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FAST Grade 7 Math study materials
FAST Grade 7 Math study resources

FAST Grade 7 Math practice questions

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Question 1Number Sense and Operations (rational numbers, integers, exponents)

What is the value of (−8) + 15?

  1. 7 Correct answer.
  2. −23
  3. 23
  4. −7

Explanation

When adding integers with opposite signs, subtract the smaller absolute value from the larger and keep the sign of the number with the larger absolute value. Here |15| − |−8| = 15 − 8 = 7, and 15 is positive, so the sum is 7.

Question 2Number Sense and Operations (rational numbers, integers, exponents)

What is the value of (−6) × (−9)?

  1. −15
  2. 15
  3. −54
  4. 54 Correct answer.

Explanation

The product of two negative integers is positive, and 6 × 9 = 54, so (−6) × (−9) = 54.

Question 3Number Sense and Operations (rational numbers, integers, exponents)

What is 3⁴ written in standard form?

  1. 34
  2. 64
  3. 12
  4. 81 Correct answer.

Explanation

The exponent 4 tells you to use 3 as a factor four times: 3 × 3 × 3 × 3 = 81. Multiplying the base by the exponent (3 × 4) is a common error but does not represent repeated multiplication.

Question 4Number Sense and Operations (rational numbers, integers, exponents)

Which number is the additive inverse of −3/4?

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

Explanation

An additive inverse is the number that sums to zero with the given number. Since −3/4 + 3/4 = 0, the additive inverse is 3/4, which has the same absolute value but the opposite sign.

Question 5Number Sense and Operations (rational numbers, integers, exponents)

Which list shows the numbers ordered from least to greatest? −2.5, 1/3, −0.75, 2, −1/2

  1. 1/3, −0.75, −1/2, −2.5, 2
  2. −2.5, −0.75, −1/2, 1/3, 2 Correct answer.
  3. −2.5, −1/2, −0.75, 1/3, 2
  4. −0.75, −2.5, −1/2, 1/3, 2

Explanation

On a number line, negatives lie to the left of positives, and among negatives the one with the larger absolute value is smaller. Since −2.5 < −0.75 < −0.5 < 1/3 < 2, the correct order is −2.5, −0.75, −1/2, 1/3, 2.

Question 6Number Sense and Operations (rational numbers, integers, exponents)

What is the value of |−17|?

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

Explanation

Absolute value measures distance from zero on the number line, so it is never negative. The distance from −17 to 0 is 17 units, so |−17| = 17.

Question 7Number Sense and Operations (rational numbers, integers, exponents)

What is 5⁰ + 5¹?

  1. 5
  2. 6 Correct answer.
  3. 0
  4. 10

Explanation

Any nonzero base raised to the power 0 equals 1, so 5⁰ = 1, while 5¹ = 5. Adding them gives 1 + 5 = 6.

Question 8Number Sense and Operations (rational numbers, integers, exponents)

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

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

Explanation

Rising means moving in the positive direction, so the new position is −18 + 7. Subtracting the absolute values gives 18 − 7 = 11, and the sign follows the larger absolute value (−18), so the result is −11 meters.

Question 9Number Sense and Operations (rational numbers, integers, exponents)

What is −3/8 ÷ 3/4?

  1. −2
  2. −1/2 Correct answer.
  3. 1/2
  4. −9/32

Explanation

Dividing by a fraction multiplies by its reciprocal: −3/8 × 4/3. The 3s cancel, leaving −4/8 = −1/2, and a negative divided by a positive is negative.

Question 10Number Sense and Operations (rational numbers, integers, exponents)

What is (−2)³ × (−2)² expressed as a single power?

  1. (−2)¹
  2. (−2)⁶
  3. 4⁵
  4. (−2)⁵ Correct answer.

Explanation

When multiplying powers with the same base, keep the base and add the exponents: 3 + 2 = 5, so the product is (−2)⁵. The value is negative because the base is negative and the exponent is odd.

Question 11Number Sense and Operations (rational numbers, integers, exponents)

Which expression is equivalent to 0.6 − (−0.45)?

  1. −0.6 + 0.45
  2. 0.6 + (−0.45)
  3. −0.6 − 0.45
  4. 0.6 + 0.45 Correct answer.

Explanation

Subtracting a negative number is the same as adding its opposite, so 0.6 − (−0.45) = 0.6 + 0.45 = 1.05.

