3.2 Proportion

• In direct proportion, two quantities increase or decrease together at the same rate.

  True
• Direct proportion occurs when two quantities increase or decrease together at the same rate
• Steps to identify a direct proportion relationship:

  1️⃣ Check if quantities increase or decrease together

  2️⃣ Express the relationship as y = kx

  3️⃣ Determine the constant of proportionality
• Match the example with the type of proportion:

  Cost vs. quantity ↔️ Direct proportion

  Number of workers vs. time ↔️ Inverse proportion
• What does the constant of proportionality represent in direct proportion?

  The rate of change
• When two quantities increase or decrease together at the same rate, they are in direct proportion.
• If y is directly proportional to x, the relationship can be expressed as y = kx.
• What is the equation for direct proportion?

  y = kx
• To find the constant of proportionality, you need to use given data in the direct proportion formula.


  True
• What are the two main types of proportion in mathematics?

  Direct and inverse
• In direct proportion, substituting known values into the formula helps solve for the unknown.


  True
• If 3 apples cost £1.50, then 6 apples cost £3 in direct proportion.


  True
• In inverse proportion, the relationship between quantities is that one increases as the other decreases.

  True
• The cost of buying apples is directly proportional to the number of apples
• In direct proportion, the constant of proportionality is denoted by the letter k
• In direct proportion, the cost of an item is proportional to the number purchased
• In direct proportion, the constant of proportionality is denoted by the letter k
• If speed is constant, the distance traveled is directly proportional to the time
• In the direct proportion formula, 'y' represents the dependent variable.


  True
• If 3 apples cost £1.50, what is the constant of proportionality for the cost of apples?

  0.5
• What is the equation for inverse proportion?

  y = k/x
• In inverse proportion, quantities move in opposite directions.


  True
• In direct proportion, quantities increase or decrease together at the same rate
• In the inverse proportion example, time and the number of workers are identified as inversely proportional
• What is the constant of proportionality in direct proportion called?

  k
• Give an example of a direct proportion relationship.

  Cost vs. quantity
• In inverse proportion, quantities increase together

  False
• What is the formula for direct proportion?

  y = kx
• Inverse proportion occurs when one quantity increases while the other decreases.

  True
• Match the type of proportion with its characteristic:

  Direct Proportion ↔️ Quantities move in the same direction

  Inverse Proportion ↔️ Quantities move in opposite directions
• If 4 workers take 3 hours to complete a job, the constant of proportionality is 12
• What is the time it takes for 2 workers to complete a job if 4 workers take 3 hours?

  6 hours
• Proportion in mathematics refers to the relationship between two quantities where one changes in relation to the other
• Match the type of proportion with its equation:

  Direct proportion ↔️ y = kx

  Inverse proportion ↔️ y = k/x
• In inverse proportion, the product of the two quantities is constant.

  True
• When two quantities increase or decrease together at the same rate, they are in direct proportion
• What happens to one quantity in inverse proportion when the other increases?

  It decreases
• What is the cost of 6 apples if 3 apples cost £1.50 and the cost is directly proportional to the number of apples?

  £3.00
• The cost of buying apples is directly proportional to the number of apples purchased.


  True
• Match the direct proportion examples with their relationships:

  Cost vs. quantity ↔️ The cost increases with the number purchased

  Speed vs. time ↔️ The distance increases with time if speed is constant

  Volume vs. weight ↔️ The volume increases with weight if density is constant