7th Grade Math Midterm Exam

1) Jenisa used 4/5 of her allowance to purchase a gift. How is this fraction represented as a percent?

40%

45%

50%

80%

Jenisa used 4/5 of her allowance, which means she spent 4 parts out of 5. To convert this fraction to a percent, we need to find what percent 4 parts out of 5 is. By dividing 4 by 5 and multiplying by 100, we get 80%. Therefore, 4/5 is represented as 80%.

Explanation

Jenisa used 4/5 of her allowance, which means she spent 4 parts out of 5. To convert this fraction to a percent, we need to find what percent 4 parts out of 5 is. By dividing 4 by 5 and multiplying by 100, we get 80%. Therefore, 4/5 is represented as 80%.

2) Jessica had $115 dollars and spent 1/3 of that amount on a new stereo. Which of the following is the most reasonable estimate of how much she spent on the stereo?

$15

$40

$60

$100

Jessica had $115 dollars and spent 1/3 of that amount on a new stereo. To find out how much she spent on the stereo, we need to calculate 1/3 of $115. One way to do this is to divide $115 by 3, which equals approximately $38.33. Since the options given are rounded estimates, the most reasonable estimate would be $40, which is the closest option to the calculated amount.

Explanation

Jessica had $115 dollars and spent 1/3 of that amount on a new stereo. To find out how much she spent on the stereo, we need to calculate 1/3 of $115. One way to do this is to divide $115 by 3, which equals approximately $38.33. Since the options given are rounded estimates, the most reasonable estimate would be $40, which is the closest option to the calculated amount.

3) What is the value of 2/3 x 1/5

2/15

3/8

3/10

1/4

To find the value of 2/3 x 1/5, we multiply the numerators (2 x 1) to get 2, and multiply the denominators (3 x 5) to get 15. Therefore, the answer is 2/15.

Explanation

To find the value of 2/3 x 1/5, we multiply the numerators (2 x 1) to get 2, and multiply the denominators (3 x 5) to get 15. Therefore, the answer is 2/15.

4) Which fraction is greater than 1/6 but less than 1/3?

1/9

1/2

1/4

1/8

The fraction 1/4 is greater than 1/6 because the denominator is smaller, indicating larger parts. It is also less than 1/3 because the denominator is larger, indicating smaller parts. Therefore, 1/4 satisfies the condition of being greater than 1/6 but less than 1/3.

Explanation

The fraction 1/4 is greater than 1/6 because the denominator is smaller, indicating larger parts. It is also less than 1/3 because the denominator is larger, indicating smaller parts. Therefore, 1/4 satisfies the condition of being greater than 1/6 but less than 1/3.

5) Advanced University accepted 15000 students in their masters of science program. Only 6000 of those students completed the program. What percent of the students completed the program?

6%

15%

25%

40%

Out of the 15000 students accepted into the masters of science program, only 6000 completed it. To find the percentage of students who completed the program, we divide the number of students who completed (6000) by the total number of students accepted (15000) and multiply by 100. This gives us a percentage of 40%.

Explanation

Out of the 15000 students accepted into the masters of science program, only 6000 completed it. To find the percentage of students who completed the program, we divide the number of students who completed (6000) by the total number of students accepted (15000) and multiply by 100. This gives us a percentage of 40%.

6) Spencer cam run 1 mile in about 8 minutes. Ande can run1 mile in about 10 minutes. If both boys run for 30 minutes, about how much father will Spencer run?

.07 mile

.75 mile

1 mile

2 miles

Spencer can run 1 mile in about 8 minutes, while Ande can run 1 mile in about 10 minutes. Therefore, in 30 minutes, Spencer will be able to run 30/8 = 3.75 miles, while Ande will be able to run 30/10 = 3 miles. The difference between the distances covered by Spencer and Ande is 3.75 - 3 = 0.75 miles.

Explanation

Spencer can run 1 mile in about 8 minutes, while Ande can run 1 mile in about 10 minutes. Therefore, in 30 minutes, Spencer will be able to run 30/8 = 3.75 miles, while Ande will be able to run 30/10 = 3 miles. The difference between the distances covered by Spencer and Ande is 3.75 - 3 = 0.75 miles.

7) Gretchen was up to bat 56 times during her softball season. She reached first base 33 times. About which percentage of the time did she reach first base?

