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Worksheet: Simplifying Ratios

Q1:

If 1 7 1 1 of the sum of two numbers is 51, where the ratio between them is 4 ∶ 7 , find the two numbers.

  • A28, 49
  • B51, 33
  • C20, 35
  • D12, 21

Q2:

Given that 𝑎 ∶ 𝑏 = 3 ∶ 2 , and 𝑎 − 𝑏 = 4 9 , calculate the value of 𝑎 .

Q3:

A boy has 209 LE and his sister has 132 LE. What is the ratio between his money and hers in its simplest form?

  • A 1 2 ∶ 1 9
  • B 1 2 ∶ 7
  • C 7 ∶ 1 2
  • D 1 9 ∶ 1 2
  • E 7 ∶ 1 9

Q4:

The ratio of Mason’s weight to his father’s weight is . His father weighs 60 kg, so how much does Mason weigh?

  • A 30 kg
  • B 42 kg
  • C 240 kg
  • D 36 kg
  • E 100 kg

Q5:

If 𝑥 ∶ 𝑦 = 1 1 ∶ 3 , then which of the following represent the ratio 2 0 𝑥 − 2 5 𝑦 ∶ 2 1 𝑥 + 1 0 𝑦 in its simplest form?

  • A − 2 1 5 ∶ 1 7 3
  • B 9 ∶ 5
  • C 1 7 3 ∶ − 2 1 5
  • D 5 ∶ 9
  • E 2 9 5 ∶ 2 0 1

Q6:

A square and a rectangle have the same length perimeters, and the length of the rectangle is five times its width. What is the ratio between the area of the rectangle and the area of the square in its simplest form?

  • A 1 2 ∶ 5
  • B 9 ∶ 5
  • C 5 ∶ 1 2
  • D 5 ∶ 9

Q7:

The ratio of the areas of two plots of land, A and B, is 1 7 ∶ 5 . Given that the area of plot A is 60 m2 larger than plot B, what is the area of plot B?

  • A 300 m2
  • B 85 m2
  • C 720 m2
  • D 25 m2
  • E 17 m2

Q8:

Express the ratio 1 0 7 ∶ 5 3 in its simplest form.

  • A 7 ∶ 6
  • B 5 0 ∶ 2 1
  • C 2 1 ∶ 5 0
  • D 6 ∶ 7
  • E 3 0 ∶ 3 5

Q9:

A student got 30 out of 90 marks in the first-term exam in physics, and he got 81 out of 90 in the second-term exam. Express the ratio of his total marks scored in the two exams to the total marks available in its simplest form.

  • A 3 7 ∶ 3 0
  • B 1 0 ∶ 2 7
  • C 1 ∶ 3
  • D 3 7 ∶ 6 0

Q10:

Which of the following ratios is equivalent to 1.5 : 4.6?

  • A3 : 2.3
  • B7.5 : 10.6
  • C7.5 : 4.6
  • D7.5 : 23
  • E3 : 4.6

Q11:

The success rate of the third preparatory in a governorate is 8 2 % , where the percentage of success of the boys is 5 4 % , and that of the girls is 8 3 % . Determine the ratio between the number of boys and the number of girls in this grade.

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

Q12:

The ratio between Mason’s money and Emma’s money is . If the sum of their money is 480 LE, how much money does Mason have?

Q13:

The given table shows the number of points each student scored on a math test. Each question was worth an equal number of points. If Mason answered 37 questions correctly, determine the number of questions Daniel answered correctly.

Student Daniel Mason William
Points 58 74 60

Q14:

Given that 4 𝑥 − 2 7 𝑦 = − 3 𝑥 𝑦 2 2 , which of the following correctly express the ratio 𝑥 ∶ 𝑦 ?

  • A 4 ∶ 9 or − 3 ∶ 1
  • B 4 ∶ 9 or − 1 ∶ 3
  • C 9 ∶ 4 or − 1 ∶ 3
  • D 9 ∶ 4 or − 3 ∶ 1

Q15:

In Jacob’s class, 6 out of every 14 students play tennis. In Noah’s class, 9 out of every 27 play tennis. Is the ratio of students who play tennis in Jacob’s class the same as the ratio who play tennis in Noah’s class?

  • Ano
  • Byes

Q16:

We can find equivalent ratios by multiplying or dividing both sides by the same number. For example, 1 : 5 is equivalent to 2 : 10.

Write a ratio equivalent to 5 9 by 4 that is the result of multiplying both sides by 4.

  • A 2 0 3 2
  • B 9 1 3
  • C 1 0 1 8
  • D 2 0 3 6
  • E 3 6 2 0

Write a ratio equivalent to 3 : 8 that is the result of multiplying both sides by 5.

  • A15 : 40
  • B3 : 40
  • C15 : 8
  • D40 : 15
  • E8 : 13

Q17:

9 1 0 of the circle’s area is shaded and 1 8 1 9 of the triangle’s area is shaded. What is the ratio between the area of the circle and the area of the triangle?

  • A 3 7 0 ∶ 3 6 1
  • B 1 9 ∶ 1 0
  • C 3 6 1 ∶ 3 7 0
  • D 1 0 ∶ 1 9
  • E 2 0 ∶ 1 9

Q18:

The ratio of girls to boys in a junior high band is 5 to 4. Which of the following shows the possible numbers of girls and boys in the band?

  • A70 girls, 60 boys
  • B65 girls, 56 boys
  • C60 girls, 52 boys
  • D70 girls, 56 boys

Q19:

Which of the following ratios is equivalent to 3 : 7?

  • A1 : 5
  • B7 : 3
  • C7 : 11
  • D12 : 28
  • E1 : 21