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NLN NEX Math study materials
NLN NEX Math study resources

NLN NEX Math practice questions

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Question 1Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Evaluate: 5 + 3 × 4 − 2

  1. 16
  2. 30
  3. 15 Correct answer.
  4. 11

Explanation

In the order of operations, multiplication is performed before addition and subtraction. Multiply first: 3 × 4 = 12, then work left to right with 5 + 12 − 2 to get 15.

Question 2Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

In the number 47,382, what is the value of the digit 7?

  1. 70
  2. 700
  3. 70,000
  4. 7,000 Correct answer.

Explanation

Place value increases by a factor of 10 with each position moving left. The 7 sits in the thousands place, so its value is 7 × 1,000 = 7,000; the 4 in the same number is worth 40,000.

Question 3Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Round 6.487 to the nearest hundredth.

  1. 6.48
  2. 6.4
  3. 6.49 Correct answer.
  4. 6.5

Explanation

To round to the hundredths place, look at the digit immediately to its right, the thousandths digit. That digit is 7, which is 5 or greater, so the 8 in the hundredths place rounds up to 9, giving 6.49.

Question 4Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What is 3/8 + 1/8 in simplest form?

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

Explanation

When denominators match, add only the numerators and keep the denominator: 3/8 + 1/8 = 4/8. Dividing the numerator and denominator of 4/8 by their common factor 4 gives 1/2.

Question 5Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What is 12.6 + 3.75?

  1. 16.30
  2. 16.1
  3. 16.35 Correct answer.
  4. 15.35

Explanation

Align the decimal points and pad with a zero: 12.60 + 3.75. Adding column by column gives 5 hundredths, 13 tenths (write 3, carry 1), and 16 wholes, for a total of 16.35.

Question 6Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What is 15% of 240?

  1. 16
  2. 36 Correct answer.
  3. 3.6
  4. 24

Explanation

Write the percent as a decimal and multiply: 0.15 × 240 = 36. A second route is to take 10% of 240 (which is 24) and add 5% of 240 (which is 12), giving 36.

Question 7Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What is 3/4 ÷ 2/5?

  1. 8/15
  2. 1 7/8 Correct answer.
  3. 6/9
  4. 3/10

Explanation

Dividing by a fraction is the same as multiplying by its reciprocal: 3/4 × 5/2 = 15/8. Rewriting 15/8 as a mixed number gives 1 7/8.

Question 8Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Solve for x: 5/8 = x/40

  1. 25 Correct answer.
  2. 64
  3. 45
  4. 40

Explanation

Cross-multiplying gives 5 × 40 = 8x, so 200 = 8x and x = 25. Equivalently, 8 was multiplied by 5 to reach 40, so 5 must also be multiplied by 5.

Question 9Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Express the ratio 18:24 in simplest form.

  1. 9:12
  2. 2:3
  3. 6:8
  4. 3:4 Correct answer.

Explanation

Divide both terms by their greatest common factor. The greatest common factor of 18 and 24 is 6, and 18 ÷ 6 : 24 ÷ 6 = 3:4, which cannot be reduced further.

Question 10Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What is 0.6 × 0.45?

  1. 0.027
  2. 2.7
  3. 0.27 Correct answer.
  4. 0.30

Explanation

Multiply as if the numbers were whole: 6 × 45 = 270. The factors contain one and two decimal places, three in total, so place the decimal point three places from the right: 0.270 = 0.27.

Question 11Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Write 7/20 as a percent.

  1. 20%
  2. 35% Correct answer.
  3. 70%
  4. 7%

Explanation

Divide the numerator by the denominator, then multiply by 100: 7 ÷ 20 = 0.35, and 0.35 × 100 = 35%. Multiplying 7/20 by 5/5 gives 35/100, which is 35%.

Question 12Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

A package of 12 pencils costs $3.60. What is the cost per pencil?

  1. $4.32
  2. $0.30 Correct answer.
  3. $0.36
  4. $0.03

Explanation

A unit rate is found by dividing the total cost by the number of items: $3.60 ÷ 12 = $0.30 per pencil. Checking the result, 12 × $0.30 = $3.60.

Question 13Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What is 7 1/4 − 2 3/4?

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

Explanation

Because 1/4 is smaller than 3/4, borrow 1 from the 7 and rewrite it as 4/4, giving 6 5/4 − 2 3/4. Subtracting wholes and fractions separately gives 4 2/4, which simplifies to 4 1/2.

Question 14Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

A jacket's price rises from $40 to $50. What is the percent increase?

  1. 125%
  2. 25% Correct answer.
  3. 20%
  4. 10%

Explanation

Percent change compares the amount of change with the original value. The change is $50 − $40 = $10, and $10 ÷ $40 = 0.25, which is a 25% increase.

