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GED Math: Ratios, Proportions, and Percents Concepts

Importance ★★★★★ · 20% (estimate)

Overview

This chapter covers rates, ratios, proportions, scale drawings, unit conversions, and percent problems such as tax, tips, discounts, markups, commissions, percent change, and simple interest. The GED assessment targets name real-world percent problems such as tips, commissions, and percent increase and decrease.

A unit rate tells how much of one thing for one unit of another, such as dollars per ounce or miles per hour. To compare prices, divide each total price by the number of units and pick the smallest. A proportion sets two equal ratios side by side, and cross-multiplying solves for the missing value. Scale drawings work the same way: multiply each drawing length by the scale to get the real length.

To find a percent of a number, change the percent to a decimal and multiply. Percent change is the amount of change divided by the original amount. When two percents are applied one after the other, such as a discount and then tax, the second percent is taken of the new amount, not the original.

Simple interest uses the formula I = Prt from the formula sheet, where P is the amount borrowed or saved, r is the yearly rate as a decimal, and t is the time in years.

Key concepts

  • Unit rate

    An amount per one unit, found by dividing. Examples: price ÷ number of items, miles ÷ hours.

    Memory tipFor the best buy, compare the price per unit, not the total price.

  • Proportion

    Two equal ratios, such as 3/1,050 = x/1,750. Cross-multiply and divide to find the missing number.

    Memory tipKeep the same units on top in both ratios.

  • Percent of a number

    Change the percent to a decimal by moving the decimal point two places left (18% = 0.18), then multiply.

    Memory tip10% is easy to find in your head; use it to check your answer.

  • Percent change

    Percent change = (new − old) ÷ old × 100. A positive result is an increase and a negative result is a decrease.

    Memory tipAlways divide by the original (old) amount.

  • Simple interest

    I = Prt, where I = interest, P = principal (amount borrowed or saved), r = yearly rate as a decimal, t = time in years. The total owed is P + I.

    Memory tipUse 0.04 for 4%, not 4.

    Source: GED Testing Service (Mathematics Formula Sheet) · as of 2026

  • Unit conversion

    Multiply or divide by a conversion fact one step at a time, such as 60 minutes = 1 hour or 5,280 feet = 1 mile.

    Memory tipWrite the units next to each number so you can see them cancel.

Often tested

  • A discount and a markup of the same percent do not cancel out.
  • Total with tax = price × (1 + tax rate); sale price = price × (1 − discount rate).
  • Area on a scale drawing grows by the scale factor squared.
  • Commission pay = base pay + rate × sales.

3 sample questions

Verified practice questions from this unit.

Practice questionReviewedQuantitative Problem Solving › Ratios, Proportions, and Percents★★★★★

Question 1. A restaurant bill is $45.00. You want to leave an 18% tip. How much is the tip?

  1. ① $8.10
  2. ② $53.10
  3. ③ $0.81
  4. ④ $2.50
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ① $8.10

Key point: Percent of a number: change % to a decimal and multiply

  1. Change 18% to a decimal: 18% = 0.18.
  2. Multiply: 0.18 × $45.00 = $8.10.

Check: 10% of $45 is $4.50, so 20% is $9.00. 18% should be a little less than $9.00, and $8.10 is.

Wrong choices

  • $0.81: $0.81 uses 0.018 instead of 0.18; the decimal point was moved one place too far.
  • $2.50: $2.50 divides 45 by 18 instead of finding 18% of 45.
  • $53.10: $53.10 is the bill plus the tip, not the tip alone.
Practice questionReviewedQuantitative Problem Solving › Ratios, Proportions, and Percents★★★★★

Question 2. Monthly rent went up from $1,200 to $1,290. What was the percent increase?

  1. ① 7.0%
  2. ② 90%
  3. ③ 9%
  4. ④ 7.5%
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ④ 7.5%

Key point: Percent change = (new − old) ÷ old × 100

  1. Amount of increase: $1,290 − $1,200 = $90.
  2. Divide by the original amount: 90 ÷ 1,200 = 0.075.
  3. Change to a percent: 0.075 × 100 = 7.5%.

Check: 7.5% of $1,200 is $90, and $1,200 + $90 = $1,290.

Wrong choices

  • 7.0%: 7.0% divides by the new rent ($1,290) instead of the original rent; 90 ÷ 1,290 is about 0.070.
  • 9%: 9% treats the $90 increase as if it were 9 percent.
  • 90%: 90% uses the dollar increase as the percent without dividing by the original rent.
Practice questionReviewedQuantitative Problem Solving › Ratios, Proportions, and Percents★★★★★

Question 3. Bottled water is sold in four pack sizes: 12 bottles for $5.40, 18 bottles for $7.38, 24 bottles for $10.32, and 30 bottles for $13.80. Which pack has the lowest price per bottle?

  1. ① 30 bottles for $13.80
  2. ② 18 bottles for $7.38
  3. ③ 12 bottles for $5.40
  4. ④ 24 bottles for $10.32
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ② 18 bottles for $7.38

Key point: Unit price = total price ÷ number of units

  1. 12-pack: $5.40 ÷ 12 = $0.45 per bottle.
  2. 18-pack: $7.38 ÷ 18 = $0.41 per bottle.
  3. 24-pack: $10.32 ÷ 24 = $0.43 per bottle.
  4. 30-pack: $13.80 ÷ 30 = $0.46 per bottle.
  5. The lowest is $0.41, the 18-pack.

Check: 18 × $0.41 = $7.38.

Wrong choices

  • 30 bottles for $13.80: The 30-pack is the biggest, but it costs $0.46 per bottle, the highest of all.
  • 12 bottles for $5.40: The 12-pack has the lowest total price, but it costs $0.45 per bottle.
  • 24 bottles for $10.32: The 24-pack costs $0.43 per bottle, more than the 18-pack.
Practice 5 questions from this unit →

AI-written · Verified · Written by AI. Only units that passed a separate AI check (re-reading facts and numbers) are published. Tell us if you find a mistake.