Fiche de révision : Equivalent Ratios

📋 Course Outline

1. Equivalent Ratio Meaning
2. Finding Missing Ratio Numbers
3. Ratio Tables And Number Lines
4. Ratio Word Problems
5. Ratio Rules And Mistakes

📖 1. Equivalent Ratio Meaning

🔑 Key Concepts & Definitions

• Equivalent ratios : Different ratios that show the same comparison.

📝 Essential Points

★ Must-know

📌 An equivalent ratio is created by multiplying or dividing both numbers by the same non-zero number.

Further detail

• The ratios 2:3, 4:6, and 6:9 are equivalent because each ratio is formed by applying the same multiplier to both terms.

💡 Memory Hook

Same comparison, same multiplier

📖 2. Finding Missing Ratio Numbers

📝 Essential Points

★ Must-know

🧮 Formula — The multiplier equals the new number divided by the original number.

🔄 Process — To find a missing number in an equivalent ratio, match corresponding numbers, divide the new number by the original number to find the multiplier, and apply that multiplier to the other term.

• In 4:
  • 7 = 20:□
  • the multiplier is 20 ÷ 4 = 5
  • so the missing number is 7 × 5 = 35

💡 Memory Hook

Match, divide, repeat

📖 3. Ratio Tables And Number Lines

📝 Essential Points

★ Must-know

🔄 Process — A ratio table generates equivalent ratios by applying the same multiplier to both rows in each column.

• 🔄 A double number line for the ratio 3:
  1. 4 uses the same multiplier on both lines
  2. producing 3:4
  3. 6:8
  4. 9:12
  5. and 12:16

Further detail

• For the ratio 2:
  • 5
  • multiplying both terms by 1
  • 2
  • 3
  • and 4 gives the pairs 2:5
  • 4:10
  • 6:15
  • and 8:20

💡 Memory Hook

Same jump on both lines

📖 4. Ratio Word Problems

📝 Essential Points

★ Must-know

🔄 Process — To solve a ratio word problem, divide the known quantity by its corresponding ratio term to find the multiplier, then multiply the other ratio term by that multiplier.

• If the ratio of boys to girls is 2:
  • 5 and there are 10 girls
  • the multiplier is 10 ÷ 5 = 2
  • the number of boys is 2 × 2 = 4

💡 Memory Hook

Find the multiplier, then apply it

📖 5. Ratio Rules And Mistakes

📝 Essential Points

★ Must-know

⚡ When a corresponding number becomes bigger, use multiplication; when it becomes smaller, use division.

Further detail

📌 Common equivalent-ratio mistakes include multiplying only one number, dividing only one number, using different multipliers, and matching the wrong numbers.

🔄 Process — The calculator method is to identify matching numbers, divide to find the multiplier, apply the multiplier to the other number, and check the answer.

💡 Memory Hook

Whatever you do, do it twice

📊 Synthesis Tables

Equivalent Ratio Methods

⚠️ Common Pitfalls & Confusions

1. Equivalent ratios are not ratios with unrelated numbers; both numbers must change by the same multiplier.
2. The multiplier must be found from matching positions, not from unrelated terms.
3. The multiplier cannot differ between the two rows.
4. The known quantity must be matched with the correct part of the ratio.
5. The operation must be applied to both terms, not just to the term that changed.
6. Changing only one number does not create an equivalent ratio.
7. The division must use corresponding numbers in the same part of the ratio.