Worksheet: Multiplying Fractions: Area Models

In this worksheet, we will practice finding the product of two proper fractions using area models and relating the numerator and denominator of the product to those of the factors.

Q1:

The diagram shows the different stages to find the number ๐‘ that 23 is 45 of.

Express ๐‘Ž in terms of 23.

  • A ๐‘Ž = 1 4 ร— 2 3
  • B ๐‘Ž = 1 5 รท 2 3
  • C ๐‘Ž = 1 5 ร— 2 3
  • D ๐‘Ž = 1 4 รท 2 3
  • E ๐‘Ž = 2 3 รท 1 4

What operation on number ๐‘Ž gives number ๐‘?

  • A ๐‘ = ๐‘Ž ร— 5
  • B ๐‘ = ๐‘Ž ร— 4
  • C ๐‘ = ๐‘Ž + 5
  • D ๐‘ = ๐‘Ž ร— 6
  • E ๐‘ = ๐‘Ž + 4

Find the value of ๐‘.

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

Q2:

There is 14 of a cake left. Noah eats 23 of it. What fraction of the whole cake does Noah eat?

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

Q3:

How much is 14 of 13?

  • A3
  • B 1 1 2
  • C12
  • D 1 4
  • E 1 3

Q4:

Multiply 23 by 45 using models.

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

Q5:

Write a fraction equation to find what fraction of the given figure is shaded.

  • A 2 7 ร— 6 4 = 6 2 8
  • B 2 7 ร— 3 4 = 6 2 4
  • C 2 7 ร— 3 4 = 6 2 8
  • D 2 7 ร— 3 4 = 3 2 8
  • E 2 6 ร— 3 4 = 6 2 8

Q6:

Anthony usually runs 75 of a running track in one hour. What fraction of the running track does he run in 12 h?

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

Q7:

Scarlett spends 18 of her day relaxing. She spends 34 of this time drawing. What fraction of her day does she spend drawing?

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

Q8:

A man bought 32 of an acre of land. He planted flowers on 14 of the land he bought. On what fraction of the acre did he plant flowers?

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

Q9:

Find the product of 52 and 34 using models.

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

Q10:

Find 12 of 15 using models.

  • A 1 2
  • B 1 5
  • C10
  • D 1 1 0
  • E5

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