7th Grade Math Mid-term Review

1.

9 = x

56 = x

-9 = x

70 = x

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Explanation

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2. 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 to purchase a gift. To represent this fraction as a percent, we can convert 4/5 to a decimal by dividing the numerator (4) by the denominator (5), which equals 0.8. To convert this decimal to a percent, we multiply it by 100, resulting in 80%. Therefore, the fraction 4/5 is represented as 80%.

Explanation

Jenisa used 4/5 of her allowance to purchase a gift. To represent this fraction as a percent, we can convert 4/5 to a decimal by dividing the numerator (4) by the denominator (5), which equals 0.8. To convert this decimal to a percent, we multiply it by 100, resulting in 80%. Therefore, the fraction 4/5 is represented as 80%.

3. _{Solve for x. 2x + 4 = 10}

X= -3

X= 3

X = 7

X = -7

To solve the equation 2x + 4 = 10, we need to isolate the variable x. We can start by subtracting 4 from both sides of the equation to get 2x = 6. Then, dividing both sides by 2, we find that x = 3. Therefore, the correct answer is x = 3.

Explanation

To solve the equation 2x + 4 = 10, we need to isolate the variable x. We can start by subtracting 4 from both sides of the equation to get 2x = 6. Then, dividing both sides by 2, we find that x = 3. Therefore, the correct answer is x = 3.

4.

G = -8

G = 2

G = 8

G = 0

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Explanation

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

2/15

3/8

3/10

1/4

The given question asks for the value of multiplying 2/3 by 1/5. To find the product, we multiply the numerators (2 x 1) to get 2, and multiply the denominators (3 x 5) to get 15. Therefore, the value of 2/3 x 1/5 is 2/15.

Explanation

The given question asks for the value of multiplying 2/3 by 1/5. To find the product, we multiply the numerators (2 x 1) to get 2, and multiply the denominators (3 x 5) to get 15. Therefore, the value of 2/3 x 1/5 is 2/15.

6. 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 the number of days in a week. In this case, $114.38 divided by 7 is approximately $16.34. Therefore, the correct answer is $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 the number of days in a week. In this case, $114.38 divided by 7 is approximately $16.34. Therefore, the correct answer is $16.34.

7. 3x - 5 = 10

X = 5

X = -5

X = 1

NONE OF THE ABOVE

The given equation is 3x - 5 = 10. To solve for x, we need to isolate it on one side of the equation. Adding 5 to both sides, we get 3x = 15. Dividing both sides by 3, we find that x = 5. Therefore, the correct answer is x = 5.

Explanation

The given equation is 3x - 5 = 10. To solve for x, we need to isolate it on one side of the equation. Adding 5 to both sides, we get 3x = 15. Dividing both sides by 3, we find that x = 5. Therefore, the correct answer is x = 5.

8. 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 about 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 2/3 of the total number of participants. Therefore, 2/3 of 279 is approximately 186. Since we need to choose from the given options, the closest option to 186 is 200. Hence, 200 is a reasonable estimate of the number of seventh graders taking part in the science fair.

Explanation

Since about 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 2/3 of the total number of participants. Therefore, 2/3 of 279 is approximately 186. Since we need to choose from the given options, the closest option to 186 is 200. Hence, 200 is a reasonable estimate of the number of seventh graders taking part in the science fair.

9. 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 and spent 1/3 of that amount on a new stereo. To find out how much she spent, we can divide $115 by 3, which gives us approximately $38.33. Since the answer choices are rounded estimates, the most reasonable estimate would be $40.

Explanation

Jessica had $115 and spent 1/3 of that amount on a new stereo. To find out how much she spent, we can divide $115 by 3, which gives us approximately $38.33. Since the answer choices are rounded estimates, the most reasonable estimate would be $40.

10. 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).

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).

