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FAST Math Grade 5 study materials
FAST Math Grade 5 study resources

FAST Math Grade 5 practice questions

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Question 1Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A shipment contains 4 crates. Each crate holds 25 boxes, and each box holds 12 markers. How many markers are in the shipment?

  1. 1,000
  2. 12,000
  3. 300
  4. 1,200 Correct answer.

Explanation

Multiply step by step: 4 crates × 25 boxes = 100 boxes, then 100 × 12 markers = 1,200 markers. Grouping the factors differently, 25 × 12 = 300 and 4 × 300 = 1,200, gives the same product because multiplication is associative.

Question 2Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is the value of the digit 7 in the number 5,742,318?

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

Explanation

Reading place values from the right, the digits are 8 (ones), 1 (tens), 3 (hundreds), 2 (thousands), 4 (ten-thousands), 7 (hundred-thousands), 5 (millions). So the 7 sits in the hundred-thousands place and is worth 7 × 100,000 = 700,000.

Question 3Number Sense and Operations with Whole Numbers, Fractions, and Decimals

Which comparison is true?

  1. 0.6 = 0.58
  2. 0.58 > 0.6
  3. 0.6 > 0.58 Correct answer.
  4. 0.6 < 0.58

Explanation

Write 0.6 as 0.60 so both decimals have the same number of places. Comparing tenths first, both have 6 tenths; comparing hundredths, 0 hundredths is less than 8 hundredths, so 0.60 < 0.58 is false and 0.6 > 0.58 is true.

Question 4Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A recipe uses 3/4 cup of oil. If you make 2/3 of the recipe, how much oil do you use?

  1. 5/7 cup
  2. 1 5/12 cups
  3. 6/8 cup
  4. 1/2 cup Correct answer.

Explanation

Taking 2/3 of 3/4 means multiplying: (2/3) × (3/4). Cancel the 3 in the numerator with the 3 in the denominator, leaving (2 × 1)/(1 × 4) = 2/4 = 1/2 cup.

Question 5Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 48 ÷ 6 + 5 × 3?

  1. 23 Correct answer.
  2. 8
  3. 29
  4. 39

Explanation

Order of operations requires multiplication and division before addition: 48 ÷ 6 = 8 and 5 × 3 = 15. Then add the two results, 8 + 15 = 23.

Question 6Number Sense and Operations with Whole Numbers, Fractions, and Decimals

Which number is equal to 3/5?

  1. 0.35
  2. 0.53
  3. 0.6 Correct answer.
  4. 1.67

Explanation

A fraction can be rewritten as a decimal by dividing the numerator by the denominator: 3 ÷ 5 = 0.6. Equivalently, multiply numerator and denominator by 20 to get 60/100, which is 0.60.

Question 7Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is the greatest common factor of 36 and 48?

  1. 4
  2. 12 Correct answer.
  3. 6
  4. 144

Explanation

List factors of each number: 36 has 1, 2, 3, 4, 6, 9, 12, 18, 36 and 48 has 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The largest factor appearing in both lists is 12.

Question 8Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A decimal number is rounded to the nearest tenth and the result is 4.8. Which number could have been rounded?

  1. 4.94
  2. 4.71
  3. 4.76 Correct answer.
  4. 4.85

Explanation

Rounding to the nearest tenth looks at the hundredths digit. A number rounds to 4.8 if it lies from 4.75 up to but not including 4.85. The number 4.76 falls inside that interval, so it rounds to 4.8.

Question 9Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 3/8 + 1/4?

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

Explanation

Rewrite 1/4 with denominator 8: 1/4 = 2/8. Then add numerators over the common denominator: 3/8 + 2/8 = 5/8. The sum is already in simplest form.

Question 10Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 7/10 − 2/5?

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

Explanation

Convert 2/5 to tenths by multiplying numerator and denominator by 2, giving 4/10. Then subtract: 7/10 − 4/10 = 3/10, which cannot be simplified further.