23%

33%

59%

70%

Gretchen reached first base 33 times out of 56 at-bats during her softball season. To find the percentage, we divide the number of times she reached first base (33) by the total number of at-bats (56) and multiply by 100. This gives us a percentage of approximately 59%.

Explanation

Gretchen reached first base 33 times out of 56 at-bats during her softball season. To find the percentage, we divide the number of times she reached first base (33) by the total number of at-bats (56) and multiply by 100. This gives us a percentage of approximately 59%.

8) Celia fond many items on sale in her favorite store. Teh items were 1/2 off, 25% off, 40% off , and 1/3 off. Which of the following shows the discounts in order from least to greatest?

1/3 < 1/2 < 25% < 40%

1/2 < 1/3 < 25% < 40%

1/2 < 40% < 1/3 < 25%

25% < 1/3 < 40% < 1/2

The correct answer is 25%

Explanation

The correct answer is 25%

9) Bob owns some DVDs. He owns 8 comedies, 5 animated movies, and 7 action movies. What is the ratio of comedies to the total number of DVDs Bob owns?

1/8

1/3

2/5

2/3

The ratio of comedies to the total number of DVDs Bob owns is 2/5. This can be calculated by dividing the number of comedies (8) by the total number of DVDs (8+5+7=20). Simplifying the ratio gives us 2/5.

Explanation

The ratio of comedies to the total number of DVDs Bob owns is 2/5. This can be calculated by dividing the number of comedies (8) by the total number of DVDs (8+5+7=20). Simplifying the ratio gives us 2/5.

10) A biologist studies a pond and finds that it has 25 fish and 75 frogs. What is the ratio of fish to frogs?

1:3

1:4

2:5

2:7

The ratio of fish to frogs in the pond is 1:3. This means that for every fish in the pond, there are three frogs.

Explanation

The ratio of fish to frogs in the pond is 1:3. This means that for every fish in the pond, there are three frogs.

11) How should you write .07 as a percent?

.07%

.70%

7.0%

70%

To write .07 as a percent, you need to move the decimal point two places to the right and add a percent sign. This means that .07 is equal to 7.0%.

Explanation

To write .07 as a percent, you need to move the decimal point two places to the right and add a percent sign. This means that .07 is equal to 7.0%.

12) Sylvia bought 4 2/3 yards of fabric costing $5.49 per yard. Which amount is a reasonable estimate for the cost of the fabric?

$10

$20

$25

$35

The cost of the fabric is estimated by multiplying the number of yards by the cost per yard. In this case, Sylvia bought 4 2/3 yards of fabric, which can be rounded up to 5 yards. Multiplying 5 yards by $5.49 per yard gives an estimated cost of $27.45. Among the given options, $25 is the closest reasonable estimate to the actual cost.

Explanation

The cost of the fabric is estimated by multiplying the number of yards by the cost per yard. In this case, Sylvia bought 4 2/3 yards of fabric, which can be rounded up to 5 yards. Multiplying 5 yards by $5.49 per yard gives an estimated cost of $27.45. Among the given options, $25 is the closest reasonable estimate to the actual cost.

13) Cassandra recorded the average amount spent on groceries each week by her family of four as $114.38. How much is this per day for a 7-day week?

$16.34

$16.00

$15.34

%15.00

To find the amount spent per day for a 7-day week, we divide the average amount spent on groceries each week by 7. So, $114.38 divided by 7 equals $16.34.

Explanation

To find the amount spent per day for a 7-day week, we divide the average amount spent on groceries each week by 7. So, $114.38 divided by 7 equals $16.34.

14) Vale Mountain has a snow making machine that will lay down an inch of snow per hour over an area of 50000 square feet. Which expression shows how to find the number of hours this machine takes to lay down 1 inch of new snow on a ski run that is 700 feet long and 120 feet wide?

(700x120)/50,000

50,000/(700x120)

120x50,000/700

(700x50,000)/120

The given expression (700x120)/50,000 calculates the number of hours it takes for the snow making machine to lay down 1 inch of new snow on a ski run that is 700 feet long and 120 feet wide. This is determined by multiplying the length and width of the ski run (700 and 120) and then dividing it by the area that the snow making machine can cover in an hour (50,000 square feet).

