Percent Increase and Decrease

Learn percent increase, percent decrease.

Lesson 2 of 32 parts Practice Flashcards

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Percent Increase

Objective: Explain percent increase, apply the stated method, and check its conditions.

For a positive original quantity W and increase rate r in decimal form, new value is W(1+r). Percent change uses the original quantity as its denominator. Equal percent increases and decreases do not generally undo one another. Use the original amount when measuring a percent change.

Formulas

$New=old(1+r)$

Worked examples

Try itAn item costs $600 before a 7% increase. What is its new price?Show answer

Step 1: A percent increase uses multiplier 1+r. Step 2: The increase is (7/100)(600)=42. Step 3: Add it to get $642.

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Percent Increase

Objective: Explain percent increase, apply the stated method, and check its conditions.

Formulas

$New=old(1+r)$

Worked examples

Try itAn item costs $600 before a 7% increase. What is its new price?Show answer

Step 1: A percent increase uses multiplier 1+r. Step 2: The increase is (7/100)(600)=42. Step 3: Add it to get $642.

Percent Decrease

Objective: Explain percent decrease, apply the stated method, and check its conditions.

A decrease by rate r keeps the fraction 1−r of the original amount. For ordinary discounts use 0≤r≤1. Successive discounts multiply retention factors; they do not generally equal adding the percentage labels. Two successive percentage discounts act on changing reference amounts.

Formulas

$New=old(1−r)$

Worked examples

Try itAn item costs $600 before a 7% decrease. What is its new price?Show answer

Step 1: A percent decrease keeps the share 1−r. Step 2: The decrease is (7/100)(600)=42. Step 3: Subtract it to get $558.

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