Fractions & Division — A Workbook for Independent Practice

Set I

Equal Groups, Arrays & the Unknown Factor

Grade 3

Key ConceptMultiplication means putting together equal-sized groups — 3 groups of 4 is 3 × 4. Division answers the reverse question: it's really asking, “what number, multiplied by this one, gives that total?” For example, 12 ÷ 3 asks 3 × ? = 12.

Question 1 of 100

Mia has 3 bags of marbles with 4 marbles in each bag. How many marbles does she have in all?

Think of it as 3 equal groups of 4. Multiply: 3 x 4.

Question 2 of 100

A garden has 5 rows of flowers with 2 flowers in each row. How many flowers are there in all?

Think of it as 5 equal groups of 2. Multiply: 5 x 2.

Question 3 of 100

There are 4 shelves with 6 books on each shelf. How many books in total?

Think of it as 4 equal groups of 6. Multiply: 4 x 6.

Question 4 of 100

A baker makes 7 trays of muffins with 3 muffins on each tray. How many muffins in all?

Think of it as 7 equal groups of 3. Multiply: 7 x 3.

Question 5 of 100

There are 6 boxes with 5 crayons in each box. How many crayons in all?

Think of it as 6 equal groups of 5. Multiply: 6 x 5.

Question 6 of 100

A classroom has 8 rows of desks with 4 desks in each row. How many desks in all?

Think of it as 8 equal groups of 4. Multiply: 8 x 4.

Question 7 of 100

Sam buys 9 packs of stickers with 3 stickers in each pack. How many stickers in all?

Think of it as 9 equal groups of 3. Multiply: 9 x 3.

Question 8 of 100

There are 6 egg cartons with 6 eggs in each carton. How many eggs in all?

Think of it as 6 equal groups of 6. Multiply: 6 x 6.

Question 9 of 100

A parking lot has 7 rows with 7 cars in each row. How many cars in all?

Think of it as 7 equal groups of 7. Multiply: 7 x 7.

Question 10 of 100

There are 8 teams with 8 players on each team. How many players in all?

Think of it as 8 equal groups of 8. Multiply: 8 x 8.

Question 11 of 100

12 apples are shared equally into 3 baskets. How many apples in each basket?

Ask: 3 x ? = 12. Find the missing factor.

Question 12 of 100

A teacher has 20 pencils to give equally to 4 students. How many pencils does each student get?

Ask: 4 x ? = 20. Find the missing factor.

Question 13 of 100

18 stickers are divided equally among 6 friends. How many stickers does each friend get?

Ask: 6 x ? = 18. Find the missing factor.

Question 14 of 100

A farmer has 21 eggs to pack equally into 7 cartons. How many eggs go in each carton?

Ask: 7 x ? = 21. Find the missing factor.

Question 15 of 100

24 cookies are shared equally among 8 plates. How many cookies on each plate?

Ask: 8 x ? = 24. Find the missing factor.

Question 16 of 100

35 chairs are arranged equally into 5 rows. How many chairs in each row?

Ask: 5 x ? = 35. Find the missing factor.

Question 17 of 100

A coach splits 42 players equally into 6 teams. How many players on each team?

Ask: 6 x ? = 42. Find the missing factor.

Question 18 of 100

48 books are placed equally on 8 shelves. How many books on each shelf?

Ask: 8 x ? = 48. Find the missing factor.

Question 19 of 100

54 crayons are shared equally among 9 boxes. How many crayons in each box?

Ask: 9 x ? = 54. Find the missing factor.

Question 20 of 100

63 marbles are divided equally into 7 bags. How many marbles in each bag?

Ask: 7 x ? = 63. Find the missing factor.

Set II

Multi-Digit Division

Grade 4–5

Key ConceptLong division breaks a big division problem into small, repeatable steps: divide, multiply, subtract, bring down. When a number doesn't divide evenly, whatever is left over is called the remainder.

Question 21 of 100

84 stickers are shared equally among 4 students. How many stickers does each student get?

Divide 84 by 4 using long division. It divides evenly.

Question 22 of 100

A shop arranges 96 apples equally into 6 boxes. How many apples in each box?

Divide 96 by 6 using long division. It divides evenly.

Question 23 of 100

72 chairs are split equally into 3 rows. How many chairs in each row?

Divide 72 by 3 using long division. It divides evenly.

Question 24 of 100

A baker divides 65 cupcakes equally among 5 trays. How many cupcakes on each tray?

Divide 65 by 5 using long division. It divides evenly.

Question 25 of 100

91 pencils are shared equally among 7 classrooms. How many pencils does each classroom get?

Divide 91 by 7 using long division. It divides evenly.

Question 26 of 100

A library sorts 156 books equally onto 4 shelves. How many books on each shelf?

Divide 156 by 4 using long division. It divides evenly.

Question 27 of 100

216 tickets are divided equally among 6 gates. How many tickets at each gate?

Divide 216 by 6 using long division. It divides evenly.

Question 28 of 100

A farmer packs 315 eggs equally into 5 crates. How many eggs in each crate?

Divide 315 by 5 using long division. It divides evenly.

Question 29 of 100

432 seats are arranged equally into 8 rows. How many seats in each row?

Divide 432 by 8 using long division. It divides evenly.

Question 30 of 100

A charity splits 504 donated cans equally among 7 families. How many cans does each family get?

Divide 504 by 7 using long division. It divides evenly.

Question 31 of 100

194 beads are shared equally among 3 bracelets, with some left over. How many beads on each bracelet, and how many are left over?

