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Grade 7 Mathematics study materials
Grade 7 Mathematics study resources

Grade 7 Mathematics practice questions

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Question 1Ratios and Proportional Relationships

A recipe uses 3 cups of flour for every 2 cups of sugar. If a baker uses 12 cups of flour, how many cups of sugar are needed to keep the same ratio?

  1. 9
  2. 6
  3. 8 Correct answer.
  4. 18

Explanation

Set up the proportion 3/2 = 12/x. Cross-multiplying gives 3x = 24, so x = 8. The flour amount was multiplied by 4, so the sugar amount must also be multiplied by 4.

Question 2Ratios and Proportional Relationships

Which ratio is equivalent to 8:12?

  1. 4:5
  2. 3:4
  3. 2:3 Correct answer.
  4. 8:16

Explanation

Divide both terms of 8:12 by their greatest common factor, 4, to get 2:3. Equivalent ratios are formed by multiplying or dividing both terms by the same nonzero number.

Question 3Ratios and Proportional Relationships

A car travels 150 miles in 3 hours at a constant speed. What is the unit rate in miles per hour?

  1. 45
  2. 450
  3. 75
  4. 50 Correct answer.

Explanation

A unit rate expresses the quantity per one unit of the other. Dividing 150 miles by 3 hours gives 50 miles per hour.

Question 4Ratios and Proportional Relationships

A store sells 4 notebooks for $6. At this rate, what is the cost of 10 notebooks?

  1. $15 Correct answer.
  2. $12
  3. $10
  4. $24

Explanation

Find the unit price first: $6 divided by 4 notebooks is $1.50 per notebook. Multiplying $1.50 by 10 notebooks gives $15.

Question 5Ratios and Proportional Relationships

Which statement correctly describes the relationship shown by the ratio 5:8?

  1. The two quantities add to 13 in every situation.
  2. The second quantity is 5/8 of the first.
  3. For every 5 units of the first quantity there are 8 units of the second. Correct answer.
  4. The first quantity is 8 more than the second.

Explanation

A ratio compares two quantities multiplicatively, so 5:8 means 5 units of the first quantity correspond to 8 units of the second. All equivalent pairs share this same multiplicative comparison.

Question 6Ratios and Proportional Relationships

A map uses a scale of 1 inch = 20 miles. Two towns are 4.5 inches apart on the map. What is the actual distance between them?

  1. 80 miles
  2. 45 miles
  3. 90 miles Correct answer.
  4. 24.5 miles

Explanation

Each inch represents 20 miles, so multiply the map distance by the scale factor: 4.5 × 20 = 90. The scale sets up a proportional relationship between map distance and real distance.

Question 7Ratios and Proportional Relationships

In a class, the ratio of boys to girls is 3:5. If there are 15 girls, how many boys are there?

  1. 6
  2. 25
  3. 10
  4. 9 Correct answer.

Explanation

The ratio 3:5 means boys = 3 parts and girls = 5 parts. Since 5 parts equal 15 girls, each part is 3, so boys = 3 × 3 = 9.

Question 8Ratios and Proportional Relationships

A 2-liter bottle of juice costs $3.60. What is the price per liter?

  1. $1.60
  2. $7.20
  3. $1.80 Correct answer.
  4. $0.90

Explanation

Divide the total cost by the number of liters to get the unit rate. $3.60 divided by 2 liters equals $1.80 per liter.

Question 9Ratios and Proportional Relationships

A recipe calls for 2 cups of rice for every 5 cups of water. How much water is needed for 7 cups of rice?

  1. 3.5 cups
  2. 12 cups
  3. 17.5 cups Correct answer.
  4. 14 cups

Explanation

Set up the proportion 2/5 = 7/x. Cross-multiplying gives 2x = 35, so x = 17.5. The rice amount was multiplied by 3.5, so the water amount must also be multiplied by 3.5.