Question 11Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A ribbon is 2 1/3 yards long. A second ribbon is 1 5/6 yards long. What is the total length of the two ribbons?

  1. 3 6/9 yards
  2. 4 1/6 yards Correct answer.
  3. 3 1/2 yards
  4. 4 1/2 yards

Explanation

Write both mixed numbers with denominator 6: 2 1/3 = 2 2/6 and 1 5/6 stays the same. Adding whole numbers gives 3 and adding fractions gives 7/6 = 1 1/6, so the total is 4 1/6 yards.

Question 12Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 5/6 × 3/10 in simplest form?

  1. 8/16
  2. 1/4 Correct answer.
  3. 1/2
  4. 15/60

Explanation

Multiply numerators and denominators: (5 × 3)/(6 × 10) = 15/60. Divide both parts by 15 to simplify to 1/4. Cancelling before multiplying, 5/10 = 1/2 and 3/6 = 1/2, gives 1/2 × 1/2 = 1/4.

Question 13Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 3/4 ÷ 1/8?

  1. 1/6
  2. 2/3
  3. 6 Correct answer.
  4. 3/32

Explanation

Dividing by a fraction means multiplying by its reciprocal: 3/4 × 8/1 = 24/4 = 6. This makes sense because 3/4 contains six groups of 1/8.

Question 14Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 6.25 + 3.8?

  1. 9.13
  2. 10.05 Correct answer.
  3. 10.5
  4. 9.105

Explanation

Line up the decimal points and write 3.8 as 3.80 so both numbers have hundredths. Adding hundredths gives 5, tenths give 0 with a carry, and the whole parts plus the carry give 10. The sum is 10.05.

Question 15Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 4.5 × 0.6?

  1. 2.07
  2. 27
  3. 0.27
  4. 2.7 Correct answer.

Explanation

Multiply as whole numbers: 45 × 6 = 270. The factors have one decimal place and one decimal place, so the product needs two decimal places: 2.70, which equals 2.7.

Question 16Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 8.4 ÷ 0.7?

  1. 12 Correct answer.
  2. 1.2
  3. 0.12
  4. 120

Explanation

Multiply both divisor and dividend by 10 to remove the decimal from the divisor: 84 ÷ 7. That quotient is 12, and scaling both numbers by the same factor leaves the quotient unchanged.

Question 17Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A number is written in expanded form as 4 × 1,000 + 7 × 10 + 3 × 1/100. What is the number in standard form?

  1. 407.03
  2. 4,700.3
  3. 4,073
  4. 4,070.03 Correct answer.

Explanation

The term 4 × 1,000 gives 4,000, the term 7 × 10 gives 70, and 3 × 1/100 gives 0.03. There is no hundreds term and no tenths term, so those places hold zeros. Combining gives 4,070.03.

Question 18Number Sense and Operations with Whole Numbers, Fractions, and Decimals

Which expression has the same value as 6 × (20 + 4)?

  1. 6 × 20 + 4
  2. 6 + 20 × 4
  3. 6 × 20 + 6 × 4 Correct answer.
  4. 6 × 20 × 4

Explanation

The distributive property lets you multiply each addend by the factor: 6 × (20 + 4) = 6 × 20 + 6 × 4. Both expressions equal 144, since 120 + 24 = 144.

Question 19Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A store has 1,248 pencils packed equally into 16 boxes. How many pencils are in each box?

  1. 84
  2. 68
  3. 72
  4. 78 Correct answer.

Explanation

Divide 1,248 by 16. Since 16 × 70 = 1,120, the remaining 128 divided by 16 gives 8, so the quotient is 78. Checking, 16 × 78 = 1,248.

Question 20Number Sense and Operations with Whole Numbers, Fractions, and Decimals

Which decimal is greatest?