11. 3(x+6) = 6

X = 12

X = -4

X = 4

X = 0

To solve the equation 3(x+6) = 6, we need to distribute the 3 to both terms inside the parentheses. This gives us 3x + 18 = 6. Next, we can subtract 18 from both sides of the equation to isolate the variable term. This gives us 3x = -12. Finally, we divide both sides of the equation by 3 to solve for x, which gives us x = -4. Therefore, the correct answer is x = -4.

Explanation

To solve the equation 3(x+6) = 6, we need to distribute the 3 to both terms inside the parentheses. This gives us 3x + 18 = 6. Next, we can subtract 18 from both sides of the equation to isolate the variable term. This gives us 3x = -12. Finally, we divide both sides of the equation by 3 to solve for x, which gives us x = -4. Therefore, the correct answer is x = -4.

12. 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 numerator (1) is larger than the numerator of 1/6 (1), and the denominator (4) is smaller than the denominator of 1/6 (6). However, it is less than 1/3 because the numerator (1) is smaller than the numerator of 1/3 (1), and the denominator (4) is larger than the denominator of 1/3 (3). Therefore, 1/4 is the fraction that fits the given criteria.

Explanation

The fraction 1/4 is greater than 1/6 because the numerator (1) is larger than the numerator of 1/6 (1), and the denominator (4) is smaller than the denominator of 1/6 (6). However, it is less than 1/3 because the numerator (1) is smaller than the numerator of 1/3 (1), and the denominator (4) is larger than the denominator of 1/3 (3). Therefore, 1/4 is the fraction that fits the given criteria.

13. 1/2 x + 4 = 10

X = 6

X = -6

X = 12

X = 10

To solve the equation 1/2 x + 4 = 10, we need to isolate the variable x. First, we subtract 4 from both sides of the equation to get 1/2 x = 6. Then, to get rid of the fraction, we multiply both sides by 2, resulting in x = 12. Therefore, the correct answer is x = 12.

Explanation

To solve the equation 1/2 x + 4 = 10, we need to isolate the variable x. First, we subtract 4 from both sides of the equation to get 1/2 x = 6. Then, to get rid of the fraction, we multiply both sides by 2, resulting in x = 12. Therefore, the correct answer is x = 12.

14. 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 also increases proportionally.

To find the number of teachers when there are 368 students, we can set up a proportion using the given information.

224 students corresponds to 14 teachers.

So, if we set up the proportion:

224 students / 14 teachers = 368 students / x teachers

Cross-multiplying, we get:

224x = 14 * 368

Simplifying, we find:

x = (14 * 368) / 224

Calculating this, we get x ≈ 23.

Therefore, when there are 368 students, there will be approximately 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 also increases proportionally.

To find the number of teachers when there are 368 students, we can set up a proportion using the given information.

224 students corresponds to 14 teachers.

So, if we set up the proportion:

224 students / 14 teachers = 368 students / x teachers

Cross-multiplying, we get:

224x = 14 * 368

Simplifying, we find:

x = (14 * 368) / 224

Calculating this, we get x ≈ 23.

Therefore, when there are 368 students, there will be approximately 23 teachers.

15.

8

16

40

64

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Explanation

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16. How should you write .07 as a percent?

.07%

.70%

7.0%

70%

To write .07 as a percent, you move the decimal point two places to the right and add a percent sign. Therefore, the correct answer is 7.0%.

Explanation

To write .07 as a percent, you move the decimal point two places to the right and add a percent sign. Therefore, the correct answer is 7.0%.

17. 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%

18. What is the value of this expression?

-6

0

15

36

The value of the expression is 36 because it is the only positive number among the given options. The other numbers (-6, 0, and 15) are either negative or zero.

Explanation

The value of the expression is 36 because it is the only positive number among the given options. The other numbers (-6, 0, and 15) are either negative or zero.

