Worksheet: Evaluating Expressions by Dividing Mixed Numbers

In this worksheet, we will practice dividing a mixed number by another and using this to evaluate algebraic expressions in real-life situations.

Q1:

Find 𝑥 ÷ 𝑦 given that 𝑥 = 3 6 7 and 𝑦 = 6 5 7 .

  • A 1 1 5
  • B 1 2 0 2 7
  • C 1 2
  • D 2 7 4 7
  • E 2 6 7

Q2:

Without evaluating each expression, decide whether 8 1 4 ÷ 8 7 8 is greater than or less than 8 1 4 ÷ 5 3 8 .

  • Aless than
  • Bgreater than

Q3:

Adam’s room is 173 inches long. Express, in feet, his room’s length as a mixed number in the simplest form.

  • A 7 5 2 4 ft
  • B 2 8 5 6 ft
  • C 1 3 5 1 2 ft
  • D 1 4 5 1 2 ft
  • E 1 5 5 1 2 ft

Q4:

To finish making curtains for her 18 windows, Dalia needs 1 2 7 yards of fabric per window. At the store, she found a bolt of fabric she liked with 2 5 8 yards on it. How many windows can she finish the curtains for?

Q5:

Yara is making bed sheets that will take 6 1 3 3 6 yards of fabric. If that fabric is sold in half yards , determine how many yards of fabric she will need.

  • A 7 yd
  • B 6 yd
  • C 6 1 4 yd
  • D 6 1 2 yd
  • E 6 3 4 yd

Q6:

A cloth of length 5 2 3 meters was cut into 17 equal pieces. How long is each piece?

  • A 1 1 1 3 m
  • B 9 6 1 3 m
  • C 2 2 2 3 m
  • D 1 3 m

Q7:

A school wants to organise a 5 km race. A lap around the park is 5 6 miles. Given that 5 = 3 1 8 k m m i l e s , how many laps will the children run? Give your answer as a mixed number.

  • A 1 1 3
  • B 4 1 5
  • C6
  • D 3 3 4
  • E 1 3 5

Q8:

3 7 1 3 ÷ = 1 .

  • A 2 7 1 3
  • B 1 3 4 6
  • C 1 3 3 3
  • D 3 7 1 3

Q9:

Evaluate 3 3 5 ÷ 6 giving the answer in its simplest form.

  • A 1 5
  • B 7 1 5
  • C 1 2
  • D 3 5
  • E 2 5

Q10:

Evaluate 3 1 3 ÷ 1 0 giving the answer in its simplest form.

  • A 2 1 5
  • B 1 5
  • C 3 1 0
  • D 1 3
  • E 4 1 5

Q11:

Amira and Amir have walked 1 3 1 4 km in 2 1 4 hours.

As they want to walk for 3 hours, what fraction of their walk have they completed so far?

  • A 4 5 1 2
  • B 1 1 3
  • C 1 7 2 3
  • D 3 4
  • E 5 8 9

If they keep up the same pace, what distance will they have walked in 3 hours?

  • A 1 7 2 3 km
  • B 9 1 5 1 6 km
  • C 3 9 3 4 km
  • D 5 8 9 km
  • E 4 5 1 2 km

Q12:

Identify, without performing any division, the expression which has a quotient greater than 1.

  • A 5 1 4 ÷ 9 2 7
  • B 4 3 7 ÷ 6 2 5
  • C 2 2 5 ÷ 5 3 4
  • D 7 1 2 ÷ 2 6 7
  • E 3 1 9 ÷ 4 3 5

Q13:

Shady and Maged want to make some cupcakes for their younger sister’s birthday. Shady goes to the store and buys 2 1 4 cups of sugar. When he gets home, Maged says he located 7 8 of a cup of sugar. The recipe says that they can make a dozen cupcakes with 1 1 2 cups of sugar. If they combine the sugar they have, and they have all the other necessary ingredients, how many full batches of a dozen cupcakes can they make?

  • A1 batch
  • BNone because they do not have enough sugar
  • C3 batches
  • D2 batches

Q14:

A worker earns 2 1 4 L E per hour. One day he earns 4 1 2 L E . How long did he work that day?

Q15:

A shirt can be made from 2 2 3 yards of fabric. How many shirts can you make with 48 yards of fabric?

  • A 16 shirts
  • B 17 shirts
  • C 19 shirts
  • D 18 shirts

Q16:

A wire that is 88 metres long was cut into pieces of 5 1 2 metres each. Find the number of pieces produced.

Q17:

Find 𝑥 ÷ 𝑦 given that 𝑥 = 2 1 2 and 𝑦 = 5 9 .

  • A 9 1 0
  • B 2 9
  • C 3 3 5
  • D 4 1 2
  • E 1 8 2 5

Q18:

Find 𝑥 ÷ 𝑦 given that 𝑥 = 9 and 𝑦 = 7 2 9 .

  • A 4 0 1 2
  • B 6 5 8 1
  • C 1 2 7
  • D 1 1 6 6 5
  • E65

Q19:

Sameh’s room is 167 inches long. Express, in feet, his room’s length as a mixed number in the simplest form.

  • A 6 2 3 2 4 ft
  • B 2 7 5 6 ft
  • C 1 2 1 1 1 2 ft
  • D 1 3 1 1 1 2 ft
  • E 1 4 1 1 1 2 ft

Q20:

Without evaluating each expression, decide whether 8 1 7 ÷ 2 4 9 is greater than or less than 8 1 7 ÷ 7 1 2 .

  • Agreater than
  • Bless than

Q21:

Calculate 9 1 0 ÷ 7 1 5 . Give your answer in its simplest form.

  • A 8
  • B 9 1 4
  • C 3 8
  • D 1 8
  • E 1 1 1 2 5

Q22:

It took Adel one hour and a half to clean two-thirds of the house. How long will it take him to clean the whole house? Give your answer as a mixed number in hours and minutes.

  • A 2 1 4 hours, 2 3 0 h o u r s m i n u t e s
  • B 2 1 4 hours, 2 2 5 h o u r s m i n u t e s
  • C 2 1 4 hours, 4 3 0 h o u r s m i n u t e s
  • D 2 1 4 hours, 2 1 5 h o u r s m i n u t e s
  • E 2 1 4 hours, 4 5 0 h o u r s m i n u t e s

Q23:

Yara spent 1 1 1 4 d o l l a r s , or three-quarters of her pocket money, on books. How much pocket money did she have before she bought the books?

Q24:

Calculate 1 4 × 1 1 8 ÷ 1 2 . Give your answer in its simplest form.

  • A 9 6 4
  • B 4 9
  • C 1 9
  • D 9 1 6

Q25:

Use the diagram to find 3 4 ÷ 2 7 (i.e., the number that 3 4 is 2 7 of).

  • A 8 2 1
  • B 3 1 4
  • C 4 2 3
  • D 2 5 8
  • E 1 1 2 8

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