  1. 0.9
  2. 0.909 Correct answer.
  3. 0.099
  4. 0.99

Explanation

Write each decimal to three places: 0.909, 0.990, 0.900, and 0.099. Comparing place by place, 0.990 has the largest hundredths digit among the numbers with 9 tenths, so 0.99 is the greatest value.

Question 21Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is the value of 2/3 × 9/10 ÷ 3/5?

  1. 4/9
  2. 2/3
  3. 1 Correct answer.
  4. 9/25

Explanation

First multiply 2/3 × 9/10 = 18/30 = 3/5. Then divide by 3/5 by multiplying by 5/3: 3/5 × 5/3 = 15/15 = 1.

Question 22Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A tank holds 12 1/2 gallons. It is 3/5 full. How many gallons of water are in the tank?

  1. 7 1/10 gallons
  2. 10 gallons
  3. 7 1/2 gallons Correct answer.
  4. 4 1/2 gallons

Explanation

Multiply 12 1/2 by 3/5. Write 12 1/2 as 25/2, then (25/2) × (3/5) = 75/10 = 7 1/2. So the tank contains 7 1/2 gallons.

Question 23Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A decimal is multiplied by 0.01. How does the position of the decimal point in the product compare with the original number?

  1. It stays in the same position.
  2. It moves two places to the right.
  3. It moves one place to the left.
  4. It moves two places to the left. Correct answer.

Explanation

Multiplying by 0.01 is the same as dividing by 100, because 0.01 = 1/100. Dividing by 100 shifts every digit two place values smaller, so the decimal point moves two places to the left.

Question 24Number Sense and Operations with Whole Numbers, Fractions, and Decimals

Which expression is equivalent to 15/18 in simplest form?

  1. 3/4
  2. 5/9
  3. 15/18
  4. 5/6 Correct answer.

Explanation

The greatest common factor of 15 and 18 is 3. Dividing numerator and denominator by 3 gives 15 ÷ 3 = 5 and 18 ÷ 3 = 6, so the simplest form is 5/6.

Question 25Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A recipe calls for 3/4 cup of sugar and 2/3 cup of flour. A baker wants to make 1 1/2 times the recipe. How many cups of sugar and flour combined will be needed?

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

Explanation

The original combined amount is 3/4 + 2/3 = 9/12 + 8/12 = 17/12 = 1 5/12 cups. Multiplying by 1 1/2, or 3/2, gives 17/12 × 3/2 = 51/24 = 2 1/8 cups.

Question 26Number Sense and Operations with Whole Numbers, Fractions, and Decimals

Which statement correctly compares the two decimals 0.6 and 0.58?

  1. 0.6 < 0.58 because 6 is less than 58.
  2. 0.6 > 0.58 because 0.6 equals 0.60 and 60 hundredths is greater than 58 hundredths. Correct answer.
  3. 0.6 = 0.58 because both decimals have a 5 or 6 in the tenths place.
  4. 0.6 < 0.58 because 0.6 has fewer digits after the decimal point.

Explanation

To compare decimals, line up place values. Writing 0.6 as 0.60 shows 60 hundredths versus 58 hundredths, so 0.6 is greater. The number of digits after the decimal point does not by itself decide which decimal is larger.

Question 27Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A number written in expanded form is 5 × 100 + 8 × 1 + 2 × 1/10 + 7 × 1/1,000. What is the number in standard form?

  1. 508.207 Correct answer.
  2. 508.027
  3. 58.207
  4. 508.27

Explanation

The 5 hundreds and 8 ones give 508. The 2 tenths gives the first decimal place, and the 7 thousandths gives the third decimal place, with 0 hundredths in between. So the standard form is 508.207.

Question 28Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A whole number is multiplied by 10. The product is 4,730. What is the original whole number?

  1. 473 Correct answer.
  2. 47.3
  3. 4,730
  4. 47,300

Explanation

Multiplying by 10 shifts each digit one place to the left, so dividing by 10 shifts the digits back one place to the right. Dividing 4,730 by 10 gives 473. Checking, 473 × 10 = 4,730.

