Algebra 3 Guided Notes: NAME: _________________________________ Connecting Multiplication and Percents DATE: ______________ Learning Targets: • Relate multiplication by a constant term to increasing/decreasing a number by a percentage. Converting a percent to a decimal: Divide the percent by _______, or move the decimal ____ places to the _________. Examples: Convert to a decimal. a) 85% = ________ b) 2% = ________ c) 20% = _________ d) 8.7% = _______ e) 50.5% = ________ f) 0.8% = _________ g) 100% = ________ h) 155% = ________ i) 300% = _________ Converting a decimal to a percent: Multiply by ________, or move the decimal ____ places to the ________. Examples: Convert to a percent. a) 0.05 = ________% b) 0.43 = ________% c) 0.6 = ________% c) 0.125 = ________% d) 1.08 = ________% e) 2.5 = ________% Finding a percentage of a value: Multiply the value by the percent in _____________________________. Examples: a) 12% of 63 is __________ b) 2.5% of $12,000 is __________ c) 75% of 16.52 is __________ d) 105% of $89.99 is ____________ Solving percentage problems: Translate into an equation. “OF” translates to _________________ when dealing with percents. Examples: a) 17% of what is 50? _________ b) 25 is what percent of 158? _________ c) What is 3.5% of $76.59? _________ d) What percent of 120 is 52? _________ Percentage increase/decrease problems – the long way: First find the percentage, then add or subtract. Examples: a) What is the result if $44.99 is decreased by 30%? b) What is the result if 17,000 is increased by 8%? Percentage increase/decrease – the efficient way: Multiply the original value by a decimal value o Decrease: ___________________________________ o Increase: ____________________________________ Examples: a) What is the result if $44.99 is decreased by 30%? b) What is the result if 17,000 is increased by 8%? Percentage increase/decrease – the efficient way (continued): Examples: a) Increase by 15% means multiply by ______________. b) Decrease by 6% means multiply by _______________. c) Reduce by 30% means multiply by _______________. d) Grow 6.7% means multiply by ________________. e) Multiplying by 1.15 means increase / decrease by ____________%. f) Multiplying by 0.96 means increase / decrease by ____________%. g) Multiplying by 1.108 means increase / decrease by ____________%. Percent increase/decrease applications: Find the result when… a) a population of 126,000 grows by 8%. b) a company’s $2.6 million annual revenue plummets 18%. c) a $65.99 sweater is on sale for 40% off. d) a 15% tip is added to a $37.50 dinner bill. Percent off sales made easier: Estimate the sale price – no calculator! a) A $40 shirt is 30% off. b) A $90 coat is 40% off d) A $29.95 hat is 85% off c) A $119.99 pair of shoes is 60% off Multiple‐step increase/decrease problems: a) Find the total for a $28.37 lunch bill after a 6.5% sales tax is included and a 20% tip is added on top of that. b) Find the total cost of a $44.99 pair of jeans on sale for 45% off after a 7.2% sales tax is added to the sale price. Algebra 3 Homework: NAME: _________________________________ Connecting Multiplication and Percents DATE: ______________ 1) What is 35% of 250? 2) What is 6.5% of 27? 3) What is 125% of 13,800? 4) What percent of 16 is 9.5? 5) 230 is 85% of what? 6) 81 is what percent of 93? 7) What is 17% of 0.012 8) $225,000 is what percent of $8 million? 9) $165 is 3.7% of what? 10) 105% of $823 is what? 11) What percent of 3 is 7? 12) Decrease by 12% means multiply by ______ 13) Increase by 40% means multiply by ______ 14) Grow 9% means multiply by ______ 15) Decline by 3.2% means multiply by ______ 16) Shrink 82% means multiply by ______ 17) Take 35% off means multiply by ______ Find the result when… 18) a population of 3.2 million declines by 24% 19) someone’s $32,000 salary goes up 2% 20) a person’s $13,600 debt is lowered by 17% 21) a 6.5% sales tax is added to a $6.99 pair of socks. 22) the price of a $17,000 car is reduced by 30% 23) $250,300 in sales falls by 28% 24) a $459.99 sofa is sold at 30% off with a 4.2% sales tax added to the sales price. 25) Write a word problem about a tent that is on sale. Here is the work: 189.95 * 0.85 = 161.4575 → $161.46 26) Write a word problem about a company’s annual expenses. Here is the work: 1,305,000 * 1.08 = 1,409,400 → $1,409,400 27) Write a word problem about the population of fish in a lake. Here is the work: 3,500 * x = 3,900 x = 1.114 → Grew by 11.4%