Question 15Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Evaluate: 2³ + 4 × (6 − 2)

  1. 16
  2. 24 Correct answer.
  3. 20
  4. 48

Explanation

Work through the order of operations: parentheses first (6 − 2 = 4), then the exponent (2³ = 8) and the multiplication (4 × 4 = 16), and finally the addition (8 + 16 = 24).

Question 16Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What is 4.5 ÷ 0.09?

  1. 5
  2. 500
  3. 0.5
  4. 50 Correct answer.

Explanation

Multiply both the dividend and the divisor by 100 to clear the decimals: 4.5 ÷ 0.09 becomes 450 ÷ 9. Since 9 × 50 = 450, the quotient is 50, and scaling both numbers by the same factor leaves the quotient unchanged.

Question 17Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

A jacket priced at $80 is discounted 25%, and then an additional 10% is taken off the sale price. What is the final price?

  1. $54 Correct answer.
  2. $52
  3. $60
  4. $56

Explanation

Each discount applies to the price in effect at that moment. After the first discount the price is $80 × 0.75 = $60, and the second discount applies to $60, giving $60 × 0.90 = $54.

Question 18Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Evaluate: (3/4 + 1/6) ÷ 11/12

  1. 1 Correct answer.
  2. 12/11
  3. 11/12
  4. 11/18

Explanation

Add inside the parentheses using the common denominator 12: 9/12 + 2/12 = 11/12. Then divide by multiplying by the reciprocal: 11/12 × 12/11 = 1.

Question 19Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

A recipe that makes 6 servings uses 4.5 cups of flour. At the same rate, how many cups of flour are needed for 15 servings?

  1. 13.5 cups
  2. 9 cups
  3. 10.5 cups
  4. 11.25 cups Correct answer.

Explanation

Set up the proportion 4.5 cups / 6 servings = x / 15 servings. The number of servings grows by a factor of 15 ÷ 6 = 2.5, so the flour needed is 4.5 × 2.5 = 11.25 cups.

Question 20Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

After a 20% increase, a number becomes 96. What was the original number?

  1. 115.2
  2. 76
  3. 80 Correct answer.
  4. 76.8

Explanation

A 20% increase makes the new value 120% of the original, so 1.20x = 96. Dividing both sides by 1.20 gives x = 80, and checking, 80 + 0.20(80) = 96.

Question 21Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What is the greatest common factor of 24 and 36?

  1. 12 Correct answer.
  2. 72
  3. 6
  4. 18

Explanation

The greatest common factor is the largest whole number that divides both values evenly. Both 24 ÷ 12 = 2 and 36 ÷ 12 = 3 are whole numbers, and no number larger than 12 divides both.

Question 22Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Which fraction is 0.75 written in simplest form?

  1. 75/100
  2. 5/8
  3. 7/10
  4. 3/4 Correct answer.

Explanation

The decimal 0.75 means 75 hundredths, so it equals 75/100. Dividing the numerator and denominator by their greatest common factor of 25 gives 3/4, which cannot be reduced further.

Question 23Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

A class has 12 boys and 18 girls. What is the ratio of boys to the total number of students, in simplest form?

  1. 2:3
  2. 3:5
  3. 2:5 Correct answer.
  4. 12:18

Explanation

The total number of students is 12 + 18 = 30, so the ratio of boys to all students is 12:30. Dividing both terms by 6 gives 2:5, which is simplest form.

Question 24Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

A runner covers 3.6 km, then 2.75 km, then 4.125 km. What is the total distance?

  1. 6.875 km
  2. 10.475 km Correct answer.
  3. 9.475 km
  4. 6.35 km

Explanation

Line up the decimal points and pad with zeros: 3.600 + 2.750 + 4.125. Adding the thousandths, hundredths, tenths, and whole-number columns with carrying gives a total of 10.475 km.

Question 25Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Three-fifths of a number is 42. What is five-sevenths of that same number?

  1. 42
  2. 70
  3. 60
  4. 50 Correct answer.

Explanation

If 3/5 of the number is 42, then 1/5 of it is 42 ÷ 3 = 14, so the whole number is 14 × 5 = 70. Taking 5/7 of 70 gives 50.

Question 26Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

A warehouse receives 4,786 boxes on Monday and 2,539 boxes on Tuesday. How many boxes does it receive in all?

  1. 7,325 Correct answer.
  2. 7,315
  3. 7,215
  4. 6,325

Explanation

Line up the digits by place value and add column by column from the right, carrying whenever a column totals 10 or more. The ones column gives 15 (write 5, carry 1), the tens column gives 12 (write 2, carry 1), the hundreds column gives 13 (write 3, carry 1), and the thousands column gives 7.

