7th Grade Math Quiz: Multi Step Ratio And Percent Problems

What this quiz covers

This quiz focuses on Multi Step Ratio And Percent Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for 7th Grade Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. 24.25% (correct answer)
2. 22.50%
3. 21.75%
4. 23.25%

Explanation: The automatic gratuity is $240 \times 0.18 =$43.20. Total tip is $43.20 +$15.00 = $58.20. The percent tip is$\frac{58.20}{240} \times 100% = 24.25%$. Choice B results from calculating only 18% + additional tip percentage without considering the automatic gratuity amount. Choice C comes from calculation errors. Choice D results from rounding errors in intermediate steps.

Question 2

1. 36 months
2. 30 months (correct answer)
3. 42 months
4. 33 months

Explanation: The interest earned is 556.25 - 500 = $56.25. Using I = PRT, this gives 56.25 = 500 x 0.045 x T, so T = 56.25 / (500 x 0.045) = 56.25/22.5 = 2.5 years, which is 30 months. Choice A, choice C, and choice D come from arithmetic slips or from using an incorrect rate or time conversion when solving for T.

Question 3

1. 15% increase; her boss is incorrect (correct answer)
2. 12% increase; her boss is correct
3. 13.6% increase; her boss is incorrect
4. 14.2% increase; her boss is incorrect

Explanation: The actual increase is $3,680 -$3,200 = $480. The percent increase is$\frac{480}{3200} \times 100% = 15%$. Her boss is incorrect. Choice B would be correct if the increase were actually$384. Choice C results from calculating $\frac{480}{3680} \times 100\%$ (using new salary as base). Choice D comes from estimation errors in the division.

Question 4

1. $8\%$ (correct answer)
2. $4\%$
3. $7.4\%$
4. $10\%$

Explanation: This problem tests multi-step problems with percents, specifically percent error calculation. Using the given formula: percent error = |estimate - actual|/actual × 100%, we get |54 - 50|/50 × 100% = 4/50 × 100% = 0.08 × 100% = 8%. The percent error is 8%. A common error would be using the estimate in the denominator (4/54 ≈ 7.4%) or forgetting the absolute value (though not relevant here since estimate > actual). Strategy: (1) identify estimate (54g) and actual (50g), (2) find absolute difference |54 - 50| = 4, (3) divide by actual value (4/50 = 0.08), (4) convert to percent (0.08 × 100% = 8%), (5) verify reasonableness (4g error on 50g base is 8%✓). Percent error always uses actual value as the reference.

Question 5

1. $20.20$
2. $21.06$
3. $21.38$ (correct answer)
4. $20.34$

Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount ($8\%$ of $40 = 40 \times 0.08 = 3.20$), increasing by percent (add: $40 + 3.20 = 43.20$, or multiply: $40 \times 1.08 = 43.20$ directly), decreasing (subtract or multiply by complement: $25\%$ off $80 = 80 \times 0.75 = 60$). Multi-step: tax then tip (meal $45$, tax $7\%$: $45 \times 1.07 = 48.15$, tip $20\%$ on total: $48.15 \times 1.20 \approx 57.78$, or combined: $45 \times 1.07 \times 1.20$). Simple interest $I = P r t$ (principal $\times$ rate $\times$ time in years: $1000 \times 0.05 \times 2 = 100$). Percent change: $( \text{new} - \text{old} ) / \text{old} \times 100\%$ ($200 \to 250$: $50 / 200 = 25\%$ increase). For example, an item costs $18$, with $8\%$ tax: $18 \times 0.08 = 1.44$ tax, total $18 + 1.44 = 19.44$; then add $10\%$ donation on total: $19.44 \times 0.10 = 1.944$, altogether $19.44 + 1.944 = 21.384$ or directly $18 \times 1.08 \times 1.10 = 21.384$, rounded to $21.38$. The correct calculation is to first apply the $8\%$ tax to $18$ getting $19.44$, then add $10\%$ of that as donation, totaling $21.38$. A common error is calculating the donation on the pre-tax amount instead of the taxed total, leading to $18 \times 0.10 = 1.80$, then $18 + 1.44 + 1.80 = 21.24$, which is incorrect. Strategy: (1) identify operations needed (tax: multiply by $1 + \text{rate}$, tip: multiply by $1 + \text{rate}$ on appropriate base, interest: $I = P r t$), (2) sequence properly (tax before tip usually, markups before markdowns if both), (3) use decimal form of percents ($8\% = 0.08$, $20\% = 0.20$), (4) multiply for efficiency (increase by $8\%$ then $20\%$: $\times 1.08 \times 1.20$ in one calculation), (5) verify reasonable (total with tax and tip should be ~$30\%$ more than meal: $45 \to \sim 58$ reasonable✓). Common formulas: simple interest $I = P r t$ (interest = principal $\times$ rate decimal $\times$ years), percent change = $( \text{new} - \text{old} ) / \text{old}$ (positive: increase, negative: decrease), percent error = $| \text{estimate} - \text{actual} | / \text{actual}$ (absolute difference over actual). Mistakes: percent as whole number (most common: $\times 8$ not $\times 0.08$), wrong base for sequential percents (compounding error), order wrong (operations applied in wrong sequence), formula errors ($I = P r$ without $t$, or wrong denominator in percent change).

