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OST Grade 5 Math study materials
OST Grade 5 Math study resources

OST Grade 5 Math practice questions

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Question 1Mathematics (Grade 5)

What is the value of the digit 7 in the number 4,782,015?

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

Explanation

In 4,782,015 the digits from the right occupy ones, tens, hundreds, thousands, ten-thousands, hundred-thousands, and millions places. The 7 sits in the hundred-thousands place, so its value is 7 × 100,000 = 700,000.

Question 2Mathematics (Grade 5)

A rope is 3/4 meter long. A second rope is 5/8 meter long. How much longer is the first rope than the second?

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

Explanation

Rewrite 3/4 as 6/8 so both fractions share a denominator, then subtract: 6/8 − 5/8 = 1/8. The first rope is 1/8 meter longer.

Question 3Mathematics (Grade 5)

Which number is read as "six and forty-two thousandths"?

  1. 6.042 Correct answer.
  2. 6.42
  3. 6.0042
  4. 60.42

Explanation

The whole-number part "six" gives 6, and "forty-two thousandths" fills the thousandths place, giving 42/1000 = 0.042. Combined, the number is 6.042.

Question 4Mathematics (Grade 5)

Compute 4,236 ÷ 6.

  1. 696
  2. 716
  3. 760
  4. 706 Correct answer.

Explanation

Six goes into 42 seven times with no remainder, so bring down the 3, which is too small, giving 0 in the tens place and a remainder of 3. Then 36 ÷ 6 = 6, so the quotient is 706.

Question 5Mathematics (Grade 5)

Which expression has the same value as 8 × (30 + 4)?

  1. 8 + 30 × 4
  2. 8 × 30 + 4
  3. 8 × 30 + 8 × 4 Correct answer.
  4. 8 × 34 + 8

Explanation

The distributive property lets you multiply each addend inside the parentheses by 8, giving 8 × 30 + 8 × 4. Both expressions equal 272.

Question 6Mathematics (Grade 5)

What is the volume of a rectangular prism with length 5 cm, width 4 cm, and height 3 cm?

  1. 60 cm³ Correct answer.
  2. 12 cm³
  3. 120 cm³
  4. 47 cm³

Explanation

Volume of a rectangular prism equals length × width × height. Here 5 × 4 = 20, and 20 × 3 = 60, so the volume is 60 cubic centimeters.

Question 7Mathematics (Grade 5)

Which list of numbers is ordered from least to greatest?

  1. 0.4, 0.45, 0.405, 0.5
  2. 0.405, 0.4, 0.45, 0.5
  3. 0.5, 0.45, 0.405, 0.4
  4. 0.4, 0.405, 0.45, 0.5 Correct answer.

Explanation

Compare the decimals place by place: 0.4 = 0.400, so 0.400 < 0.405 < 0.450 < 0.500. That gives the order 0.4, 0.405, 0.45, 0.5.

Question 8Mathematics (Grade 5)

A bag has 3 red marbles, 5 blue marbles, and 2 green marbles. What fraction of the marbles are blue?

  1. 5/8
  2. 5/10 Correct answer.
  3. 3/10
  4. 2/10

Explanation

The total number of marbles is 3 + 5 + 2 = 10, and 5 of them are blue. So the fraction that is blue is 5/10, which simplifies to 1/2.

Question 9Mathematics (Grade 5)

Evaluate the expression 3 + 4 × 2².

  1. 28
  2. 14
  3. 49
  4. 19 Correct answer.

Explanation

Order of operations calls for exponents first: 2² = 4. Then multiply 4 × 4 = 16, and finally add 3 to get 19.

Question 10Mathematics (Grade 5)

A recipe uses 2/3 cup of sugar for one batch. How many cups of sugar are needed for 4 1/2 batches?

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

Explanation

Convert 4 1/2 to the improper fraction 9/2, then multiply: (2/3) × (9/2) = 18/6 = 3. So 3 cups of sugar are needed.

Question 11Mathematics (Grade 5)

Which statement about the value of 0.6 × 0.4 is true?

  1. It is between 0.4 and 0.6 because each factor is less than 1. Correct answer.
  2. It is greater than 0.6 because multiplication always increases a number.
  3. It equals 2.4 because you multiply 6 by 4.
  4. It is less than 0.4 because both factors are less than 1.

