Equivalent ratios: word problems

Key Notes :

1. Understanding Equivalent Ratios

• Two ratios are considered equivalent if they represent the same relationship between the two quantities.
• Equivalent ratios can be found by multiplying or dividing both terms of a ratio by the same non-zero number.

Example:

• Ratio 1: 4:6
• Ratio 2: 8:12
• These are equivalent because both ratios simplify to 2:3.

2. Simplifying Ratios to Find Equivalent Ratios

• To find equivalent ratios, simplify the given ratio by dividing both terms by their greatest common factor (GCF).
• Example:
  For the ratio 12:18, the GCF is 6. Divide both terms by 6:

• Therefore, 12:18 is equivalent to 2:3.

3. Multiplying to Find Equivalent Ratios

• Alternatively, you can multiply both terms of a ratio by the same number to generate an equivalent ratio.
• Example: If the ratio is 2:3 and you multiply both parts by 4, you get 8:12, which is equivalent to 2:3.

4. Setting Up Word Problems

• Identify the ratio described in the word problem.
• Set up a proportion if the problem involves finding an unknown value.
• Use the property of equivalent ratios to solve for the unknown.

5. Solving Word Problems

• Step 1: Write the given ratios.
• Step 2: Set up a proportion (an equation where two ratios are equal).
• Step 3: Solve for the unknown variable.

Learn with an example

Let’s practice! 🖊️