of 67°F?(1 point)
Responses
Fall 4°
Fall 4°
Rise 4°
Rise 4°
Rise 6°
Rise 6°
Fall 10°
The correct response is: $380
Explanation:
Starting with $650, Madison makes a $350 withdrawal, which leaves her with $300.
After depositing $100, her account balance becomes $400.
Finally, she gets charged a $20 fee, so her final account balance is $380.
Question 2
6. On Friday morning the temperature was 67°F. The temperature dropped 6°F and then rose 10°F. How much does the temperature need to rise or fall to return to the initial temperature of 67°F?(1 point)
Responses
Fall 4°
Fall 4°
Rise 4°
Rise 4°
Rise 6°
Rise 6°
Fall 10°
The correct response is: Rise 6°
Explanation:
The temperature starts at 67°F. It then drops 6°F, bringing it to 67°F - 6°F = 61°F.
To return to the initial temperature of 67°F, the temperature needs to rise by 67°F - 61°F = 6°F.
. The Snake Eyes Roller Coaster climbs 125 feet from ground level then drops 60 feet before climbing another 135 feet. How far does the coaster need to drop or climb to be back at ground level? (Hint: Draw a picture or use a number line.)(1 point)
Responses
Climb 200 feet
Climb 200 feet
Drop 200 feet
Drop 200 feet
Climb 50 feet
Climb 50 feet
Drop 50 feet
The correct response is: Drop 50 feet
Explanation:
The coaster starts at ground level, climbs 125 feet, drops 60 feet, and then climbs another 135 feet.
To find out how far the coaster needs to drop or climb to be back at ground level, we can add up the total climbs and subtract the total drops: 125 + 135 - 60 = 200 feet.
However, since the question asks for the distance in terms of dropping or climbing, we take the absolute value of 200, which is 200 feet. But since the coaster needs to return to ground level, it needs to drop, not climb. Therefore, the correct answer is Drop 200 feet.
Before it started to rain, Amnar cut 1/6
of the grass and Aayush cut 1/3
of the grass.
Which statement is true?
(1 point)
Responses
The boys cut exactly half of the yard.
The boys cut exactly half of the yard.
Together the boys cut three-fourths of the yard.
Together the boys cut three-fourths of the yard.
The boys cut almost the whole yard.
The boys cut almost the whole yard.
Together the boys didn’t even cut half of the yard.
The correct response is: Together the boys cut three-fourths of the yard.
Explanation:
Amnar cut 1/6 of the grass, and Aayush cut 1/3 of the grass. To find out how much grass they cut together, we need to add these fractions: 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2.
Therefore, the boys together cut half of the yard, which can be represented as "Together the boys cut three-fourths of the yard."
The Sweet Surprise Bake Shop sold slices of cake at the arts festival last weekend. Each cake was cut into eight slices. They sold 214
chocolate cakes, 212
red velvet cakes, 34
of a carrot cake and 312
sugar cream cakes.
Which statement tells the total number of cakes they sold and explains how the total can be calculated?
(1 point)
Responses
First, add across the numerators and denominators: 14+12+34+12=612
. Next, add whole numbers: 2 + 2 + 3 = 7. Then combine, 7612=712
.
First, add across the numerators and denominators: 1 fourth plus 1 half plus 3 fourths plus 1 half is equal to 6 over 12 . Next, add whole numbers: 2 + 2 + 3 = 7. Then combine, 7 and 6 over 12 is equal to 7 and 1 half .
First, change the numerators to 3 to make them common, and then add: 234+232+34+334=71214
. Next, simplify: 71214=767
.
First, change the numerators to 3 to make them common, and then add: 2 and 3 fourths plus 2 and 3 halves plus 3 fourths plus 3 and 3 fourths is equal to 7 and 12 over 14. Next, simplify: 7 and 12 over 14 is equal to 7 and 6 sevenths .
First, change the fractions to make denominators common, and then add: 214+224+34+324=784
. Next, simplify: 784=9
.
First, change the fractions to make denominators common, and then add: 2 and 1 fourth plus 2 and 2 fourths plus 3 fourths plus 3 and 2 fourths is equal to 7 and 8 fourths . Next, simplify: 7 and 8 fourths is equal to 9 .
First, find the least common multiple and change only the denominators: 214+214+34+314=764
. Next, simplify: 764=812
.
The correct response is: First, add across the numerators and denominators: 214+212+34+312=772. Next, add whole numbers: 2 + 2 + 0 + 3 = 7. Then combine: 7727=109.
Explanation:
To find the total number of cakes sold, we need to add the individual counts for each type of cake: 214 + 212 + 34 + 312 = 772.
Then, we add the corresponding whole numbers: 2 + 2 + 0 + 3 = 7.
Combining these results, we get 7727, which means a total of 109 cakes were sold.
Mrs. Taylor is crocheting a blanket for her daughter. She made 3/8
of the blanket green, 1/4
of the blanket blue, and the rest of the blanket was yellow. Which fraction represents the yellow part of the blanket?(1 point)
Responses
3/4
3 fourths
3/8
3 eighths
5/8
5 eighths
1/2
The correct response is: 5/8
Explanation:
Mrs. Taylor made 3/8 of the blanket green and 1/4 of the blanket blue. To find the fraction that represents the yellow part of the blanket, we need to subtract the fractions of green and blue from 1 (since the yellow part is the remaining part of the blanket).
1 - 3/8 - 1/4 = 8/8 - 3/8 - 2/8 = 5/8
The yellow part of the blanket is represented by the fraction 5/8.
. For Aliyah’s graduation party, her mom made her a chocolate cake. Her siblings ate 1/4
of the cake, and her friends ate 2/3
of the cake. How much of the cake was left?(1 point)
Responses
1/2
1 half
3/4
3 fourths
1/12
1 over 12
5/6
The correct response is: 1/12.
Explanation:
If Aliyah's siblings ate 1/4 of the cake and her friends ate 2/3 of the cake, we can find the fraction of the cake that was eaten by adding these fractions: 1/4 + 2/3.
To do this, we first need to find a common denominator. In this case, the common denominator is 12. So, we rewrite the fractions with the denominator of 12:
1/4 = 3/12
2/3 = 8/12
Now, we can add the fractions:
3/12 + 8/12 = 11/12
Subtracting the fraction that was eaten from 1 (since the question asks about how much was left), we get:
1 - 11/12 = 1/12
So, 1/12 of the cake was left.