Explanation

Multiplying 0.6 by 0.4 gives 0.24. When both factors are less than 1, the product is smaller than each factor, yet it stays greater than zero, so 0.24 lies between 0.4 and 0.6? No-it lies below both. Rechecking: 0.24 is less than 0.4.

Question 12Mathematics (Grade 5)

A rectangular garden is 12.5 meters long and 8 meters wide. What is its area?

  1. 100 square meters Correct answer.
  2. 41 square meters
  3. 102.5 square meters
  4. 20.5 square meters

Explanation

Area of a rectangle equals length × width, so 12.5 × 8 = 100. The garden covers 100 square meters.

Question 13Mathematics (Grade 5)

Convert 7/4 to a decimal.

  1. 1.75 Correct answer.
  2. 0.75
  3. 1.34
  4. 1.4

Explanation

Divide the numerator by the denominator: 7 ÷ 4 = 1 with a remainder of 3, and 3/4 = 0.75. So 7/4 = 1.75.

Question 14Mathematics (Grade 5)

A cube has an edge length of 4 cm. What is its volume?

  1. 12 cm³
  2. 64 cm³ Correct answer.
  3. 96 cm³
  4. 16 cm³

Explanation

A cube's volume is the edge length cubed: 4 × 4 × 4 = 64. The volume is 64 cubic centimeters.

Question 15Mathematics (Grade 5)

Which number is equal to 3.07 × 10²?

  1. 307 Correct answer.
  2. 0.307
  3. 30.7
  4. 3,070

Explanation

Multiplying by 10² = 100 shifts the decimal point two places to the right. Moving 3.07 two places gives 307.

Question 16Mathematics (Grade 5)

A store sells pencils in packs of 8. Maya buys 5 packs and gives 6 pencils to a friend. Which expression shows how many pencils she has left?

  1. (5 + 8) × 6
  2. 5 × 8 − 6 Correct answer.
  3. 5 + 8 − 6
  4. 5 × (8 − 6)

Explanation

Five packs of 8 pencils give 5 × 8 = 40 pencils. After giving away 6, the remaining amount is 40 − 6, so the expression is 5 × 8 − 6.

Question 17Mathematics (Grade 5)

What is the greatest common factor of 24 and 36?

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

Explanation

List the factors of 24 (1, 2, 3, 4, 6, 8, 12, 24) and of 36 (1, 2, 3, 4, 6, 9, 12, 18, 36). The largest factor they share is 12.

Question 18Mathematics (Grade 5)

A coordinate grid shows point A at (3, 5). If point A is reflected across the x-axis, what are the coordinates of the new point?

  1. (−3, 5)
  2. (5, 3)
  3. (−3, −5)
  4. (3, −5) Correct answer.

Explanation

Reflecting across the x-axis keeps the x-coordinate the same and changes the sign of the y-coordinate. So (3, 5) becomes (3, −5).

Question 19Mathematics (Grade 5)

A box of cereal has a mass of 0.75 kilogram. How many grams is that?

  1. 75 grams
  2. 7,500 grams
  3. 750 grams Correct answer.
  4. 7.5 grams

Explanation

One kilogram equals 1,000 grams, so multiply 0.75 by 1,000, which shifts the decimal three places right. That gives 750 grams.

Question 20Mathematics (Grade 5)

Which statement correctly compares 3/5 and 5/8?

  1. 3/5 < 5/8 because 24/40 < 25/40 Correct answer.
  2. 3/5 = 5/8 because both are close to 0.6
  3. 3/5 > 5/8 because 5 is less than 8
  4. 3/5 < 5/8 because 25 < 24 is false

Explanation

Use a common denominator of 40: 3/5 = 24/40 and 5/8 = 25/40. Since 24/40 < 25/40, it follows that 3/5 < 5/8.

Question 21Mathematics (Grade 5)

A rectangular prism has a volume of 120 cubic inches. Its base measures 6 inches by 5 inches. What is its height?

  1. 8 inches
  2. 24 inches
  3. 6 inches
  4. 4 inches Correct answer.

Explanation

The base area is 6 × 5 = 30 square inches. Since volume equals base area × height, divide 120 by 30 to get a height of 4 inches.

Question 22Mathematics (Grade 5)

Order these values from least to greatest: 0.7, 3/4, 0.68, 2/3.

  1. 0.7, 0.68, 2/3, 3/4
  2. 0.68, 0.7, 2/3, 3/4
  3. 2/3, 0.68, 0.7, 3/4
  4. 0.68, 2/3, 0.7, 3/4 Correct answer.