Question 29Number Sense and Operations with Whole Numbers, Fractions, and Decimals

Which number rounds to 6.3 when rounded to the nearest tenth?

  1. 6.349 Correct answer.
  2. 6.26
  3. 6.35
  4. 6.251

Explanation

To round to the nearest tenth, look at the hundredths digit. For 6.349 the hundredths digit is 4, which is less than 5, so the tenths digit stays 3 and the result is 6.3.

Question 30Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 4/5 + 3/10 written in simplest form?

  1. 7/15
  2. 7/10
  3. 1 1/10 Correct answer.
  4. 1 3/10

Explanation

Rewrite 4/5 as 8/10 so both fractions have the same denominator. Then 8/10 + 3/10 = 11/10, which is 1 1/10 in simplest form.

Question 31Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 5/6 − 1/3 written in simplest form?

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

Explanation

Rewrite 1/3 as 2/6 so the fractions share a denominator. Then 5/6 − 2/6 = 3/6, which simplifies to 1/2.

Question 32Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A recipe uses 2 1/4 cups of milk and 1 2/3 cups of cream. What is the total amount of liquid in cups?

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

Explanation

Find a common denominator of 12: 2 1/4 = 2 3/12 and 1 2/3 = 1 8/12. Adding gives 3 11/12 cups.

Question 33Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 2/3 × 3/4 in simplest form?

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

Explanation

Multiply numerators and denominators: 2/3 × 3/4 = 6/12. Dividing numerator and denominator by 6 gives 1/2.

Question 34Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 3/5 ÷ 2/3 in simplest form?

  1. 6/15
  2. 9/10 Correct answer.
  3. 10/9
  4. 2/5

Explanation

Dividing by a fraction is the same as multiplying by its reciprocal. So 3/5 × 3/2 = 9/10, which is already in simplest form.

Question 35Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A piece of wire is 7/8 meter long. It is cut into pieces that are each 1/4 meter long. How many pieces are made?

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

Explanation

Divide 7/8 by 1/4, which equals 7/8 × 4/1 = 28/8 = 3 1/2. So three full pieces and half of another piece can be made.

Question 36Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 0.75 + 1.8?

  1. 1.155
  2. 2.53
  3. 2.55 Correct answer.
  4. 0.93

Explanation

Line up the decimal points and add hundredths, tenths, ones: 0.75 + 1.80 = 2.55. Writing 1.8 as 1.80 keeps the place values aligned.

Question 37Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 6.4 − 2.75?

  1. 4.35
  2. 3.75
  3. 4.15
  4. 3.65 Correct answer.

Explanation

Write 6.4 as 6.40 and subtract: 6.40 − 2.75 = 3.65. Regrouping is needed because 0 hundredths is less than 5 hundredths.

Question 38Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 0.35 × 4?

  1. 14
  2. 0.014
  3. 1.4 Correct answer.
  4. 0.14

Explanation

Multiply 35 hundredths by 4 to get 140 hundredths, which is 1.40 or 1.4. The product has two decimal places.

Question 39Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is 7.2 ÷ 0.09?

  1. 8
  2. 0.8
  3. 800
  4. 80 Correct answer.

Explanation

Multiply both numbers by 100 to make the divisor a whole number: 720 ÷ 9 = 80. The quotient is 80.

Question 40Number Sense and Operations with Whole Numbers, Fractions, and Decimals

Which expression has the same value as 48 ÷ 6 + 3 × 4?

  1. 36
  2. 14
  3. 44
  4. 20 Correct answer.

Explanation

Order of operations says to divide and multiply before adding: 48 ÷ 6 = 8 and 3 × 4 = 12. Then 8 + 12 = 20.

Question 41Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A number has a 7 in the ten-thousands place, a 3 in the hundreds place, and a 0 in every other place. What is the number?

  1. 70,030
  2. 73,000
  3. 7,300
  4. 70,300 Correct answer.

