Proportions How to Write and Solve Them PROBLEM

Proportions How to Write and Solve Them

PROBLEM: I saw at Office Depot that pencils were priced at a dozen for $1. 50 • • • How much is it for one pencil? How much is it for 8 pencils? How much is it for 20 pencils? How many pencils can I buy for $2 ? How many pencils can I buy for $5 ?

Problems like these can be solved using proportions. . . What are proportions? How do you solve them?

Proportion: an equation showing two equal ratios. . . Examples: 2 4 = 3 6 5 7 x 3 4 = 6 15 = 21 3 18 4 = 24 2 4 = 3 x

Writing (Setting Up) Proportions • Write a rate (ratio) from the information you know: 12 pencils $1. 50 • Choose a variable for the unknown • Write a second ratio, keeping the units in the same order.

How much is it for one pencil? • Write the rate 12 pencils $1. 50 1 pencil = X • Choose a variable for the unknown • Write a second ratio, keeping the units in the same order.

How to solve proportions. . . METHOD ONE: METHOD TWO: • Look for a pattern and use “guess and check” • Cross multiply to form a new equation • Solve this equation by dividing • Check your answer

METHOD ONE Example: Looking for a Pattern. . Divided by 12 12 pencils $1. 50 1 pencil = X Divided by 12

METHOD TWO Example: Cross Multiply … 12 pencils $1. 50 1 pencil = 12 x = $ 1. 50 12 12 X Solve for x

Try to work these out in your notes. . . How much is it for 8 pencils? How much is it for 20 pencils? How many pencils can I buy for $2 ? How many pencils can I buy for $5 ?