Question 27Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What is 9.4 − 3.68?

  1. 6.28
  2. 6.72
  3. 5.82
  4. 5.72 Correct answer.

Explanation

Write the numbers with the same number of decimal places (9.40 − 3.68), stack them by decimal point, and subtract from the right, borrowing as needed: 10 − 8 = 2, 13 − 6 = 7, and 8 − 3 = 5.

Question 28Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What is 2/3 × 3/8?

  1. 5/24
  2. 1/4 Correct answer.
  3. 6/11
  4. 5/11

Explanation

To multiply fractions, multiply numerators together and denominators together: (2 × 3)/(3 × 8) = 6/24. Dividing the numerator and denominator by 6 gives 1/4.

Question 29Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Write 45% as a decimal.

  1. 45.0
  2. 0.045
  3. 0.45 Correct answer.
  4. 4.5

Explanation

A percent is a fraction with denominator 100, so 45% = 45/100. Dividing by 100 moves the decimal point two places to the left, giving 0.45.

Question 30Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Round 4,682 to the nearest hundred.

  1. 4,800
  2. 4,700 Correct answer.
  3. 4,600
  4. 4,680

Explanation

The hundreds digit is 6 and the digit to its right in the tens place is 8. Since 8 is 5 or more, round the hundreds digit up to 7 and replace the tens and ones digits with zeros, giving 4,700.

Question 31Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Which fraction is equivalent to 2/5?

  1. 6/15 Correct answer.
  2. 4/15
  3. 2/10
  4. 5/2

Explanation

Multiplying the numerator and the denominator of a fraction by the same nonzero number produces an equivalent fraction. Multiplying both parts of 2/5 by 3 gives 6/15.

Question 32Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Evaluate: 48 ÷ 8 + 5 × 2

  1. 13
  2. 22
  3. 10
  4. 16 Correct answer.

Explanation

In the order of operations, multiplication and division are performed before addition, working left to right within that tier. So 48 ÷ 8 = 6 and 5 × 2 = 10, and then 6 + 10 = 16.

Question 33Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Which of the following numbers has the greatest value?

  1. 0.58 Correct answer.
  2. 0.51
  3. 0.5
  4. 0.508

Explanation

Compare place by place from left to right, writing each number to three decimal places: 0.508, 0.510, 0.580, 0.500. The tenths digits are all 5, and the largest hundredths digit is 8, so 0.58 is greatest.

Question 34Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What is 3 2/5 + 1 7/10?

  1. 4 9/10
  2. 4 1/10
  3. 5 9/10
  4. 5 1/10 Correct answer.

Explanation

Rewrite 2/5 as 4/10 so the fractions share a denominator, then add: 4/10 + 7/10 = 11/10 = 1 1/10. Adding the whole numbers 3 + 1 = 4 and then the renamed fraction gives 5 1/10.

Question 35Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What is the least common multiple of 12 and 18?

  1. 216
  2. 72
  3. 36 Correct answer.
  4. 6

Explanation

Factor both numbers: 12 = 2² × 3 and 18 = 2 × 3². The least common multiple takes the highest power of each prime, giving 2² × 3² = 4 × 9 = 36.

Question 36Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What percent of 80 is 12?

  1. 20%
  2. 6.7%
  3. 15% Correct answer.
  4. 12%

Explanation

Percent means part per hundred, so divide the part by the whole and multiply by 100: 12 ÷ 80 = 0.15, and 0.15 × 100 = 15%.

Question 37Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

If 5 pounds of apples cost $9.50, how much do 8 pounds cost at the same rate?

  1. $16.00
  2. $12.80
  3. $15.20 Correct answer.
  4. $14.25

Explanation

Find the unit price first: $9.50 ÷ 5 = $1.90 per pound. Multiplying by 8 pounds gives $1.90 × 8 = $15.20.

Question 38Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Express the ratio 24:36:60 in simplest form.

  1. 2:3:5 Correct answer.
  2. 8:12:20
  3. 4:6:10
  4. 12:18:30

Explanation

A ratio is in simplest form when the greatest common factor of all its terms is 1. The greatest common factor of 24, 36, and 60 is 12, and dividing every term by 12 gives 2:3:5.

Question 39Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

A school has 480 students. Three-eighths of the students ride the bus. How many students ride the bus?

  1. 120
  2. 160
  3. 180 Correct answer.
  4. 200

Explanation

To take a fraction of a quantity, divide by the denominator and multiply by the numerator: 480 ÷ 8 = 60, and 60 × 3 = 180.

Question 40Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What is 12.6 ÷ 4?