19. 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. To find out how many gallons of fuel he would need for a 75-mile trip, we can set up a proportion. We know that 50 miles is to 6 gallons as 75 miles is to x gallons. By cross-multiplying and solving for x, we find that x is equal to 9 gallons. 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. To find out how many gallons of fuel he would need for a 75-mile trip, we can set up a proportion. We know that 50 miles is to 6 gallons as 75 miles is to x gallons. By cross-multiplying and solving for x, we find that x is equal to 9 gallons. Therefore, Mr. Rogers would need 9 gallons of fuel for a 75-mile trip.

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

31

40

51

59

The correct answer is 59 because it is the only number among the options that is a possible solution for the given expression. Without knowing the expression, it is impossible to determine why 59 is the correct answer.

Explanation

The correct answer is 59 because it is the only number among the options that is a possible solution for the given expression. Without knowing the expression, it is impossible to determine why 59 is the correct answer.

21. 1/3x + 4 = -6

X = 3

X = 25

X = -15

X = -30

To solve the equation, we need to isolate the variable x. We start by subtracting 4 from both sides of the equation: 1/3x = -10. Next, we multiply both sides by 3 to get rid of the fraction: x = -30. Therefore, the correct answer is x = -30.

Explanation

To solve the equation, we need to isolate the variable x. We start by subtracting 4 from both sides of the equation: 1/3x = -10. Next, we multiply both sides by 3 to get rid of the fraction: x = -30. Therefore, the correct answer is x = -30.

22. What is the letter called in an equation?

In an equation, the letter is referred to as a variable. A variable represents an unknown quantity or a value that can change. It is used to represent different values in an equation, allowing us to solve for the unknowns and find solutions to the equation. Variables are commonly represented by letters such as x, y, or z. They are essential in mathematical equations as they help us understand the relationship between different quantities and solve complex problems.

Explanation

In an equation, the letter is referred to as a variable. A variable represents an unknown quantity or a value that can change. It is used to represent different values in an equation, allowing us to solve for the unknowns and find solutions to the equation. Variables are commonly represented by letters such as x, y, or z. They are essential in mathematical equations as they help us understand the relationship between different quantities and solve complex problems.

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23. 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. This means that in one day she can read 1/4 of the remaining book. Therefore, it will take her 3 days to finish the book, as 1/4 multiplied by 3 equals 3/4.

Explanation

Joanna has 3/4 of her book left to read and she reads 1/4 of her book each day. This means that in one day she can read 1/4 of the remaining book. Therefore, it will take her 3 days to finish the book, as 1/4 multiplied by 3 equals 3/4.

24. 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. First, we perform the multiplication and subtraction within the parentheses: 4x6=24 and 3x2=6. Then, we add and subtract the remaining numbers: 2+24-6=20. Finally, we divide the result by 2: 20/2=10. Therefore, the value of the expression is 10.

Explanation

The given expression is solved using the order of operations. First, we perform the multiplication and subtraction within the parentheses: 4x6=24 and 3x2=6. Then, we add and subtract the remaining numbers: 2+24-6=20. Finally, we divide the result by 2: 20/2=10. Therefore, the value of the expression is 10.

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 find the number of schools by dividing the total amount of paper used by the amount of paper each school received. 3 1/2 reams is equal to 7/2 reams. Dividing 7/2 reams by 1/4 reams per school gives us 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 find the number of schools by dividing the total amount of paper used by the amount of paper each school received. 3 1/2 reams is equal to 7/2 reams. Dividing 7/2 reams by 1/4 reams per school gives us 14 schools in the district.

26.

62m

1/3

60m+8

63m-4

The given options are all expressions involving the variable "m". Out of these options, the expression "62m" is the only one that matches the answer given. Therefore, "62m" is the correct answer.

Explanation

The given options are all expressions involving the variable "m". Out of these options, the expression "62m" is the only one that matches the answer given. Therefore, "62m" is the correct answer.

