GED Math Ratios, Proportions, and Percents Summary

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.

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.

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.

1. Speed = distance ÷ time.
2. 186 ÷ 3 = 62 miles per hour.

Check: 62 × 3 = 186 miles.

Wrong choices

• 558: 558 multiplies distance by time instead of dividing.
• 93: 93 divides by 2 instead of by 3.
• 52: 52 drops a step in the division; 52 × 3 = 156, not 186.

1. Change 7.5% to a decimal: 0.075.
2. Tax: 0.075 × $60.00 = $4.50.
3. Total: $60.00 + $4.50 = $64.50.

Check: $60.00 × 1.075 = $64.50.

Wrong choices

• $4.50: $4.50 is the tax only; it must be added to the price.
• $60.45: $60.45 uses 0.0075 (which is 0.75%) instead of 0.075.
• $55.50: $55.50 subtracts the tax instead of adding it.

1. Each inch on the map is 20 miles.
2. 3.5 × 20 = 70 miles.

Check: 3 inches is 60 miles and half an inch is 10 miles. 60 + 10 = 70 miles.

Wrong choices

• 5.71 miles: 5.71 miles divides 20 by 3.5 instead of multiplying.
• 23.5 miles: 23.5 miles adds 3.5 and 20 instead of multiplying.
• 0.175 miles: 0.175 miles divides 3.5 by 20 instead of multiplying.

1. Coverage per gallon: 1,050 ÷ 3 = 350 square feet.
2. Gallons needed: 1,750 ÷ 350 = 5 gallons.

Check: Set up a proportion: 3/1,050 = x/1,750. Cross-multiply: 1,050x = 5,250, so x = 5.

Wrong choices

• 1.8 gallons: 1.8 gallons flips the proportion (1,050 ÷ 1,750 × 3); the bigger wall must need more paint, not less.
• 3.5 gallons: 3.5 gallons would cover only 3.5 × 350 = 1,225 square feet.
• 6 gallons: 6 gallons would cover 6 × 350 = 2,100 square feet, more than needed.

1. Discount: 25% of $80 = $20. Sale price: $80 − $20 = $60.
2. Tax: 6% of $60 = $3.60.
3. Final cost: $60 + $3.60 = $63.60.

Check: $80 × 0.75 × 1.06 = $63.60.

Wrong choices

• $64.80: $64.80 combines the percents into 19% off the original price; the tax is taken on the sale price, not on $80.
• $60.00: $60.00 is the sale price before tax.
• $84.80: $84.80 adds tax to the original price and forgets the discount.

1. P = $2,500, r = 4% = 0.04, t = 3 years.
2. I = 2,500 × 0.04 × 3.
3. 2,500 × 0.04 = 100; 100 × 3 = $300.

Check: $100 of interest each year for 3 years is $300.

Wrong choices

• $30,000: $30,000 uses 4 instead of 0.04 for the rate.
• $100: $100 is the interest for only one year.
• $2,800: $2,800 is the total she pays back (loan plus interest), not the interest.

1. Commission: 5% of $8,600 = 0.05 × 8,600 = $430.
2. Total pay: $400 + $430 = $830.

Check: 1% of $8,600 is $86, so 5% is 5 × $86 = $430. $430 + $400 = $830.

Wrong choices

• $430: $430 is the commission only; the $400 base pay must be added.
• $4,700: $4,700 uses 0.5 (50%) instead of 0.05 for 5%.
• $9,000: $9,000 adds the base pay to the total sales; she does not earn all of her sales.