Worksheet: Proportions

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In this worksheet, we will practice getting an unknown value in a proportional relation using cross multiplication and applying that in real-life situations.

Q1:

Given that 819=4𝑦, which of the following expressions must be equal to 8×𝑦?

  • A 1 9 × 4
  • B 1 9 × 8
  • C 8 × 4
  • D 1 9 × 7

Q2:

3 5 = ⋯ 1 0 0 .

Q3:

If 66𝑥=0.75, find the value of 𝑥.

Q4:

If 8 and 3 are in the same ratio as 96 and 𝑥, then find the value of 𝑥.

Q5:

The numbers 6 and 19 are in the same proportion as 𝑥 and 22. Calculate the value of 𝑥, giving your answer as a top heavy fraction in its simplest form.

  • A 1 3 2 1 9
  • B 2 0 9 3
  • C114
  • D132
  • E 5 7 1 1

Q6:

What is the value of 𝑥 if 3, 𝑥+6, 4, and 44 are in proportion?

  • A27
  • B39
  • C126
  • D33

Q7:

Which of the following shows a proportional relationship?

  • A 4 7 = 2 0 3 2
  • B 5 8 = 2 2 4 0
  • C 3 4 = 2 1 3 6
  • D 4 9 = 1 8 2 7
  • E 3 5 = 2 1 3 5

Q8:

If 7𝑥=4278, find the value of 𝑥.

Q9:

If 53=𝑥2.16, find the value of 𝑥.

Q10:

James ran 7 km in 45 minutes. How long would it take him to run 14 km at the same speed?

Q11:

It took Liam 30 minutes to bike 7 miles. At this rate, use a ratio table to find how long it would take him to bike for 21 miles.

Q12:

A person walks 10 kilometers in 40 minutes walking at a constant speed. If they continue walking at this speed, how long will it take them to walk 6 kilometers?

  • A16 minutes
  • B60 minutes
  • C240 minutes
  • D4 minutes
  • E24 minutes

Q13:

Find the number that should be added to each of the numbers 32, 9, 22, and 4 to make them proportional.

Q14:

If 𝑎𝑏=𝑐𝑑, then 𝑎×𝑑=.

  • A 𝑐 𝑏
  • B 𝑏 × 𝑑
  • C 𝑏 × 𝑐
  • D 𝑏 𝑐

Q15:

Given that 𝑐4=2432, find the value of 𝑐.

Q16:

Given that 25=12𝑏, find the value of 𝑏.

Q17:

Fill in the blanks in the figure such that the corresponding numbers in the two rows are proportional.

  • A248, 34, 288, 40
  • B39, 280, 44, 328
  • C 248, 2,176, 288, 2,560
  • D39, 264, 44, 312

Q18:

Complete the missing values in the figure below so that the corresponding numbers in the two columns are proportional.

  • A0.9, 0.99, 3.4, 0.9
  • B0.09, 0.99, 0.34, 0.09
  • C0.09, 0.99, 3.4, 0.09
  • D0.9, 9.9, 0.34, 0.9

Q19:

Fill in the blanks in the figure below to make the corresponding numbers in the two rows proportional.

  • A12, 32, 412, 51
  • B48, 32, 82, 51
  • C48, 8, 82, 514
  • D12, 8, 412, 514

Q20:

Fill in the blanks in the figure below to make the corresponding numbers in the two columns proportional.

  • A1.5, 4.2, 4.4, 1.5
  • B1.5, 0.42, 0.44, 1.5
  • C0.667, 4.2, 4.4, 0.667
  • D0.667, 0.42, 0.44, 0.667
  • E4.2, 1.5, 1.5, 4.4

Q21:

Fill in the blanks in the given figure such that the corresponding numbers in the two rows are proportional.

  • A 10, 110, 1,900, 10
  • B10, 110, 19, 10
  • C54, 65, 136, 54
  • D54, 65, 244, 54

Q22:

Complete the missing values from left to right in the figure below so that the corresponding numbers in the two rows are proportional.

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

Q23:

Given that 𝑥15=𝑦5=𝑧7=7𝑥−6𝑦+4𝑧𝑎, calculate the value of 𝑎.

Q24:

Fill in the blanks: 52=15⋯=3⋯=⋯14=⋯8.

  • A6, 1.2, 37, 20
  • B37.5, 1.2, 35, 3.2
  • C37.5, 7.5, 35, 20
  • D6, 1.2, 5.6, 3.2

Q25:

If 2𝑎=9𝑏, determine 13𝑏2𝑎.

  • A 9 1 3
  • B 4 1 1 7
  • C 1 3 9
  • D 1 1 7 4

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