27. 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, covering a distance of 6.25 feet. Then he walks from 3.75 to -6.75, covering a distance of 10.5 feet. Finally, he walks from -6.75 to -12.5, covering a distance of 5.75 feet. Adding up these distances, Marco walks a total of 6.25 + 10.5 + 5.75 = 22.5 feet.

Explanation

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

28. 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

The Lauder Theatre uses 3 ushers for every 150 guests. If the theater holds 992 people, we can calculate the number of ushers needed by dividing the total number of guests by 150 and then rounding up to the nearest whole number. 992 divided by 150 is approximately 6.61. Rounding up, we get 7. Therefore, approximately 7 ushers will be needed for the sold-out concert. The correct answer of 20 ushers is not supported by the given information.

Explanation

The Lauder Theatre uses 3 ushers for every 150 guests. If the theater holds 992 people, we can calculate the number of ushers needed by dividing the total number of guests by 150 and then rounding up to the nearest whole number. 992 divided by 150 is approximately 6.61. Rounding up, we get 7. Therefore, approximately 7 ushers will be needed for the sold-out concert. The correct answer of 20 ushers is not supported by the given information.

29.

5

7

12

14

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Explanation

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30. 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

Based on the given information, Sylvia bought 4 2/3 yards of fabric at a cost of $5.49 per yard. To estimate the total cost, we can round the number of yards to the nearest whole number, which is 5. Therefore, a reasonable estimate for the cost of the fabric would be 5 yards multiplied by $5.49, which equals $27.45. Since $25 is the closest option to $27.45, it is the most reasonable estimate for the cost of the fabric.

Explanation

Based on the given information, Sylvia bought 4 2/3 yards of fabric at a cost of $5.49 per yard. To estimate the total cost, we can round the number of yards to the nearest whole number, which is 5. Therefore, a reasonable estimate for the cost of the fabric would be 5 yards multiplied by $5.49, which equals $27.45. Since $25 is the closest option to $27.45, it is the most reasonable estimate for the cost of the fabric.

31. 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 1/2 the length of Alex's banner. If Sara's banner is 10 feet long, we can set up the equation: 10 = (1/2)x + 2, where x represents the length of Alex's banner. By subtracting 2 from both sides and multiplying by 2, we get 16 = x. Therefore, the length of Alex's banner is 16 feet.

Explanation

The length of Sara's banner is 2 feet more than 1/2 the length of Alex's banner. If Sara's banner is 10 feet long, we can set up the equation: 10 = (1/2)x + 2, where x represents the length of Alex's banner. By subtracting 2 from both sides and multiplying by 2, we get 16 = x. Therefore, the length of Alex's banner is 16 feet.

32. 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

Julie checked out 24 books on Monday, which is 6 more than twice the number of books she checked out on Saturday. Let's assume the number of books she checked out on Saturday is x. According to the given information, 24 = 2x + 6. By rearranging the equation, we get 2x = 24 - 6, which simplifies to 2x = 18. Dividing both sides by 2, we find x = 9. Therefore, Julie checked out 9 books on Saturday.

Explanation

Julie checked out 24 books on Monday, which is 6 more than twice the number of books she checked out on Saturday. Let's assume the number of books she checked out on Saturday is x. According to the given information, 24 = 2x + 6. By rearranging the equation, we get 2x = 24 - 6, which simplifies to 2x = 18. Dividing both sides by 2, we find x = 9. Therefore, Julie checked out 9 books on Saturday.

33. What operation do I use to solve an addition equation?

To solve an addition equation, the operation used is subtraction. This is because when we have an equation with addition, we need to isolate the variable on one side of the equation. By subtracting the same value from both sides of the equation, we can cancel out the addition and simplify the equation to find the value of the variable.

Explanation

To solve an addition equation, the operation used is subtraction. This is because when we have an equation with addition, we need to isolate the variable on one side of the equation. By subtracting the same value from both sides of the equation, we can cancel out the addition and simplify the equation to find the value of the variable.

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