solving proportions 

Proportions

• Definition of Proportion

  • A proportion is a statement that two ratios are equal.

  • Example: The statement ( \frac{1}{4} = \frac{2}{8} ) is a proportion because both fractions represent the same value.

• Checking Proportions Using Cross Multiplication

  • Method: To verify if a proportion is true, one can use the technique of cross multiplication.

  • Steps:

    1. Multiply the first number (from the first ratio) by the fourth number (from the second ratio).

    2. Multiply the second number (from the first ratio) by the third number (from the second ratio).

  • Conclusion: If the products of both multiplication operations are equal, then the statement is a valid proportion.

• Example of Cross Multiplication

  • Given the proportion: ( \frac{1}{2} = \frac{2}{4} )

  • Step 1: Multiply the first number, 1 (from ( \frac{1}{2} )), by the fourth number, 4 (from ( \frac{2}{4} )):

  • Calculation: ( 1 \times 4 = 4 )

  • Step 2: Multiply the second number, 2 (from ( \frac{1}{2} )), by the third number, 2 (from ( \frac{2}{4} )):

  • Calculation: ( 2 \times 2 = 4 )

  • Result: Since both products are equal (( 4 = 4 )), it confirms that the statement ( \frac{1}{2} = \frac{2}{4} ) is indeed a proportion.