  1. 3.015
  2. 3.15 Correct answer.
  3. 31.5
  4. 0.315

Explanation

Divide as with whole numbers: 126 ÷ 4 = 31.5. Since 12.6 has one decimal place and the divisor is a whole number, the quotient also has one decimal place, giving 3.15. Checking, 3.15 × 4 = 12.6.

Question 41Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

What is 7/8 − 1/3?

  1. 6/5
  2. 13/24 Correct answer.
  3. 13/48
  4. 20/24

Explanation

The least common denominator of 8 and 3 is 24. Rewrite both fractions as 21/24 and 8/24, then subtract the numerators: 21 − 8 = 13, giving 13/24.

Question 42Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

A sum of $180 is divided between two people in the ratio 4:5. How much does the person with the larger share receive?

  1. $100 Correct answer.
  2. $108
  3. $90
  4. $80

Explanation

The ratio 4:5 creates 4 + 5 = 9 equal parts. Each part is $180 ÷ 9 = $20, and the larger share is 5 parts, or 5 × $20 = $100.

Question 43Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

A machine fills 84 bottles in 6 minutes. At the same rate, how many bottles does it fill in 15 minutes?

  1. 180
  2. 240
  3. 1,260
  4. 210 Correct answer.

Explanation

Find the rate per minute first: 84 ÷ 6 = 14 bottles per minute. Multiplying by 15 minutes gives 14 × 15 = 210 bottles.

Question 44Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Write 3/8 as a decimal.

  1. 0.125
  2. 0.3
  3. 0.375 Correct answer.
  4. 2.667

Explanation

A fraction bar means division, so divide the numerator by the denominator: 3 ÷ 8 = 0.375. Checking, 0.375 × 8 = 3.

Question 45Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Which of the following numbers is prime?

  1. 63
  2. 57
  3. 51
  4. 59 Correct answer.

Explanation

A prime number greater than 1 has exactly two factors, 1 and itself. Testing 59 against the primes up to its square root (2, 3, 5, 7) shows no divisor, so 59 is prime.

Question 46Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

A bicycle has an original price of $250. It is marked down 20%, and then a 5% sales tax is added to the sale price. What is the final cost?

  1. $187.50
  2. $212.50
  3. $200
  4. $210 Correct answer.

Explanation

A 20% markdown leaves 80% of the price: $250 × 0.80 = $200. The 5% tax applies to that sale price, so multiply by 1.05: $200 × 1.05 = $210.

Question 47Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

A 12-ounce box of cereal costs $3.84, and an 18-ounce box of the same cereal costs $5.22. Which box is the better buy, and by how much per ounce?

  1. They cost the same per ounce
  2. The 18-ounce box, by $0.06 per ounce
  3. The 12-ounce box, by $0.03 per ounce
  4. The 18-ounce box, by $0.03 per ounce Correct answer.

Explanation

Compare unit prices: $3.84 ÷ 12 = $0.32 per ounce, and $5.22 ÷ 18 = $0.29 per ounce. The 18-ounce box is cheaper per ounce, and the difference is $0.32 − $0.29 = $0.03.

Question 48Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

Which list orders the values 0.58, 7/12, 3/5, and 5/8 from least to greatest?

  1. 3/5, 0.58, 7/12, 5/8
  2. 0.58, 3/5, 7/12, 5/8
  3. 7/12, 0.58, 5/8, 3/5
  4. 0.58, 7/12, 3/5, 5/8 Correct answer.

Explanation

Convert every value to a decimal: 0.58, 7/12 ≈ 0.5833, 3/5 = 0.600, and 5/8 = 0.625. Comparing the thousandths place gives the order 0.58, 7/12, 3/5, 5/8.

Question 49Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

A punch recipe mixes juice and soda in the ratio 3:2. To make 45 cups of punch, how many cups of juice are needed?

  1. 18
  2. 27 Correct answer.
  3. 22.5
  4. 30

Explanation

The ratio 3:2 makes 3 + 2 = 5 equal parts in the mixture. Each part is 45 ÷ 5 = 9 cups, and juice is 3 parts, so 3 × 9 = 27 cups.

Question 50Arithmetic and Number Sense (operations with whole numbers, fractions, decimals, percents, ratios and proportions)

A tank is 2/5 full. After 14 gallons of water are added, the tank is 3/4 full. What is the capacity of the tank in gallons?

  1. 35
  2. 56
  3. 40 Correct answer.
  4. 20

Explanation

The added water fills the difference between the two fractions: 3/4 − 2/5 = 15/20 − 8/20 = 7/20 of the tank. If 7/20 of the capacity is 14 gallons, then the capacity is 14 ÷ 7/20 = 14 × 20/7 = 40 gallons.