Solve the proportion

Key Notes :

Definition of Proportion

• A proportion is an equation that shows two ratios are equal.
• Example: 2/3 = 4/6​.

Parts of a Proportion

• A proportion consists of two fractions or ratios.
• Example: a/b = c/d​, where a,b,c, and d are numbers.

Solving a Proportion using Cross Multiplication

Multiply the numerator of the first ratio by the denominator of the second ratio.

Multiply the denominator of the first ratio by the numerator of the second ratio.

Set both products equal to each other and solve for the unknown.

Example: Solve 3/4 = x/8​

• 3 × 8 = 4 × x3
• 24 = 4x
• x = 6.

Finding a Missing Number in a Proportion

If one value is unknown, use cross multiplication to find it.

Example: 5/x = 10/20​

• 5 × 20 = x × 10
• 100 = 10x
• x = 10.

Checking if Two Ratios Form a Proportion

Cross multiply and see if the products are equal.

Example: Is 6/9 = 8/12​?

• 6 × 12 = 72
• 9 × 8 = 72

Since both products are equal, the ratios form a proportion.

Real-Life Applications of Proportion

• Recipe Adjustments: If a recipe needs 2 cups of flour for 4 servings, how much flour is needed for 6 servings?
• Map Scale: A map shows 1 inch = 10 miles. If the distance between two cities is 5 inches on the map, the actual distance is 50 miles.
• Conversions: If 5 pencils cost $10, then how much do 8 pencils cost?

Solving Word Problems Involving Proportion

• Identify the two ratios in the problem.
• Set up a proportion equation.
• Use cross multiplication to solve for the missing value.
• Check if the answer makes sense in the given context.

Learn with an example

let’s practice! 🖊️