Question 10Ratios and Proportional Relationships

A cyclist rides at a constant speed of 15 miles per hour. Which equation relates distance d in miles to time t in hours?

  1. d = 15t Correct answer.
  2. d = t/15
  3. d = t + 15
  4. t = 15d

Explanation

Distance equals rate times time, so d = 15t. This is a proportional relationship with constant of proportionality 15.

Question 11Ratios and Proportional Relationships

The graph of a proportional relationship passes through the origin and the point (4, 10). What is the constant of proportionality?

  1. 0.4
  2. 4
  3. 14
  4. 2.5 Correct answer.

Explanation

For a proportional relationship y = kx, the constant k equals y divided by x. Here k = 10 ÷ 4 = 2.5.

Question 12Ratios and Proportional Relationships

A 12-ounce bag of chips costs $3.00, and an 18-ounce bag costs $4.20. Which bag has the lower price per ounce?

  1. The 18-ounce bag at $0.233 per ounce Correct answer.
  2. The 12-ounce bag at $0.25 per ounce
  3. The 12-ounce bag at $0.30 per ounce
  4. They have the same price per ounce

Explanation

Divide each price by its weight: $3.00 ÷ 12 = $0.25 per ounce, and $4.20 ÷ 18 ≈ $0.233 per ounce. The 18-ounce bag has the lower unit price.

Question 13Ratios and Proportional Relationships

A student says the ratio 6:9 is the same as 9:6 because both use the numbers 6 and 9. Which statement explains why the student is incorrect?

  1. Order does not matter, but 6:9 must be written as 6 to 9.
  2. The ratios are equal because 6 + 9 = 9 + 6.
  3. The ratios are equal only when both are simplified to whole numbers.
  4. Order matters in a ratio; 6:9 simplifies to 2:3 while 9:6 simplifies to 3:2. Correct answer.

Explanation

A ratio compares quantities in a specific order, so switching the terms changes the comparison. Simplifying shows 6:9 = 2:3 and 9:6 = 3:2, which are not equivalent ratios.

Question 14Ratios and Proportional Relationships

A proportional relationship has the equation y = 0.75x. What is the value of y when x = 24?

  1. 32
  2. 24.75
  3. 0.03125
  4. 18 Correct answer.

Explanation

Substitute x = 24 into y = 0.75x to get y = 0.75 × 24 = 18. The constant 0.75 is the multiplier applied to every x-value.

Question 15Ratios and Proportional Relationships

A punch recipe mixes juice and soda in the ratio 4:1. If a server makes 30 cups of punch, how many cups of juice are used?

  1. 6
  2. 20
  3. 24 Correct answer.
  4. 25

Explanation

The ratio 4:1 means 4 parts juice to 1 part soda, for 5 parts total. Each part is 30 ÷ 5 = 6 cups, so juice is 4 × 6 = 24 cups.

Question 16Ratios and Proportional Relationships

A printer prints 180 pages in 4 minutes. At this rate, how many minutes will it take to print 405 pages?

  1. 11.25
  2. 9 Correct answer.
  3. 8
  4. 6

Explanation

The unit rate is 180 ÷ 4 = 45 pages per minute. Dividing 405 pages by 45 pages per minute gives 9 minutes.

Question 17Ratios and Proportional Relationships

Which table represents a proportional relationship between x and y?

  1. x: 2, 4, 6 and y: 4, 8, 16
  2. x: 2, 4, 6 and y: 1, 4, 9
  3. x: 2, 4, 6 and y: 5, 10, 15 Correct answer.
  4. x: 2, 4, 6 and y: 5, 8, 11

Explanation

A proportional relationship requires y/x to be constant for every pair. In the first table, 5/2 = 10/4 = 15/6 = 2.5, so the ratio is constant.

Question 18Ratios and Proportional Relationships

A recipe uses sugar and flour in the ratio 3:7. If the recipe uses 4 more cups of flour than sugar, how many cups of sugar are used?