Question 12Number Sense and Operations (rational numbers, integers, exponents)

A submarine descends 4 meters every minute. After 6 minutes, where is it relative to its starting point?

  1. 2 meters below
  2. 24 meters below Correct answer.
  3. 10 meters below
  4. 24 meters above

Explanation

Descending 4 meters each minute for 6 minutes is a total change of 6 × (−4) = −24 meters. The negative sign means the submarine ends 24 meters below its starting point.

Question 13Number Sense and Operations (rational numbers, integers, exponents)

What is the value of (−3)⁴ − (−3)³?

  1. −54
  2. 108 Correct answer.
  3. 54
  4. 0

Explanation

A negative base raised to an even power is positive, so (−3)⁴ = 81, while (−3)³ = −27 because the exponent is odd. Then 81 − (−27) = 81 + 27 = 108.

Question 14Number Sense and Operations (rational numbers, integers, exponents)

Which statement about the product 5/6 × 7/8 is true without computing the exact value?

  1. It is greater than 1 because both fractions are positive.
  2. It is greater than 7/8 because 5/6 is close to 1.
  3. It is equal to 5/6 because the fractions are close.
  4. It is less than 5/6 because 7/8 is less than 1. Correct answer.

Explanation

Multiplying a positive number by a factor less than 1 produces a product smaller than the original number. Since 7/8 < 1, the product 5/6 × 7/8 must be less than 5/6.

Question 15Number Sense and Operations (rational numbers, integers, exponents)

What is 2⁻³ written as a fraction?

  1. 1/6
  2. 1/8 Correct answer.
  3. −8
  4. −1/8

Explanation

A negative exponent means the reciprocal of the corresponding positive power: 2⁻³ = 1/2³ = 1/8. The result is positive because the negative sign belongs to the exponent, not the base.

Question 16Number Sense and Operations (rational numbers, integers, exponents)

Which value is the multiplicative inverse of −5/9?

  1. 9/5
  2. 5/9
  3. −5/9
  4. −9/5 Correct answer.

Explanation

A multiplicative inverse (reciprocal) is the number that multiplies with the original to give 1. Since −5/9 × (−9/5) = 45/45 = 1, the multiplicative inverse is −9/5.

Question 17Number Sense and Operations (rational numbers, integers, exponents)

Evaluate (−4)² + (−2)³ − 3⁰.

  1. 15
  2. 9 Correct answer.
  3. −1
  4. 1

Explanation

Compute each power first: (−4)² = 16, (−2)³ = −8, and 3⁰ = 1. Then 16 + (−8) − 1 = 16 − 8 − 1 = 7... correcting carefully, 16 − 8 = 8 and 8 − 1 = 7, so the value is 7.

Question 18Number Sense and Operations (rational numbers, integers, exponents)

A number line shows points P at −1.5 and Q at 2.25. What is the distance between P and Q?

  1. 0.75
  2. 3.75 Correct answer.
  3. 3.5
  4. −3.75

Explanation

Distance on a number line is the absolute value of the difference: |2.25 − (−1.5)| = |2.25 + 1.5| = 3.75. Distance is always nonnegative.

Question 19Number Sense and Operations (rational numbers, integers, exponents)

Which expression has the greatest value?

  1. (−1)¹⁰⁰ Correct answer.
  2. (−1)⁰
  3. (−1)⁹⁹
  4. −1²

Explanation

A negative base raised to an even power is positive, so (−1)¹⁰⁰ = 1. Odd powers of −1 equal −1, and −1² means −(1²) = −1 because the exponent applies only to 1. Since 1 is greater than −1, (−1)¹⁰⁰ is the largest.

Question 20Number Sense and Operations (rational numbers, integers, exponents)

What is the value of (−2/3)² × (−3/4)³?

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

Explanation

Square the first factor: (−2/3)² = 4/9. Cube the second: (−3/4)³ = −27/64. Multiplying gives (4 × −27)/(9 × 64) = −108/576 = −3/16... simplifying −108/576 by 36 yields −3/16, so the value is negative and small.

Question 21Number Sense and Operations (rational numbers, integers, exponents)

Which statement is true for all nonzero values of a?

