2.3 Ratio and Proportion

• Ratio is a comparison of two or more quantities, expressed as a fraction or using the colon
• A proportion equates two ratios
• The unitary method involves finding the value of one unit
• What is the cost of 7 apples if one apple costs £1.50?

  £10.50
• A proportion is a statement of equality between two ratios.


  True
• What are the two forms used to express ratios?

  Fractions and colon notation
• What is the largest common factor of 12 and 18?

  6
• Proportional relationships occur when two quantities change by a constant ratio
• What is the constant ratio if 10 hours of work earn £150?

  £15
• If 3 apples cost £4.50, how much would 7 apples cost using proportion?

  £10.50
• Expressing a proportion uses the colon notation
• When cross-multiplying, you multiply the numerator of one ratio by the denominator of the other ratio.


  True
• Dividing both parts of a ratio by the same number results in an equivalent ratio.

  True
• Proportion is a statement of equality between two ratios.


  True
• Both the fraction form and the colon notation represent the same ratio.


  True
• The unitary method is adaptable and provides accurate results for ratio problems.

  True
• The unitary method is ideal for various ratio problems
• Match the concept with its definition:

  Ratio ↔️ Comparison of quantities

  Proportion ↔️ Equality between ratios
• Simplifying a ratio maintains the same proportions while using smaller whole numbers.


  True
• The unitary method involves finding the value of one unit first.


  True
• To solve problems using proportion, you cross-multiply to find the unknown value
• If 3 apples cost £4.50, how much would 7 apples cost?

  £10.50
• Steps to solve problems using proportion

  1️⃣ Set up the proportion

  2️⃣ Cross-multiply to solve for the unknown
• What equation do you get after cross-multiplying the proportion $3:1 =$$7:x$?


  $3x =$$7 \times 4.50$
• Match each ratio with its equivalent ratio:

  2:3 ↔️ 4:6

  1:5 ↔️ 3:15

  6:9 ↔️ 2:3
• A proportion states the equality between two ratios.

  True
• A ratio is a comparison of two or more quantities
• Steps to simplify a ratio

  1️⃣ Identify the largest common factor (LCF)

  2️⃣ Divide both parts of the ratio by the LCF

  3️⃣ Obtain the simplified ratio
• Match the concept with its definition:

  Ratio ↔️ Comparison of two or more quantities

  Proportion ↔️ Equality between two ratios
• What does a ratio compare?

  Two or more quantities
• Understanding how to write ratios in different forms helps in solving ratio problems
• To simplify a ratio, you first find the largest common factor
• If 4 pencils cost £6, what is the cost of 1 pencil using the unitary method?

  £1.50
• In a proportional relationship, the equation is $y =$$kx$.


  True
• Cross-multiplication involves multiplying the numerator of one ratio by the denominator of the other ratio.


  True
• Equivalent ratios express the same relationship even with different numerical values
• What is an equivalent ratio of 3:5 obtained by multiplying both parts by 2?

  6:10
• What is the proportion that shows the equality between 3:5 and its equivalent ratio?

  $3:5 =$$6:10$
• A ratio is a comparison of two or more quantities
• Cross-multiplying the proportion $3:1 =$$7:x$ results in the equation $3x =$$7 \times 4.50$, which gives $x =$$£10.50$ as the cost of 7 apples