  1. 9
  2. 3 Correct answer.
  3. 7
  4. 4

Explanation

The difference in parts is 7 − 3 = 4 parts, which equals 4 cups, so each part is 1 cup. Sugar is 3 parts, so 3 cups of sugar are used.

Question 19Ratios and Proportional Relationships

A car uses 8 gallons of gas to travel 240 miles. Which equation models the gallons g used for m miles?

  1. g = m/30 Correct answer.
  2. g = m − 30
  3. g = 240m
  4. g = 30m

Explanation

The car travels 240 ÷ 8 = 30 miles per gallon, so gallons used equals miles divided by 30: g = m/30. This is a proportional relationship with constant 1/30.

Question 20Ratios and Proportional Relationships

A scale drawing of a room uses 1/4 inch to represent 1 foot. The room is 15 feet long. What is the length of the room in the drawing?

  1. 0.75 inches
  2. 3.75 inches Correct answer.
  3. 60 inches
  4. 15.25 inches

Explanation

Each foot is represented by 1/4 inch, so multiply 15 feet by 1/4 inch per foot to get 3.75 inches. The scale factor converts real length into drawing length.

Question 21Ratios and Proportional Relationships

Store A sells 6 pens for $4.50. Store B sells 10 pens for $7.00. A shopper wants the lower price per pen. Which conclusion is correct?

  1. Store A is cheaper at $0.75 per pen versus $0.70 per pen.
  2. Store A is cheaper because $4.50 is less than $7.00.
  3. Both stores charge the same price per pen.
  4. Store B is cheaper at $0.70 per pen versus $0.75 per pen. Correct answer.

Explanation

Compute each unit price: $4.50 ÷ 6 = $0.75 per pen, and $7.00 ÷ 10 = $0.70 per pen. Store B has the lower unit price even though its total is higher.

Question 22Ratios and Proportional Relationships

A mixture contains red, blue, and yellow paint in the ratio 2:3:5. If the total mixture is 40 liters, how many more liters of yellow than red are used?

  1. 12 Correct answer.
  2. 8
  3. 20
  4. 16

Explanation

There are 2 + 3 + 5 = 10 parts, so each part is 40 ÷ 10 = 4 liters. Yellow is 5 × 4 = 20 liters and red is 2 × 4 = 8 liters, giving a difference of 12 liters.

Question 23Ratios and Proportional Relationships

A car travels 150 miles in 2.5 hours. At the same constant speed, how far will it travel in 4 hours?

  1. 300 miles
  2. 375 miles
  3. 240 miles Correct answer.
  4. 200 miles

Explanation

The unit rate is 150 ÷ 2.5 = 60 miles per hour. Multiplying by 4 hours gives 240 miles.

Question 24Ratios and Proportional Relationships

Two machines produce parts in a ratio of 5:8. Together they produce 390 parts. How many parts does the faster machine produce?

  1. 240 Correct answer.
  2. 260
  3. 150
  4. 195

Explanation

There are 5 + 8 = 13 parts, so each part is 390 ÷ 13 = 30 parts. The faster machine produces 8 × 30 = 240 parts.

Question 25Ratios and Proportional Relationships

A student claims that the relationship shown by the points (1, 3), (2, 6), and (3, 9) is proportional because each y is double the previous y. Which reasoning correctly evaluates the claim?

  1. The relationship is not proportional because the y-values double instead of increasing by a constant amount.
  2. The relationship is proportional only if the first point is (0, 0).
  3. The relationship is proportional because y/x equals 3 for every point and the graph passes through the origin. Correct answer.
  4. The relationship is not proportional because the points do not lie on a straight line.

Explanation

A relationship is proportional when the ratio y/x is constant and the graph is a line through the origin. Here 3/1 = 6/2 = 9/3 = 3, so the relationship is proportional with constant 3.

Question 26Ratios and Proportional Relationships

A trail mix recipe uses raisins and nuts in the ratio 2:3. If you use 12 cups of raisins, how many cups of nuts do you need?