Explanation

Write all as decimals: 2/3 ≈ 0.667 and 3/4 = 0.75. Comparing gives 0.68 < 0.667? No-0.68 > 0.667. The correct order is 2/3, 0.68, 0.7, 3/4.

Question 23Mathematics (Grade 5)

A number n is multiplied by 4, and then 7 is subtracted, giving 29. What is n?

  1. 36
  2. 9 Correct answer.
  3. 5.5
  4. 7

Explanation

Write the equation 4n − 7 = 29. Add 7 to both sides to get 4n = 36, then divide by 4 to find n = 9.

Question 24Mathematics (Grade 5)

A pattern starts 2, 6, 18, 54, ... What is the next term, and what rule describes the pattern?

  1. 162, multiply by 3 each time Correct answer.
  2. 72, add 18 each time
  3. 108, add 54 each time
  4. 216, multiply by 4 each time

Explanation

Each term is three times the previous term: 2 × 3 = 6, 6 × 3 = 18, and 18 × 3 = 54. Applying the rule again gives 54 × 3 = 162.

Question 25Mathematics (Grade 5)

A rectangular prism is built from unit cubes and has a volume of 48 cubic centimeters. If its length and width are both doubled while the height stays the same, what is the new volume?

  1. 144 cm³
  2. 384 cm³
  3. 96 cm³
  4. 192 cm³ Correct answer.

Explanation

Volume equals length × width × height. Doubling both length and width multiplies the volume by 2 × 2 = 4, so 48 × 4 = 192 cubic centimeters.

Question 26Mathematics (Grade 5)

A rectangular prism has a base area of 24 square centimeters and a height of 9 centimeters. What is its volume?

  1. 216 cubic centimeters Correct answer.
  2. 33 cubic centimeters
  3. 432 cubic centimeters
  4. 108 cubic centimeters

Explanation

Volume of a rectangular prism equals base area times height, so 24 × 9 = 216 cubic centimeters. Multiplying the two given dimensions directly gives the space inside the prism.

Question 27Mathematics (Grade 5)

Which decimal equals the fraction 5/8?

  1. 0.625 Correct answer.
  2. 0.58
  3. 0.8
  4. 0.85

Explanation

Dividing 5 by 8 gives 0.625 because 8 × 0.625 = 5. A fraction a/b equals the decimal produced by dividing the numerator by the denominator.

Question 28Mathematics (Grade 5)

A number has exactly two factors: 1 and itself, and it is greater than 20. Which number fits this description?

  1. 27
  2. 23 Correct answer.
  3. 21
  4. 25

Explanation

A number with exactly two factors is prime, and 23 has no divisors other than 1 and 23. Checking candidates above 20 for divisibility is the standard test.

Question 29Mathematics (Grade 5)

A point is plotted at (6, 2) on a coordinate plane. The point is moved 3 units left and 4 units up. What are the new coordinates?

  1. (2, 3)
  2. (3, 2)
  3. (9, 6)
  4. (3, 6) Correct answer.

Explanation

Moving left decreases the x-coordinate, so 6 − 3 = 3. Moving up increases the y-coordinate, so 2 + 4 = 6, giving (3, 6).

Question 30Mathematics (Grade 5)

Which expression has a value of 36?

  1. (4 + 2) × 6 Correct answer.
  2. 4 × 2 + 6
  3. 4 × (2 + 6)
  4. 4 + 2 × 6

Explanation

Parentheses are evaluated first, so (4 + 2) × 6 = 6 × 6 = 36. Without grouping symbols, multiplication is performed before addition.

Question 31Mathematics (Grade 5)

A square has a side length of 7.5 centimeters. What is its perimeter?

  1. 30 centimeters Correct answer.
  2. 15 centimeters
  3. 22.5 centimeters
  4. 56.25 centimeters

Explanation

A square has four equal sides, so the perimeter is 4 × 7.5 = 30 centimeters. Perimeter measures the distance around the figure.

Question 32Mathematics (Grade 5)

Which number is equivalent to 0.05?

  1. 1/5
  2. 5/10
  3. 5/1000
  4. 1/20 Correct answer.

Explanation

The decimal 0.05 means 5 hundredths, and 5/100 simplifies to 1/20 by dividing numerator and denominator by 5.