  1. a⁰ = 1 and a¹ = a Correct answer.
  2. a⁰ = 0 and a¹ = a
  3. a⁰ = 1 and a¹ = 0
  4. a⁰ = a and a¹ = 1

Explanation

By the properties of exponents, any nonzero base raised to the zero power equals 1, and any base raised to the first power equals itself. These two facts hold for positive, negative, and fractional values of a.

Question 22Number Sense and Operations (rational numbers, integers, exponents)

A hiker starts at an elevation of −120 feet, climbs to −35 feet, then descends 60 feet. What is the final elevation?

  1. −145 feet
  2. −85 feet
  3. −25 feet
  4. −95 feet Correct answer.

Explanation

Climbing adds and descending subtracts, so the change is −120 + 85 − 60. First −120 + 85 = −35, then −35 − 60 = −95 feet.

Question 23Number Sense and Operations (rational numbers, integers, exponents)

Which comparison is correct?

  1. −7/8 = −0.9
  2. −7/8 < −0.9
  3. −7/8 < −1
  4. −7/8 > −0.9 Correct answer.

Explanation

Convert −7/8 to a decimal: −0.875. On the number line −0.875 lies to the right of −0.9, so −0.875 > −0.9. Among negative numbers, the one closer to zero is greater.

Question 24Number Sense and Operations (rational numbers, integers, exponents)

The expression 2⁵ × 2⁻³ ÷ 2⁻¹ simplifies to which value?

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

Explanation

Add exponents when multiplying and subtract when dividing: 5 + (−3) − (−1) = 5 − 3 + 1 = 3. So the expression equals 2³ = 8.

Question 25Number Sense and Operations (rational numbers, integers, exponents)

A recipe calls for 3/4 cup of sugar, and a baker makes 2/3 of the recipe. How much sugar is used?

  1. 5/12 cup
  2. 9/8 cups
  3. 1/2 cup Correct answer.
  4. 1 5/12 cups

Explanation

Taking 2/3 of 3/4 means multiplying: (2/3) × (3/4). The 3s cancel, leaving 2/4 = 1/2 cup.

Question 26Number Sense and Operations (rational numbers, integers, exponents)

What is the value of −7 + 12 − 5?

  1. 10
  2. 0 Correct answer.
  3. −24
  4. −10

Explanation

Adding −7 and 12 gives 5, and subtracting 5 from 5 gives 0. Order of addition and subtraction from left to right produces the same result here.

Question 27Number Sense and Operations (rational numbers, integers, exponents)

Which number is the additive inverse of −4.25?

  1. 1/4.25
  2. 0
  3. −4.25
  4. 4.25 Correct answer.

Explanation

The additive inverse of a number is the value that sums with it to zero, so its sign is reversed while the magnitude stays the same. Since −4.25 + 4.25 = 0, the additive inverse is 4.25.

Question 28Number Sense and Operations (rational numbers, integers, exponents)

Which expression is equivalent to −6 − (−9)?

  1. 6 − 9
  2. −6 + 9 Correct answer.
  3. −6 − 9
  4. 6 + 9

Explanation

Subtracting a negative number is the same as adding its opposite, so −6 − (−9) becomes −6 + 9. That equals 3.

Question 29Number Sense and Operations (rational numbers, integers, exponents)

What is the value of |−9| − |4|?

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

Explanation

Absolute value gives the distance from zero, so |−9| = 9 and |4| = 4. Subtracting gives 9 − 4 = 5.

Question 30Number Sense and Operations (rational numbers, integers, exponents)

What is the value of (−5)² − 4²?

  1. −41
  2. 9 Correct answer.
  3. 41
  4. −9

Explanation

Squaring a negative number gives a positive result, so (−5)² = 25, and 4² = 16. Then 25 − 16 = 9.

Question 31Number Sense and Operations (rational numbers, integers, exponents)

A stock price changes by −$3.50 each day for 4 days, then changes by +$2.25 on the fifth day. What is the net change over the five days?

  1. −$9.25
  2. −$11.75 Correct answer.
  3. −$14.00
  4. −$16.25

Explanation

Four daily losses of $3.50 total −$14.00, and adding the +$2.25 gain gives −$14.00 + $2.25 = −$11.75. The net change is a decrease of $11.75.

Question 32Number Sense and Operations (rational numbers, integers, exponents)

Which expression is equivalent to (3/5) ÷ (−9/10)?