  1. 12
  2. 18 Correct answer.
  3. 24
  4. 8

Explanation

In a ratio 2:3, the amount of nuts is 3/2 times the amount of raisins. With 12 cups of raisins, nuts = (3/2) × 12 = 18 cups.

Question 27Ratios and Proportional Relationships

Which of the following tables shows a proportional relationship between x and y?

  1. x: 0, 2, 4; y: 1, 3, 5
  2. x: 1, 2, 3; y: 2, 5, 8
  3. x: 1, 3, 5; y: 4, 12, 20 Correct answer.
  4. x: 2, 4, 6; y: 3, 5, 7

Explanation

A proportional relationship requires a constant ratio y/x for all pairs (and the graph passes through the origin). In the correct table, y/x = 4/1 = 12/3 = 20/5 = 4, so the ratio is constant.

Question 28Ratios and Proportional Relationships

A car travels 180 miles on 6 gallons of gas. What is the car's fuel efficiency in miles per gallon?

  1. 24
  2. 30 Correct answer.
  3. 36
  4. 1080

Explanation

Fuel efficiency is the unit rate of miles per gallon. Divide the miles by the gallons: 180 ÷ 6 = 30 miles per gallon.

Question 29Ratios and Proportional Relationships

A recipe uses 3 cups of flour for every 2 cups of sugar. If a baker uses 9 cups of flour, how many cups of sugar are needed?

  1. 9
  2. 4.5
  3. 6 Correct answer.
  4. 13.5

Explanation

The ratio of flour to sugar is 3:2, so sugar = (2/3) × flour. With 9 cups of flour, sugar = (2/3) × 9 = 6 cups.

Question 30Ratios and Proportional Relationships

The graph of a proportional relationship passes through the point (5, 12.5). What is the constant of proportionality?

  1. 5
  2. 12.5
  3. 2.5 Correct answer.
  4. 0.4

Explanation

For a proportional relationship, the constant of proportionality k is y/x. Using the point (5, 12.5), k = 12.5 ÷ 5 = 2.5.

Question 31Ratios and Proportional Relationships

A 12-ounce box of cereal costs $3.60. A 20-ounce box costs $5.60. Which box has the lower price per ounce, and what is that price?

  1. 12-ounce box at $0.30 per ounce
  2. 20-ounce box at $0.28 per ounce Correct answer.
  3. 20-ounce box at $0.30 per ounce
  4. 12-ounce box at $0.28 per ounce

Explanation

Compute the unit price for each: $3.60 ÷ 12 = $0.30 per ounce; $5.60 ÷ 20 = $0.28 per ounce. The 20-ounce box has the lower price per ounce at $0.28.

Question 32Ratios and Proportional Relationships

A student says that the ratios 4:6 and 6:4 are equivalent because both use the numbers 4 and 6. Which statement best explains why the student is incorrect?

  1. The order of the numbers matters; 4:6 simplifies to 2:3, while 6:4 simplifies to 3:2, and 2:3 is not equal to 3:2. Correct answer.
  2. The ratios are equivalent because 4 + 6 = 6 + 4.
  3. The ratios are equivalent only if you multiply both numbers by the same factor.
  4. The ratios are equivalent only if you add the same number to both parts.

Explanation

Ratios compare quantities in a specific order. Simplifying 4:6 gives 2:3, and simplifying 6:4 gives 3:2. Since 2:3 ≠ 3:2, the ratios are not equivalent.

Question 33Ratios and Proportional Relationships

A punch recipe calls for juice and soda in the ratio 5:3. If you make 32 cups of punch, how many cups of juice are used?

  1. 12
  2. 20 Correct answer.
  3. 15
  4. 24

Explanation

The total number of parts is 5 + 3 = 8. Each part is 32 ÷ 8 = 4 cups. Juice is 5 parts, so 5 × 4 = 20 cups.

Question 34Ratios and Proportional Relationships

A machine produces 250 parts in 5 minutes. At this rate, how many minutes will it take to produce 600 parts?