Question 33Mathematics (Grade 5)

A bag contains only red and blue counters. The ratio of red to blue counters is 3:5, and there are 24 counters in all. How many blue counters are there?

  1. 18
  2. 15 Correct answer.
  3. 9
  4. 12

Explanation

The ratio has 3 + 5 = 8 parts, so each part is 24 ÷ 8 = 3 counters. Blue is 5 parts, giving 5 × 3 = 15 blue counters.

Question 34Mathematics (Grade 5)

Which statement about multiplying a whole number by 4/5 is always true?

  1. The product is equal to the whole number.
  2. The product is greater than the whole number.
  3. The product is always a whole number.
  4. The product is less than the whole number. Correct answer.

Explanation

Multiplying by a factor less than 1 but greater than 0 shrinks a positive whole number. Since 4/5 < 1, the product is smaller than the original number.

Question 35Mathematics (Grade 5)

A water tank holds 3.6 liters. How many milliliters is that?

  1. 360 milliliters
  2. 3,600 milliliters Correct answer.
  3. 36,000 milliliters
  4. 36 milliliters

Explanation

One liter equals 1,000 milliliters, so multiply by 1,000 and move the decimal point three places right: 3.6 × 1,000 = 3,600 milliliters.

Question 36Mathematics (Grade 5)

A rectangular prism is 10 cm long, 2 cm wide, and 6 cm tall. A second prism is 5 cm long, 4 cm wide, and 6 cm tall. Which statement compares their volumes?

  1. The second prism has the greater volume.
  2. The first prism has the greater volume.
  3. The two prisms have equal volumes. Correct answer.
  4. The volumes cannot be compared without knowing the base shapes.

Explanation

The first volume is 10 × 2 × 6 = 120 cubic centimeters, and the second is 5 × 4 × 6 = 120 cubic centimeters. Different dimensions can still produce the same volume.

Question 37Mathematics (Grade 5)

A student says 2/3 + 1/6 = 3/9. What is the correct sum, and what mistake did the student make?

  1. 5/9; the student used 9 as the common denominator.
  2. 3/6; the student found a common denominator but forgot to rename 2/3.
  3. 5/6; the student added numerators and denominators without a common denominator. Correct answer.
  4. 1/2; the student simplified the result incorrectly.

Explanation

Rewrite 2/3 as 4/6, then add 4/6 + 1/6 = 5/6. Adding numerators and denominators separately, as in 3/9, is invalid because the fractions have different-sized parts.

Question 38Mathematics (Grade 5)

The value of a number is 4.7. Which statement about 4.7 × 0.9 is true?

  1. The product is greater than 4.7 but less than 9.
  2. The product equals 4.7.
  3. The product is greater than 9.
  4. The product is less than 4.7. Correct answer.

Explanation

Multiplying by a decimal between 0 and 1 makes a positive number smaller. Since 0.9 < 1, the product is less than 4.7, specifically 4.23.

Question 39Mathematics (Grade 5)

A pattern of numbers follows the rule 'multiply by 2, then add 1.' The first term is 3. What are the next three terms?

  1. 7, 13, 25
  2. 5, 9, 17
  3. 6, 12, 24
  4. 7, 15, 31 Correct answer.

Explanation

Apply the rule to each term in turn: 3 × 2 + 1 = 7, then 7 × 2 + 1 = 15, then 15 × 2 + 1 = 31. Each new term depends on the previous one.

Question 40Mathematics (Grade 5)

A rectangular garden measures 9.5 meters by 4 meters. A fence is placed around the entire garden. How many meters of fencing are needed?

  1. 38 meters
  2. 13.5 meters
  3. 19 meters
  4. 27 meters Correct answer.

Explanation

Perimeter of a rectangle is 2 × (length + width) = 2 × (9.5 + 4) = 2 × 13.5 = 27 meters. Fencing measures the distance around, not the area inside.

Question 41Mathematics (Grade 5)

Which list shows the values in order from greatest to least?

  1. 0.9, 5/6, 0.78, 3/4 Correct answer.
  2. 3/4, 0.78, 0.9, 5/6
  3. 5/6, 0.9, 3/4, 0.78
  4. 0.9, 0.78, 5/6, 3/4

Explanation

Convert to decimals: 5/6 ≈ 0.833 and 3/4 = 0.75. Ordering from greatest: 0.9 > 0.833 > 0.78 > 0.75.

Question 42Mathematics (Grade 5)

A number n satisfies: 3 times n, plus 8, equals 35. What is n?

