Proportional ReasoningToday you will learn to:• test if ratios can form a proportion.• use cross products.

M7.A.2.2.3: Use proportions to determine if two quantities are equivalent.

What is a Proportion?

A proportion is an equation stating that two ratios are equal. You can also use cross multiplying to determine a missing values in a proportion, such as:

Are these two ratios (fractions) equivalent?

How do you know?

ProportionsFor two ratios, the cross products

are found by multiplying the denominator of one ratio and the numerator of the other ratio. The Cross Product Property states that if two ratios form a proportion, the cross products are equal, and that if two ratios have equal cross products, they form a proportion. We will be using the Cross Product Property to determine the value of an unknown variable.

Example: Determine the value of the variable h. Use cross products.

Solving Proportions with UnitsExample: Jenna is responsible for making coffee for her co-workers. While at the grocery store to purchase coffee, she notices that 500 grams of 100% Columbian coffee costs $3.00. She decides to purchase 1250 grams. How much will 1250 grams of coffee cost?

Grams (known)__ = __Grams (known)__ Cost (known) Cost (unknown)

__500 grams__ = ___1250 grams__ $3.00 n

The first rate should be your known rate.

The second rate should include the given measure and the variable (unknown).

NOTICE: The SAME UNITS appear in BOTH NUMERATORS!!!

Proportions: Example