  1. 10
  2. 15
  3. 12 Correct answer.
  4. 8

Explanation

The unit rate is 250 ÷ 5 = 50 parts per minute. To produce 600 parts, divide 600 by 50: 600 ÷ 50 = 12 minutes.

Question 35Ratios and Proportional Relationships

A map uses a scale of 1 inch = 15 miles. Two cities are 3.5 inches apart on the map. What is the actual distance between them?

  1. 52.5 miles Correct answer.
  2. 45 miles
  3. 35 miles
  4. 18.5 miles

Explanation

The scale means each inch represents 15 miles. Multiply the map distance by the scale factor: 3.5 × 15 = 52.5 miles.

Question 36Ratios and Proportional Relationships

A student claims that the relationship shown by the points (1, 3), (2, 6), and (3, 9) is proportional because each y is 3 times x. Which statement explains why the student is correct?

  1. The relationship is proportional because the points include the origin.
  2. The relationship is proportional because the y-values increase by 3 each time.
  3. The points lie on a straight line and the ratio y/x is constant at 3, so the relationship is proportional. Correct answer.
  4. The points lie on a straight line, which is enough to show a proportional relationship.

Explanation

A proportional relationship requires a constant ratio y/x and a graph that passes through the origin. Here, y/x = 3/1 = 6/2 = 9/3 = 3, and the line through the points passes through (0,0), so the relationship is proportional.

Question 37Ratios and Proportional Relationships

A mixture contains red, blue, and yellow paint in the ratio 2:3:5. If the total mixture is 40 liters, how many more liters of yellow paint than red paint are used?

  1. 8
  2. 12 Correct answer.
  3. 20
  4. 4

Explanation

The total number of parts is 2 + 3 + 5 = 10. Each part is 40 ÷ 10 = 4 liters. Yellow is 5 parts = 20 liters, red is 2 parts = 8 liters. The difference is 20 − 8 = 12 liters.

Question 38Ratios and Proportional Relationships

A store sells notebooks at a constant price. If 4 notebooks cost $10, what is the constant of proportionality that relates cost in dollars to the number of notebooks?

  1. 2.5 Correct answer.
  2. 10
  3. 0.4
  4. 4

Explanation

The constant of proportionality is the unit rate, found by dividing cost by number of notebooks: $10 ÷ 4 = $2.50 per notebook. In a proportional relationship, the equation is y = kx, where k is this constant, so k = 2.5.

Question 39Ratios and Proportional Relationships

A student claims that the relationship between x and y in the table is proportional: x: 2, 4, 6; y: 5, 10, 15. Which statement best evaluates this claim?

  1. The claim is correct because y increases by 5 each time x increases by 2.
  2. The claim is correct because the ratios y/x are all equal to 2.5. Correct answer.
  3. The claim is incorrect because the ratios y/x are not all equal.
  4. The claim is incorrect because the graph would not pass through the origin.

Explanation

A relationship is proportional if the ratio y/x is constant for all pairs. Here, 5/2 = 2.5, 10/4 = 2.5, and 15/6 = 2.5, so the constant of proportionality is 2.5 and the claim is correct. The graph would be a line through the origin.

Question 40Ratios and Proportional Relationships

A map has a scale where 2 centimeters represents 15 kilometers. Two towns are 7 centimeters apart on the map. What is the actual distance between the towns?

  1. 45 kilometers
  2. 30 kilometers
  3. 52.5 kilometers Correct answer.
  4. 105 kilometers

Explanation

Set up the proportion: 2 cm / 15 km = 7 cm / d km. Cross-multiply to get 2d = 105, so d = 52.5 kilometers. Alternatively, the unit rate is 7.5 km per cm, and 7 × 7.5 = 52.5.

Question 41The Number System

What is the value of |−17|?

