Proportions

What are proportions? a : b :: c : d An equation in which two ratios are equal is called a proportion A proportion can be written using colon notation like this a : b :: c : d or we can represent as equivalent ratios form _ a__ = _ c__ b d

Proportions In a proportion the product of the means is equal to product of the extremes. MEANS 3 : 5 = 6 : 10 Extremes

Proportions Means Extremes 6 x 5 = 3 x 10 30 = 30

Proportions Determine if the following are proportions. 1) 2)

Proportions 3 x 60 = 5 x 36 4 x 15 = 8 x 8 180 = 180 60 64 Yes, it is a proportion. No, it is not a proportion.

Solving Proportions 4 = 24 Y 30 4(30) = 24y 120 = 24y 24 24 5 = y 24 24 5 = y 1. Cross Multiply 2. Solve for the variable.

Solving Proportions y 8 8(10) = 5y 80 = 5y 5 5 16 = y 10 = 5 5 5 16 = y 1. Cross Multiply 2. Solve for the variable

Try one on your own… 3 = 12 y 28

And another… 6 = 12 n 24

Practical Examples A proportion is a statement that two given ratios are equal  Practical examples: If you are mixing paint to paint your house, you need to keep the ratio (of color pigments to white paint) constant to ensure that the color will remain exactly the same.

CONTINUED PROPORTION If a, b, c are said to be in continued proportion We can write a: b : : b : c If 4,12,x are in continued proportion how we will write??????? Can you tell?????

Answer…… 4,12,12,x are in proportion Then 4:12:: 12: x 4 x X = 12 x 12