Explanation

The given expression (700x120)/50,000 calculates the number of hours it takes for the snow making machine to lay down 1 inch of new snow on a ski run that is 700 feet long and 120 feet wide. This is determined by multiplying the length and width of the ski run (700 and 120) and then dividing it by the area that the snow making machine can cover in an hour (50,000 square feet).

15) The Lauder Theatre uses 3 ushers for every 150 guests. If the net concert is sold out, and the theater holds 992 people, approximately how many ushers will they need for the sold out concert?

7 ushers

20 ushers

50 ushers

331 ushers

Explanation

16)

5

7

12

14

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Explanation

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17) Mr. Rogers bought a small motorboat. Traveling at a speed of 30 miles per hour, he could go 50 miles on a 6 gallon tank of fuel. At that rate, how many gallons of fuel would he need for a 75 mile trip?

7 1/2

9

12

20

Based on the given information, Mr. Rogers can travel 50 miles on a 6 gallon tank of fuel. Therefore, he can travel 50/6 = 8.33 miles per gallon. To calculate how many gallons of fuel he would need for a 75 mile trip, we divide 75 by 8.33, which gives us approximately 9. Therefore, Mr. Rogers would need 9 gallons of fuel for a 75 mile trip.

Explanation

Based on the given information, Mr. Rogers can travel 50 miles on a 6 gallon tank of fuel. Therefore, he can travel 50/6 = 8.33 miles per gallon. To calculate how many gallons of fuel he would need for a 75 mile trip, we divide 75 by 8.33, which gives us approximately 9. Therefore, Mr. Rogers would need 9 gallons of fuel for a 75 mile trip.

18) There were 279 participants in the science fair. About 2/3 of them were seventh graders. Which of these is a reasonable estimate of the number of seventh graders taking part in the science fair?

100

150

200

250

Since 2/3 of the participants were seventh graders, a reasonable estimate of the number of seventh graders taking part in the science fair would be slightly less than 2/3 of the total number of participants. Since 2/3 of 279 is approximately 186, 200 would be a reasonable estimate as it is slightly higher than 186.

Explanation

Since 2/3 of the participants were seventh graders, a reasonable estimate of the number of seventh graders taking part in the science fair would be slightly less than 2/3 of the total number of participants. Since 2/3 of 279 is approximately 186, 200 would be a reasonable estimate as it is slightly higher than 186.

19) Mary and Ann collected stamps as a hobby. Mary collected 188 stamps which was less than half the number of stamps, s, Ann collected. Which inequality statement?

188 < 1/2s

188 > 1/2s

188 < 1/2 + s

Mary collected 188 stamps, which is less than half the number of stamps Ann collected. This can be represented by the inequality statement 188

Explanation

Mary collected 188 stamps, which is less than half the number of stamps Ann collected. This can be represented by the inequality statement 188

20) Joanna has 3/4 of her book left to read. If she reads 1/4 of her book each day, how many days will it take her to finish the book?

3/16

1/2

1

3

Joanna has 3/4 of her book left to read and she reads 1/4 of her book each day. To find out how many days it will take her to finish the book, we need to divide the remaining fraction (3/4) by the fraction she reads each day (1/4). When we divide 3/4 by 1/4, we get 3. Therefore, it will take Joanna 3 days to finish the book.

Explanation

Joanna has 3/4 of her book left to read and she reads 1/4 of her book each day. To find out how many days it will take her to finish the book, we need to divide the remaining fraction (3/4) by the fraction she reads each day (1/4). When we divide 3/4 by 1/4, we get 3. Therefore, it will take Joanna 3 days to finish the book.

21) The number of teachers is directly proportional to the number of students. When there are 224 students, there are 14 teachers. how many teachers are there when there are 368 students?

21 teachers

23 teachers

25 teachers

27 teachers

The given information states that the number of teachers is directly proportional to the number of students. This means that as the number of students increases, the number of teachers will also increase in direct proportion.

Using the given ratio of 224 students to 14 teachers, we can find the ratio of students to teachers: 224/14 = 16 students per teacher.

To find the number of teachers when there are 368 students, we divide the number of students by the ratio: 368/16 = 23 teachers.

Therefore, the correct answer is 23 teachers.

