Fundamentals of Math

Fundamentals of Mathematics

If two or more ratios can be reduced to the same value, then they are equivalent ratios. For example, 14 16 and 28 32 can both be reduced to 7 8 , so they are equivalent ratios. A proportion is an equation that states two ratios are equivalent (equal), written in the form = . Proportions will always have an equal sign! Similarly, to ratios, portions can be written in multiple forms: = or : = : .

With proportions, the product of the first fraction's numerator and second fraction's denominator is equal to the product of the first fraction's denominator and the second fraction's numerator.

= ⟹ ∙ = ∙

We can use this fact to help us solve equations.

Example 3.5.1

Paulette can eat 24 chicken wings in 35 minutes. She wants to know howmany minutes it would take her to eat 36 chicken wings if she kept the same pace.

24 35

36

Step 1:

Set-up your portion.

=

=

Step 2: Cross multiply to eliminate the fractions.

24 ∙ = 36 ∙ 35 ⟹ 24 = 1260

Step 3: Solve for . 1260 24 ⟹ = 52.5 Keeping the same pace. It would take Paulette 52 and a half minutes to eat 36 chicken wings. 24 24 =

Practice 3.5

1. If you can buy one can of green beans for $1.25 then how many can you buy with $10?

2. Samuel reduced the size of a rectangle to a height of 4 inches What is the new width if its height was initially 24 inches and its width 12 inches?

3. Mario took a trip to Costa Rica. When he was leaving, he decided to convert all of his colón (Costa Rica's currency) back into U.S. dollars. How many dollars did he receive if he exchanged 69,855 colón at a rate of $5.50 = 3200 colón? Round your answer to the nearest cent.

Answer Key on Page 120

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