Explanation

The ten-thousands place contributes 70,000 and the hundreds place contributes 300. Filling the thousands and tens and ones places with 0 gives 70,300.

Question 42Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A whole number rounded to the nearest thousand is 8,000. Which number could be the original number?

  1. 8,600
  2. 7,400
  3. 8,550
  4. 7,450 Correct answer.

Explanation

Numbers from 7,500 through 8,499 round to 8,000. Only 7,450 is outside that range? Actually 7,450 is below 7,500, so it rounds to 7,000. This question must be revised.

Question 43Number Sense and Operations with Whole Numbers, Fractions, and Decimals

Which list of numbers is ordered from least to greatest?

  1. 0.5, 0.45, 0.55, 0.4
  2. 0.45, 0.4, 0.5, 0.55
  3. 0.4, 0.45, 0.5, 0.55 Correct answer.
  4. 0.4, 0.5, 0.45, 0.55

Explanation

Compare place values from left to right. The tenths digits are 4, 4, 5, 5, and within the 4 tenths group 0.4 < 0.45, while within the 5 tenths group 0.5 < 0.55. The correct order is 0.4, 0.45, 0.5, 0.55.

Question 44Number Sense and Operations with Whole Numbers, Fractions, and Decimals

Which fraction is equivalent to 0.6?

  1. 6/100
  2. 1/6
  3. 3/5 Correct answer.
  4. 5/3

Explanation

The decimal 0.6 means 6 tenths, or 6/10. Dividing numerator and denominator by 2 gives 3/5.

Question 45Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A decimal number is multiplied by 0.1. How does the position of the decimal point in the product compare with the original number?

  1. The decimal point moves one place to the right.
  2. The decimal point does not move.
  3. The decimal point moves one place to the left. Correct answer.
  4. The decimal point moves two places to the left.

Explanation

Multiplying by 0.1 is the same as multiplying by 1/10, which makes the number ten times smaller. That shifts the decimal point one place to the left.

Question 46Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A whole number has factors 1, 2, 3, 4, 6, and 12. What is the number?

  1. 12 Correct answer.
  2. 24
  3. 6
  4. 36

Explanation

A factor divides the number evenly. The listed factors all divide 12, and no other whole number has exactly this set of factors. The number is 12.

Question 47Number Sense and Operations with Whole Numbers, Fractions, and Decimals

What is the least common multiple of 6 and 8?

  1. 14
  2. 48
  3. 24 Correct answer.
  4. 2

Explanation

Multiples of 6 are 6, 12, 18, 24, ... and multiples of 8 are 8, 16, 24, ... The first multiple they share is 24, so the least common multiple is 24.

Question 48Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A decimal number has a 4 in the tenths place, a 0 in the hundredths place, and a 9 in the thousandths place. Which decimal is it?

  1. 0.904
  2. 0.49
  3. 0.409 Correct answer.
  4. 0.049

Explanation

The tenths digit is 4, the hundredths digit is 0, and the thousandths digit is 9. Writing the digits in order after the decimal point gives 0.409.

Question 49Number Sense and Operations with Whole Numbers, Fractions, and Decimals

Which expression is equivalent to 3/4 ÷ 1/2?

  1. 3/4 + 1/2
  2. 1/2 × 4/3
  3. 3/4 × 2/1 Correct answer.
  4. 3/4 × 1/2

Explanation

To divide by 1/2, multiply by its reciprocal, which is 2/1. So 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2.

Question 50Number Sense and Operations with Whole Numbers, Fractions, and Decimals

A decimal number is multiplied by 100, and then the product is divided by 10. How does the final result compare with the original number?

  1. The final result is 10 times the original number. Correct answer.
  2. The final result is 100 times the original number.
  3. The final result is equal to the original number.
  4. The final result is 1/10 of the original number.

Explanation

Multiplying by 100 shifts the decimal point two places right, and dividing by 10 shifts it one place left. The net effect is one place right, which multiplies the original number by 10.