  1. (5/3) × (−9/10)
  2. (3/5) × (−10/9) Correct answer.
  3. (3/5) × (−9/10)
  4. (3/5) × (10/9)

Explanation

Dividing by a fraction is the same as multiplying by its reciprocal, and the reciprocal of −9/10 is −10/9. So the quotient equals (3/5) × (−10/9), which is −2/3.

Question 33Number Sense and Operations (rational numbers, integers, exponents)

What is the value of (−1)⁵ + (−1)⁶ + (−1)⁷?

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

Explanation

A negative base raised to an odd power is negative and to an even power is positive, so the terms are −1, 1, and −1. Their sum is −1.

Question 34Number Sense and Operations (rational numbers, integers, exponents)

Which expression is equivalent to 7⁶ ÷ 7²?

  1. 7³
  2. 7⁸
  3. 7⁴ Correct answer.
  4. 7¹²

Explanation

When dividing powers with the same base, subtract the exponents: 7⁶ ÷ 7² = 7^(6−2) = 7⁴. The base stays unchanged.

Question 35Number Sense and Operations (rational numbers, integers, exponents)

A number is multiplied by −2/3, and the result is 8/9. What is the number?

  1. 4/3
  2. −4/3 Correct answer.
  3. −16/27
  4. −3/4

Explanation

Divide the result by the factor: (8/9) ÷ (−2/3) = (8/9) × (−3/2) = −24/18 = −4/3. Checking, (−4/3) × (−2/3) = 8/9.

Question 36Number Sense and Operations (rational numbers, integers, exponents)

Which statement correctly compares −7/8 and −0.83?

  1. −7/8 > −0.83 because −7/8 is closer to zero
  2. −7/8 < −0.83 because −0.83 is negative
  3. −7/8 = −0.83 because the values round to the same hundredth
  4. −7/8 < −0.83 because −7/8 is farther from zero Correct answer.

Explanation

Since 7/8 = 0.875, the value −7/8 is −0.875, which lies farther left on the number line than −0.83. For negative numbers, the one with greater magnitude is smaller, so −7/8 < −0.83.

Question 37Number Sense and Operations (rational numbers, integers, exponents)

What is the value of (−3/4)³?

  1. −27/12
  2. 27/64
  3. −27/64 Correct answer.
  4. −9/16

Explanation

Cube the numerator and the denominator: 3³ = 27 and 4³ = 64. A negative base raised to an odd power stays negative, so the result is −27/64.

Question 38Number Sense and Operations (rational numbers, integers, exponents)

A glacier's front moves −2.4 meters per year for 3 years, then −1.75 meters per year for 2 years. What is the total movement of the front?

  1. −5.9 meters
  2. −10.7 meters Correct answer.
  3. −7.7 meters
  4. −12.45 meters

Explanation

The first phase contributes 3 × (−2.4) = −7.2 meters and the second contributes 2 × (−1.75) = −3.5 meters. Adding the two negative amounts gives −10.7 meters.

Question 39Number Sense and Operations (rational numbers, integers, exponents)

Which expression is equivalent to (2³ × 2⁻⁵) ÷ 2⁻⁴?

  1. 2⁻²
  2. 2⁶
  3. 2⁻⁶
  4. 2² Correct answer.

Explanation

Multiply inside the parentheses by adding exponents: 2^(3 + (−5)) = 2⁻². Then divide by subtracting the exponent −4: 2^(−2 − (−4)) = 2².

Question 40Number Sense and Operations (rational numbers, integers, exponents)

For a nonzero rational number r, which statement is always true?

  1. r × (−1) is always less than r
  2. r × (−1) = −r and r × (−1) has the same absolute value as r Correct answer.
  3. r × (−1) equals the reciprocal of r
  4. r × (−1) is always negative

Explanation

Multiplying by −1 reverses the sign of a number without changing its distance from zero, so r × (−1) = −r and |−r| = |r|. This holds whether r is positive or negative.

Question 41Proportional Reasoning (ratios, rates, percents, 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. 18
  2. 9
  3. 8 Correct answer.
  4. 6

Explanation

The ratio of flour to sugar is 3:2, so each part of flour corresponds to 2/3 of a cup of sugar per cup of flour. Multiplying 12 cups of flour by 2/3 gives 8 cups of sugar. Setting up the proportion 3/2 = 12/x and cross-multiplying (3x = 24) confirms x = 8.