Explanation

The given information states that the number of teachers is directly proportional to the number of students. This means that as the number of students increases, the number of teachers will also increase in direct proportion.

Using the given ratio of 224 students to 14 teachers, we can find the ratio of students to teachers: 224/14 = 16 students per teacher.

To find the number of teachers when there are 368 students, we divide the number of students by the ratio: 368/16 = 23 teachers.

Therefore, the correct answer is 23 teachers.

22) What is the value of this expression?

-6

0

15

36

Explanation

23) Mr. Roberts asked his students to solve this expression and tell me which students response is correct?

31

40

51

59

not-available-via-ai

Explanation

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24)

8

16

40

64

To evaluate the expression 2(3x - 4)^2 when x = 2, we substitute x = 2 into the expression and simplify:

2(3x - 4)^2 = 2(3(2) - 4)^2

= 2(6 - 4)^2

= 2(2)^2

= 2(4)

= 8

Explanation

To evaluate the expression 2(3x - 4)^2 when x = 2, we substitute x = 2 into the expression and simplify:

2(3x - 4)^2 = 2(3(2) - 4)^2

= 2(6 - 4)^2

= 2(2)^2

= 2(4)

= 8

25) A district office printed surveys for each school in the district to distribute to its students. The office used 3 1/2 reams of paper to print all of the surveys. Each school in the district received 1/4 of a ream of printed surveys. How many schools are in the district?

4

9

12

14

If each school received 1/4 of a ream of printed surveys and the office used 3 1/2 reams of paper in total, we can divide 3 1/2 by 1/4 to find the number of schools. Dividing 3 1/2 by 1/4 is the same as multiplying 3 1/2 by 4/1, which equals 14. Therefore, there are 14 schools in the district.

Explanation

If each school received 1/4 of a ream of printed surveys and the office used 3 1/2 reams of paper in total, we can divide 3 1/2 by 1/4 to find the number of schools. Dividing 3 1/2 by 1/4 is the same as multiplying 3 1/2 by 4/1, which equals 14. Therefore, there are 14 schools in the district.

26) What is the value of the following expression? 1/2 (2+4x6-3x2)

10

15

19

33

The given expression is solved using the order of operations (PEMDAS/BODMAS). First, we multiply 4 by 6 to get 24, and then multiply 3 by 2 to get 6. Next, we subtract 6 from 24, resulting in 18. Finally, we add 2 and 18 to get 20, and divide it by 2, giving us the final answer of 10.

Explanation

The given expression is solved using the order of operations (PEMDAS/BODMAS). First, we multiply 4 by 6 to get 24, and then multiply 3 by 2 to get 6. Next, we subtract 6 from 24, resulting in 18. Finally, we add 2 and 18 to get 20, and divide it by 2, giving us the final answer of 10.

27) The length of Sara's banner for Family Fun Night is 2 feet more than 1/2 the length of Alex's banner. Saras banner is 10 feet long. What is the length of Alexs banner?

8 feet

12 feet

16 feet

20 feet

The length of Sara's banner is 2 feet more than half the length of Alex's banner. Since Sara's banner is 10 feet long, half the length of Alex's banner would be 10 - 2 = 8 feet. Therefore, the length of Alex's banner is 8 feet x 2 = 16 feet.

Explanation

The length of Sara's banner is 2 feet more than half the length of Alex's banner. Since Sara's banner is 10 feet long, half the length of Alex's banner would be 10 - 2 = 8 feet. Therefore, the length of Alex's banner is 8 feet x 2 = 16 feet.

28) The dimensions of four rectangles are given below. Which rectangle does not have the same ratio of length to width as the other three?

14 inches x 10 inches

3 1/2 inches x 2 1/2 inches

7 inches x 5 inches

4 1/2 inches x 2 3/4 inches

The ratio of length to width for the first three rectangles is 14:10, 3.5:2.5, and 7:5 respectively. However, for the fourth rectangle, the ratio of length to width is not the same as the other three. Therefore, the fourth rectangle does not have the same ratio of length to width as the other three.

Explanation

The ratio of length to width for the first three rectangles is 14:10, 3.5:2.5, and 7:5 respectively. However, for the fourth rectangle, the ratio of length to width is not the same as the other three. Therefore, the fourth rectangle does not have the same ratio of length to width as the other three.