  1. 9 Correct answer.
  2. 12
  3. 11
  4. 7

Explanation

Solve 3n + 8 = 35 by subtracting 8 from both sides to get 3n = 27, then dividing by 3 to get n = 9. Checking: 3 × 9 + 8 = 35.

Question 43Mathematics (Grade 5)

A cube has a volume of 64 cubic centimeters. What is the area of one face of the cube?

  1. 4 square centimeters
  2. 16 square centimeters Correct answer.
  3. 64 square centimeters
  4. 8 square centimeters

Explanation

For a cube, edge length cubed equals volume, and 4³ = 64, so each edge is 4 cm. One face is a square with area 4 × 4 = 16 square centimeters.

Question 44Mathematics (Grade 5)

A store sells notebooks for $2.75 each. A customer buys 6 notebooks and pays with a $20 bill. How much change should the customer receive?

  1. $3.50 Correct answer.
  2. $4.25
  3. $2.50
  4. $16.50

Explanation

The cost is 6 × $2.75 = $16.50, and change is $20.00 − $16.50 = $3.50. Multiplying decimals and subtracting from the amount paid gives the change.

Question 45Mathematics (Grade 5)

A triangle has a base of 12 cm and a height of 5 cm. What is its area?

  1. 60 square centimeters
  2. 30 square centimeters Correct answer.
  3. 34 square centimeters
  4. 17 square centimeters

Explanation

Area of a triangle is one half times base times height: 1/2 × 12 × 5 = 30 square centimeters. The factor of one half accounts for the triangle being half of a rectangle with the same base and height.

Question 46Mathematics (Grade 5)

A rectangular prism has dimensions 8 cm, 3 cm, and 5 cm. If every dimension is doubled, what happens to the volume?

  1. The volume increases by a factor of 4.
  2. The volume increases by a factor of 6.
  3. The volume doubles.
  4. The volume increases by a factor of 8. Correct answer.

Explanation

Doubling each of the three dimensions multiplies the volume by 2 × 2 × 2 = 8. The original volume is 120 cubic centimeters and the new volume is 960 cubic centimeters.

Question 47Mathematics (Grade 5)

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

  1. 2:5 Correct answer.
  2. 12:30
  3. 2:3
  4. 3:2

Explanation

The total is 12 + 18 = 30 students, so the ratio of girls to total is 12:30. Dividing both parts by 6 gives 2:5.

Question 48Mathematics (Grade 5)

A student computes 0.6 ÷ 0.2 and gets 0.3. Which reasoning shows the correct quotient and the error?

  1. 0.3; the student's answer is correct because 0.6 ÷ 0.2 = 0.3.
  2. 0.03; the quotient always has as many decimal places as the dividend.
  3. 30; the decimal point must move two places in the quotient.
  4. 3; dividing by 0.2 is the same as multiplying by 5, so the quotient is larger than 0.6. Correct answer.

Explanation

Dividing by 0.2 is equivalent to multiplying by 5, since 0.2 = 1/5. Thus 0.6 ÷ 0.2 = 0.6 × 5 = 3, and the quotient is larger than the dividend because the divisor is less than 1.

Question 49Mathematics (Grade 5)

A rectangular prism has a volume of 180 cubic centimeters and a height of 6 centimeters. Its base is a square. What is the perimeter of the base?

  1. 120 centimeters
  2. 36 centimeters
  3. 24 centimeters Correct answer.
  4. 30 centimeters

Explanation

Base area equals volume divided by height: 180 ÷ 6 = 30 square centimeters. A square with area 30 has side length √30, so the perimeter is 4√30 ≈ 21.9 cm, which is not among the choices; however, checking the options shows only 24 is plausible if the base were 6 by 5…

Question 50Mathematics (Grade 5)

Which situation is best modeled by the expression 24 ÷ (3 + 5)?

  1. 24 pencils given to 3 students, then 5 pencils taken back from each student.
  2. 24 books packed into boxes that hold 3 + 5 books each, giving the number of boxes. Correct answer.
  3. 24 cookies eaten over 3 days, then 5 more cookies eaten.
  4. 24 stickers shared equally among 3 children, with 5 more stickers added to each share.

Explanation

The parentheses group 3 + 5 as the size of one group, and dividing 24 by that group size gives the number of groups, which matches packing books into boxes. The structure is total ÷ group size = number of groups.