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Essential Percentages and Calculations Guide for Math Learners

Learn to convert fractions, decimals, and percents easily. Understand concepts like finding percentage increase, amount of profit, sales tax, discount, and more through practical examples and equations.

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Essential Percentages and Calculations Guide for Math Learners

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  1. Percents • A ratio or comparison of a quantity to 100 • Part/whole = n/100= n% • 48 out of 100 = 48/100=48%

  2. Fractions, Decimals, Percents • To rename a percent as a fraction: • Write the percent as a fraction with the denominator of 100. • Rewrite in simplest form • To rename a percent as a decimal: • Remove the percent symbol • Move the decimal two places to the left

  3. To rename a decimal as a percent: • Move the decimal 2 spaces to the right • To rename a fraction as a percent: • Divide the numerator by the denominator • Write the decimal as a percent OR • Use a proportion using the fraction as one term and x/100 as the other

  4. Percents greater than 100% and less than 1% • Renaming fractions greater than 1 as percents: • Write as an equivalent decimals (divide) • Write as a percent (move 2 spaces to the RIGHT) OR • Write a proportion • Renaming percents as decimals or fractions: • Decimal: move decimal 2 spaces to the LEFT • Mixed number: write as a fraction with a denominator of 100. REDUCE

  5. Renaming decimals less than 1% • Renaming a decimal as a percent: • Move 2 spaces to the LEFT OR • Rename as a fraction with 100 as the denominator • Renaming fractions as percents: • Rename as a decimal and move 2 spaces to the RIGHT OR • Write a proportion and solve

  6. Finding Percentage, Base and Percent • The “is” stands for the percentage, or part, that is being compared to the whole quantity. • The “of” is the whole quantity or the base.

  7. Percent increase

  8. Percent Change • The ratio comparing a change in a quantity to the original amount. • Percent change= amount of change/original amount

  9. Percent Increase • Write an equation • Percent increase = amount of increase/original amount • Write/solve a proportion • Amount of increase/original amount = percent increase (%) / 100

  10. Find the percent increase from 12 to 15 • Equation • Amount of increase / original amount = percent increase • 15-12 =3  amount of increase • Original amount = 12 • 3/12 = .25 = 25% • Proportion • Amount of increase / original = percent increase / 100 • 3/12=x/100 • 12x=300 • X=25

  11. Find the percent increase from 40 to 45

  12. Amount of Profit • Cost- original amount spent for an item • Profit- the money gained when an item is sold at cost • To find the amount of profit: • Multiply the original cost by the percent profit

  13. A company buys microwave ovens for $200 each then sells each at a gain of 15%. What is the company’s profit? • Write an equation • P = .15 x 200 • P = $30.00 • Write/solve a proportion • Profit / original = percent profit (%) / 100 • P/200 = 15/100 • 3000 = 100p • P = $30

  14. Selling Price • Selling price- the amount for which the item is sold. Add the profit to the cost to find the selling price. • A video dealer imports large flat screen TVs for $1200 each. The dealer then sells each TV at a profit of 30%. What is the selling price? • SP = $1200 + (30% of 1200) • SP = $1200 + (.30 x 1200 = $360) • SP = $1200 + $360 • SP = $1560

  15. Sales tax- amount of tax added to the marked price by state or local government. • Write an equation • Sales tax rate x marked price = sales tax • Set up/solve a proportion • Sales tax / marked price = sales tax rate (%) / 100

  16. A calculator is priced at $29.95 with a sales tax of 6%. What is the amount of sales tax to the nearest cent? • Equation • .06 x 29.95 = 1.797 = $1.80 • Proportion • t/29.95 = 6/100 • 100t=179.70 • T-1.7970 = $1.80

  17. Discount • Discount = discount rate x list price • Sale price = list price – discount • Discount rate = amount of discount / list price

  18. Markup • Markup = list price – wholesale price • Markup rate = markup / wholesale price • Markup rate is expressed as a percent

  19. Commission-Amount of money earned for selling goods or services. • Equation • Commission = commission rate x total sales • Write/solve proportion • Commission/total sales =commission rate (%) / 100

  20. 6% commission on $25,000 in sales • .06 x 25,000 = • x/25,000 = 6/100 =

  21. 6% commission on $25,000 in sales • .06 x 25,000 = $1500 • x/25,000 = 6/100 = $1500

  22. $1755 earned on $92,000 in sales • C x 92,000 = 1755 • 1755/92000 = x/100

  23. $1755 earned on $92,000 in sales • C x 92,000 = 1,755 • C=about 1.9% • 1755/92000 = x/100 • C=about 1.9%

  24. Simple Interest • Principal (p)- amount of money borrowed or deposited • Interest (I)- amount earned or paid in exchange for the use of money • Rate of interest (r)- percent of interest earned or paid • Time (t)- how long in years the principal is borrowed or left on deposit. • Simple interest- interest earned or paid only on the principal for a stated period of time

  25. Interest = principal x rate x time • I=prt Time is expressed in years or fractional part of a year

  26. Find the simple interest (I):$800 at an annual rate of 8% for 9 months • I=prt • I=(800)(.08)(9/12) • I= $48

  27. Compound Interest • Compound interest- interest paid on the principal and on the interest accumulated to date. • balance

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