29) On Monday, Julie checked out 24 books from the public library. This is 6 more than twice the number of books she checked out on Saturday. How many books did Julie check out on Saturday?

6

8

9

15

Let's assume the number of books Julie checked out on Saturday is x. According to the given information, 24 is 6 more than twice x. So, we can write the equation 2x + 6 = 24. By subtracting 6 from both sides, we get 2x = 18. Finally, dividing both sides by 2, we find x = 9. Therefore, Julie checked out 9 books on Saturday.

Explanation

Let's assume the number of books Julie checked out on Saturday is x. According to the given information, 24 is 6 more than twice x. So, we can write the equation 2x + 6 = 24. By subtracting 6 from both sides, we get 2x = 18. Finally, dividing both sides by 2, we find x = 9. Therefore, Julie checked out 9 books on Saturday.

30)

62m

1/3

60m+8

63m-4

The given options are different expressions involving 'm'. The correct answer is 62m. This means that the value of 'm' should be multiplied by 62 to get the correct result.

Explanation

The given options are different expressions involving 'm'. The correct answer is 62m. This means that the value of 'm' should be multiplied by 62 to get the correct result.

31)

(4,2)

(5,2)

(5,3)

(6,2)

The answer (5,2) is the only point that appears more than once in the given set of coordinates. All the other points (4,2), (5,3), and (6,2) appear only once. Therefore, the correct answer is (5,2).

Explanation

The answer (5,2) is the only point that appears more than once in the given set of coordinates. All the other points (4,2), (5,3), and (6,2) appear only once. Therefore, the correct answer is (5,2).

32) Henry collects stamps. During week one, he collected 2 stamps. During week two, he collected 5 stamps. During week three, he collected 8 stamps. During week four, he collected 11 stamps. If w is the week number, which expression can be used to find the number of stamps Henry collected each week?

2.5w

2w+3

2w

3w-1

The expression 3w-1 can be used to find the number of stamps Henry collected each week. This is because the expression represents the pattern of adding 3 stamps each week, starting from 2 stamps in week one. Subtracting 1 from the week number accounts for the initial 2 stamps collected in week one. Thus, the expression 3w-1 accurately represents the number of stamps collected by Henry each week.

Explanation

The expression 3w-1 can be used to find the number of stamps Henry collected each week. This is because the expression represents the pattern of adding 3 stamps each week, starting from 2 stamps in week one. Subtracting 1 from the week number accounts for the initial 2 stamps collected in week one. Thus, the expression 3w-1 accurately represents the number of stamps collected by Henry each week.

33) Rosalba used a sketch to help her build a doghouse. The sketch is 6 inches long. The doghouse is 4 feet long. Which scale factor did Rosalba use to go from the sketch to the actual dog house?

1:8

1:12

2:3

3:2

Rosalba used a scale factor of 1:8 to go from the sketch to the actual doghouse. This means that for every 1 inch on the sketch, the actual doghouse is 8 inches long. Since the sketch is 6 inches long, the actual doghouse would be 6 x 8 = 48 inches long.

Explanation

Rosalba used a scale factor of 1:8 to go from the sketch to the actual doghouse. This means that for every 1 inch on the sketch, the actual doghouse is 8 inches long. Since the sketch is 6 inches long, the actual doghouse would be 6 x 8 = 48 inches long.

34) Standing at -2.5 on a giant number line, Marco walks to 3.75, then to -6.75, then to -12.5. What is the total distance Marco walks, if each whole number is equal to one foot?

18.75 feet

20 feet

22.5 feet

29.25 feet

Marco starts at -2.5 and walks to 3.75, which is a distance of 6.25 feet. Then, he walks from 3.75 to -6.75, which is a distance of 10.5 feet. Finally, he walks from -6.75 to -12.5, which is a distance of 5.75 feet. Adding up these distances, the total distance Marco walks is 6.25 + 10.5 + 5.75 = 22.5 feet.

Explanation

Marco starts at -2.5 and walks to 3.75, which is a distance of 6.25 feet. Then, he walks from 3.75 to -6.75, which is a distance of 10.5 feet. Finally, he walks from -6.75 to -12.5, which is a distance of 5.75 feet. Adding up these distances, the total distance Marco walks is 6.25 + 10.5 + 5.75 = 22.5 feet.