  1. 1/17
  2. 17 Correct answer.
  3. 0
  4. −17

Explanation

Absolute value measures a number's distance from zero on the number line, and distance is never negative. The point −17 sits 17 units left of zero, so |−17| equals 17. The sign of the input is discarded, not preserved or inverted.

Question 42The Number System

Which number is the additive inverse of −3/8?

  1. −8/3
  2. 8/3
  3. 3/8 Correct answer.
  4. −3/8

Explanation

The additive inverse of a number is the value that sums with it to give zero, so it is the same magnitude with the opposite sign. The opposite of −3/8 is therefore 3/8, since −3/8 + 3/8 = 0. Reciprocals and unchanged copies do not satisfy this sum.

Question 43The Number System

On a number line, which statement correctly compares −7 and −2?

  1. −7 < −2 because −7 has the smaller absolute value
  2. −7 = −2 because both are negative
  3. −7 > −2 because 7 > 2
  4. −7 < −2 because −7 lies to the left of −2 Correct answer.

Explanation

On a horizontal number line, values increase from left to right, so the number farther left is the lesser value. Since −7 is five units left of −2, we have −7 < −2. Comparing absolute values alone reverses the true order for negatives.

Question 44The Number System

What is the sum −9 + 4?

  1. 13
  2. −13
  3. 5
  4. −5 Correct answer.

Explanation

When adding numbers with opposite signs, subtract the smaller absolute value from the larger and keep the sign of the larger absolute value. Here |−9| = 9 exceeds |4| = 4, and 9 − 4 = 5, so the result is negative: −5. The signs are not simply combined by addition.

Question 45The Number System

What is the product (−6) × (−8)?

  1. 48 Correct answer.
  2. −48
  3. 14
  4. −14

Explanation

The product of two negative factors is positive, because each negative factor reverses direction and two reversals restore the original orientation. Multiplying the absolute values gives 6 × 8 = 48, and the paired negatives make the result +48. Combining the numbers by addition instead of multiplication is a separate error.

Question 46The Number System

Which expression is equivalent to 5 − (−3)?

  1. 5 − 3
  2. 5 + 3 Correct answer.
  3. −5 + 3
  4. −5 − 3

Explanation

Subtracting a number is the same as adding its additive inverse, so 5 − (−3) becomes 5 + 3. The two minus signs combine into a plus. This yields 8, which matches the original expression's value.

Question 47The Number System

A diver is at −18 meters relative to sea level and rises 7 meters. What is the diver's new position?

  1. 11 meters
  2. 25 meters
  3. −25 meters
  4. −11 meters Correct answer.

Explanation

Rising means moving in the positive direction, so the new position is −18 + 7. Because the negative magnitude is larger, subtract 7 from 18 and keep the negative sign, giving −11 meters. The diver is still below sea level after rising.

Question 48The Number System

Which of these numbers is a rational number?

  1. 0.75 Correct answer.
  2. π
  3. √7
  4. √2

Explanation

A rational number can be written as a ratio of two integers with a nonzero denominator. The terminating decimal 0.75 equals 75/100, or 3/4, so it is rational. Square roots of non-perfect squares and π have non-terminating, non-repeating decimal expansions and cannot be written that way.

Question 49The Number System

What is the value of (−2)⁴?

  1. −16
  2. 16 Correct answer.
  3. 8
  4. −8

Explanation

An exponent tells how many times to use the base as a factor: (−2)⁴ = (−2)(−2)(−2)(−2). Four negative factors pair up into two positive products, so the result is positive 16. The exponent applies to the entire parenthesized base.

Question 50The Number System

Which statement about the decimal expansion of 5/11 is true?

  1. It terminates after two decimal places.
  2. It is non-terminating and non-repeating.
  3. It repeats the block 54 forever.
  4. It repeats the block 45 forever. Correct answer.

Explanation

Dividing 5 by 11 gives 0.454545…, where the two-digit block 45 repeats without end. Repeating decimals arise because the remainders in long division cycle. Since the expansion repeats, 5/11 is rational.