2.3 Ratio and Proportion

• A ratio can be expressed in colon form as a : b
• Match the aspect with its description:

  Ratio ↔️ Comparison of two quantities

  Proportion ↔️ Equality between two ratios
• 4 : 6 is in proportion to 8 : 12


  True
• The ratios 1 : 2, 2 : 4, and 5 : 10 are equivalent because they simplify to the same proportion

  True
• Why is it essential to simplify ratios?

  For easier comparison
• What is the definition of proportion?

  Equates two ratios
• When writing ratios in different forms, it is important to simplify them for easier understanding
• A ratio can be expressed in fraction form as a/b
• Match the form of the ratio with its notation:

  Colon ↔️ a : b

  Fraction ↔️ a/b

  Word ↔️ a to b
• What is the first step in solving ratio and proportion problems?

  Identify the ratio
• How are equivalent ratios obtained?

  By multiplying or dividing
• What does simplifying ratios involve?

  Reducing to lowest terms
• Simplifying ratios makes them easier to understand and compare.


  True
• What is a ratio used for?

  Comparing two quantities
• How is proportion expressed in fraction form?

  a/b = c/d
• If there are 4 apples and 6 oranges, what is the ratio of apples to oranges in its simplest form?

  2 : 3
• Equivalent ratios are obtained by multiplying or dividing both sides by the same non-zero number
• Match the ratio form with its example:

  Colon Form ↔️ 3 : 5

  Fraction Form ↔️ 3/5

  Word Form ↔️ 3 to 5
• Proportion shows the equality between two ratios

  True
• If the ratio 2 : 3 is multiplied by 4 on both sides, what is the resulting equivalent ratio?

  8 : 12
• Ratios should always be simplified to their lowest terms for easier understanding.


  True
• What does a ratio compare?

  Two quantities
• Steps to simplify a ratio:

  1️⃣ Identify the ratio

  2️⃣ Find the HCF

  3️⃣ Divide both sides by the HCF

  4️⃣ Write the simplified ratio
• Proportion refers to the equality between two ratios.


  True
• What does simplifying a ratio involve dividing both sides by?

  HCF
• Steps to simplify a ratio

  1️⃣ Identify the original ratio

  2️⃣ Find the HCF of the two numbers

  3️⃣ Divide both sides of the ratio by the HCF

  4️⃣ Write the simplified ratio
• Simplifying ratios requires dividing both sides by their highest common factor
• Dividing 24 and 36 by their HCF simplifies the ratio to 2
• What is the key strategy for solving ratio and proportion problems?

  Finding unknown quantities
• Match the action with its example in solving ratio and proportion problems:

  Identify the ratio and proportion ↔️ 2 : 3 = x : 9

  Use multiplication/division ↔️ (2/3) = (x/9) -> x = (2/3) * 9

  Cross-multiply (if needed) ↔️ 2 * 9 = 3 * x

  Solve and simplify ↔️ x = 6
• A scale diagram showing 2 apples and 3 oranges accurately represents a 2 : 3 ratio.

  True
• Give an example of direct proportion.

  Hours worked and earnings
• In inverse proportion, the product of x and y is constant.


  True
• At 80 mph, the car would take 3 hours to travel the same distance.


  True
• What happens to the time when the speed increases in an inverse proportional relationship?

  It decreases proportionally
• In inverse proportion, the product of x and y remains constant.


  True
• Ratios are used in currency conversion to express the value of one currency in terms of another
• A ratio can be expressed in colon, fraction, or using the word "to"
• What is the key strategy for solving ratio and proportion problems?

  Cross-multiplication
• If 2 apples cost £3, how much do 6 apples cost?

  £9