Divide 194 by 3. It will not divide evenly -- there will be a remainder.

Question 32 of 100

A school has 257 students to split equally into 4 buses, with some left over. How many students on each bus, and how many are left over?

Divide 257 by 4. It will not divide evenly -- there will be a remainder.

Question 33 of 100

365 oranges are packed equally into 6 bags, with some left over. How many oranges in each bag, and how many are left over?

Divide 365 by 6. It will not divide evenly -- there will be a remainder.

Question 34 of 100

A store has 478 bottles to place equally on 5 shelves, with some left over. How many bottles on each shelf, and how many are left over?

Divide 478 by 5. It will not divide evenly -- there will be a remainder.

Question 35 of 100

529 balloons are shared equally among 8 party bags, with some left over. How many balloons in each bag, and how many are left over?

Divide 529 by 8. It will not divide evenly -- there will be a remainder.

Question 36 of 100

A factory ships 1248 toys equally into 4 boxes. How many toys in each box?

Divide 1248 by 4 using long division. It divides evenly.

Question 37 of 100

1365 students are split equally into 5 teams. How many students on each team?

Divide 1365 by 5 using long division. It divides evenly.

Question 38 of 100

A theater has 2436 seats arranged equally into 12 sections. How many seats in each section?

Divide 2436 by 12 using long division. It divides evenly.

Question 39 of 100

3150 pages are divided equally among 15 chapters. How many pages in each chapter?

Divide 3150 by 15 using long division. It divides evenly.

Question 40 of 100

A warehouse ships 4116 items equally into 21 containers. How many items in each container?

Divide 4116 by 21 using long division. It divides evenly.

Set III

Multiplying Fractions

Grade 5

Key ConceptTo multiply two fractions, multiply the numerators together and the denominators together, then simplify. Unlike addition, fractions do not need a common denominator to be multiplied.

Question 41 of 100

What is 1/2 x 1/3?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 42 of 100

What is 1/4 x 1/2?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 43 of 100

What is 2/3 x 1/2?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 44 of 100

What is 1/3 x 3/5?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 45 of 100

What is 2/5 x 1/2?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 46 of 100

What is 3/4 x 1/3?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 47 of 100

What is 2/3 x 3/4?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 48 of 100

What is 4/5 x 1/2?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 49 of 100

What is 3/5 x 2/3?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 50 of 100

What is 5/6 x 2/3?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 51 of 100

What is 3/8 x 4/9?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 52 of 100

What is 5/6 x 3/10?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 53 of 100

What is 7/8 x 2/3?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 54 of 100

What is 4/9 x 3/8?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 55 of 100

What is 5/8 x 2/5?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 56 of 100

What is 2/3 x 3/7?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 57 of 100

What is 5/9 x 3/10?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 58 of 100

What is 7/10 x 5/7?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 59 of 100

What is 8/9 x 3/4?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Question 60 of 100

What is 9/10 x 5/6?

Multiply straight across: numerator x numerator, denominator x denominator. Then simplify.

Set IV

Adding & Subtracting Fractions

Grade 5 · Unlike Denominators

Key ConceptFractions can only be added or subtracted once they share the same denominator. Find the least common denominator (LCD), rewrite each fraction, then add or subtract just the numerators.

Question 61 of 100

What is 1/2 + 1/3?

Find a common denominator (like 6) before you add.

Question 62 of 100

What is 1/4 + 1/2?

Find a common denominator (like 4) before you add.

Question 63 of 100

What is 2/3 + 1/6?

Find a common denominator (like 6) before you add.

Question 64 of 100

What is 3/4 - 1/2?

Find a common denominator (like 4) before you subtract.

Question 65 of 100

What is 3/4 - 1/6?

Find a common denominator (like 12) before you subtract.

Question 66 of 100

What is 1/3 + 1/4?

Find a common denominator (like 12) before you add.

Question 67 of 100

What is 5/6 - 1/3?

Find a common denominator (like 6) before you subtract.

Question 68 of 100

What is 2/5 + 1/10?

Find a common denominator (like 10) before you add.

Question 69 of 100

What is 3/4 - 1/8?

Find a common denominator (like 8) before you subtract.

Question 70 of 100

What is 1/6 + 2/3?

Find a common denominator (like 6) before you add.

Question 71 of 100

What is 3/8 + 1/4?

Find a common denominator (like 8) before you add.

Question 72 of 100

What is 7/8 - 1/2?

Find a common denominator (like 8) before you subtract.

Question 73 of 100

What is 2/5 + 1/3?

Find a common denominator (like 15) before you add.

Question 74 of 100

What is 5/6 - 3/4?

Find a common denominator (like 12) before you subtract.

Question 75 of 100

What is 3/10 + 2/5?

Find a common denominator (like 10) before you add.

Question 76 of 100

What is 5/6 + 3/4?

Find a common denominator (like 12) before you add.

Question 77 of 100

What is 7/9 - 1/3?

Find a common denominator (like 9) before you subtract.

Question 78 of 100

What is 5/8 + 3/4?

Find a common denominator (like 8) before you add.

Question 79 of 100

What is 11/12 - 2/3?

Find a common denominator (like 12) before you subtract.

Question 80 of 100

What is 7/10 + 5/6?

Find a common denominator (like 30) before you add.

Set V

Dividing Fractions by Fractions

Grade 6

Key ConceptTo divide by a fraction: keep the first fraction, change ÷ to ×, and flip the second fraction upside down (its reciprocal). Then multiply and simplify.

Question 81 of 100

What is 1/2 / 1/4?