Question 42Proportional Reasoning (ratios, rates, percents, proportional relationships)

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

  1. 0.02
  2. 450
  3. 50 Correct answer.
  4. 153

Explanation

A unit rate expresses the distance per one hour, found by dividing total distance by total time. Dividing 150 miles by 3 hours gives 50 miles per hour. The other values either multiply the quantities or invert the division.

Question 43Proportional Reasoning (ratios, rates, percents, proportional relationships)

What is 25% of 80?

  1. 2
  2. 25
  3. 20 Correct answer.
  4. 32

Explanation

A percent is a ratio out of 100, so 25% equals 0.25. Multiplying 0.25 by 80 gives 20. Equivalently, 25% is one quarter, and one quarter of 80 is 20.

Question 44Proportional Reasoning (ratios, rates, percents, proportional relationships)

Which pair of ratios forms a proportion?

  1. 5/8 and 8/5
  2. 3/5 and 5/7
  3. 2/3 and 3/2
  4. 4/6 and 6/9 Correct answer.

Explanation

Two ratios form a proportion when their cross products are equal. For 4/6 and 6/9, cross-multiplying gives 4 × 9 = 36 and 6 × 6 = 36, so they are equal. Both simplify to 2/3, confirming the proportion.

Question 45Proportional Reasoning (ratios, rates, percents, proportional relationships)

A store advertises a 20% discount on a jacket priced at $45. What is the sale price?

  1. $36 Correct answer.
  2. $25
  3. $9
  4. $44

Explanation

The discount amount is 20% of $45, which is 0.20 × 45 = $9. Subtracting the discount from the original price gives 45 − 9 = $36. Alternatively, paying 80% of $45 (0.80 × 45) also yields $36.

Question 46Proportional Reasoning (ratios, rates, percents, proportional relationships)

On a map, 1 inch represents 25 miles. A road measures 4.5 inches on the map. What is the actual length of the road?

  1. 112.5 miles Correct answer.
  2. 6.25 miles
  3. 100 miles
  4. 29.5 miles

Explanation

The scale is a ratio of 1 inch to 25 miles, so multiply the map length by 25. Doing 4.5 × 25 gives 112.5 miles. The proportion 1/25 = 4.5/x, solved by cross-multiplying, confirms x = 112.5.

Question 47Proportional Reasoning (ratios, rates, percents, proportional relationships)

A punch recipe mixes 2 parts juice with 5 parts sparkling water. If you make 28 cups of punch total, how many cups are juice?

  1. 14
  2. 8 Correct answer.
  3. 10
  4. 20

Explanation

The total number of parts is 2 + 5 = 7, and juice is 2 of those 7 parts. Each part is 28 ÷ 7 = 4 cups, so juice is 2 × 4 = 8 cups. Checking: water is 5 × 4 = 20 cups, and 8 + 20 = 28.

Question 48Proportional Reasoning (ratios, rates, percents, proportional relationships)

Which statement describes a proportional relationship between two quantities x and y?

  1. y is always greater than x
  2. the ratio y/x is constant for all pairs Correct answer.
  3. y equals 4 when x equals 0
  4. y increases by 3 each time x increases by 1

Explanation

A proportional relationship means y = kx for some constant k, so the ratio y divided by x stays the same for every pair. Its graph is a straight line through the origin. Having a nonzero value when x is 0 or a fixed additive change does not guarantee proportionality.

Question 49Proportional Reasoning (ratios, rates, percents, proportional relationships)

A printer prints 180 pages in 4 minutes. At this rate, how many pages does it print in 7 minutes?

  1. 270
  2. 315 Correct answer.
  3. 360
  4. 45

Explanation

First find the unit rate by dividing 180 pages by 4 minutes, giving 45 pages per minute. Multiplying by 7 minutes gives 315 pages. The proportion 180/4 = x/7 also solves to x = 315.

Question 50Proportional Reasoning (ratios, rates, percents, proportional relationships)

A student scored 45 out of 60 on a test. What percent did the student score?

  1. 60%
  2. 80%
  3. 45%
  4. 75% Correct answer.

Explanation

To convert a fraction to a percent, divide the part by the whole and multiply by 100. Doing 45 ÷ 60 = 0.75, and 0.75 × 100 = 75%. So the score is 75%.