Question 6

1. 3.15%
2. 2.94% (correct answer)
3. 2.85%
4. 3.25%

Explanation: When you see commission problems with changing rates and sales amounts, you need to work systematically through each scenario to find the unknown rate. First, let's verify the January information. With sales of $180,000 and a 3.5% commission rate: $180,000 \times 0.035 = 6,300$. This matches the given commission, so we're on track. Next, calculate February's sales. A 25% increase means: $180,000 \times 1.25 = 225,000$. Now we can find the new commission rate. Since commission equals sales times rate, we have: $225,000 \times \text{rate} = 6,615$. Solving for the rate: $\text{rate} = \frac{6,615}{225,000} = 0.0294 = 2.94\%$. Looking at the wrong answers: Choice A (3.15%) is too high—this would give a February commission of $7,087.50, much more than the actual$6,615. Choice C (2.85%) is too low—this would yield only $6,412.50 in commission. Choice D (3.25$7,312.50 in commission. The correct answer is B (2.94%). Strategy tip: In multi-step percentage problems, always verify your intermediate calculations before moving to the next step. Here, confirming the January numbers helped ensure accuracy, and calculating February sales before finding the rate kept the solution organized and error-free.

Question 7

1. $956.25
2. $900.00
3. $1,023.00
4. $976.50 (correct answer)

Explanation: When you encounter multi-step percent problems involving discounts and taxes, work through them systematically: first apply the discount to find the sale price, then calculate tax on that discounted amount. Start with the 25% markdown. The laptop costs $1,200 \times 0.25 = \$300$ less, so the sale price is $1,200 - 300 = \$900$. Now apply the 8.5% sales tax to this discounted price: $900 \times 0.085 = \$76.50$ in tax. The total amount paid is $900 + 76.50 = \$976.50$. Looking at the wrong answers: Choice A (956.25) represents a common error where students subtract the tax from the sale price instead of adding it ($$900 - 76.50$$). Choice B (900.00) is just the sale price before tax—students who choose this forget to include sales tax entirely. Choice C ($1,023.00) comes from incorrectly applying the 8.5$1,200 price instead of the discounted price, then subtracting the $300 discount afterward. The correct sequence gives you D ($976.50). Study tip: Always remember the order matters in discount and tax problems. Discounts come first, then taxes are calculated on the already-reduced price. Sales tax is never applied to the original price when there's a discount involved. Write out each step clearly to avoid mixing up the sequence.

Question 8

1. $31,200
2. $60,300
3. $28,750
4. $30,150 (correct answer)

Explanation: When you see commission problems, you're working with percentages and multi-step calculations. The key is to organize your work: find the total sales, calculate the commission, then apply any splits or deductions. First, find the total value of homes sold: $320,000 + 275,000 + 410,000 = 1,005,000$. Next, calculate the 6% commission on this total: $1,005,000 × 0.06 = 60,300$. Since she splits this commission equally with her broker, divide by 2: $60,300 ÷ 2 = 30,150$. So she personally earned $30,150. Looking at the wrong answers: Choice A ($31,200) likely comes from incorrectly calculating 6$60,300) is the total commission before splitting with the broker; this represents forgetting the final step of dividing by 2. Choice C ($28,750) might result from calculation errors in either the total sales amount or the percentage calculation, possibly confusing which operations to perform. The correct answer is D ($30,150). Remember this pattern for commission problems: total sales × commission rate = total commission, then apply any splits or deductions. Always read carefully to see if the person keeps the full commission or shares it. Many students forget that final step of splitting the commission, so double-check what the question asks for—total commission earned or the person's actual share.

Question 9

1. 2.90%
2. 2.82%
3. 2.75% (correct answer)
4. 2.65%

Explanation: Percent error questions test your ability to calculate how far off a measurement is from the true value. When you see "percent error," you're looking at the difference between what was measured and what the actual value is, expressed as a percentage of the actual value. To find percent error, use this formula: $\text{Percent Error} = \frac{|\text{Measured Value} - \text{Actual Value}|}{|\text{Actual Value}|} \times 100\%$ Here, the measured value is 24.8 grams and the actual value is 25.5 grams. First, find the absolute difference: $|24.8 - 25.5| = |-0.7| = 0.7$ grams. Then divide by the actual value: $\frac{0.7}{25.5} = 0.02745...$ Finally, convert to a percentage: $0.02745 \times 100\% = 2.745\%$, which rounds to 2.75%. Choice A (2.90%) likely comes from dividing the error by the measured value instead of the actual value: $\frac{0.7}{24.8} \times 100\% = 2.82\%$ then rounding incorrectly. Choice B (2.82%) makes the same mistake but rounds correctly. Choice D (2.65%) might result from calculation errors or using an incorrect formula altogether. Remember that percent error always uses the actual (true) value in the denominator, not the measured value. This is because you want to know how the error compares to what the measurement should have been. Also, always use absolute values since you only care about the size of the error, not its direction.

Question 10

1. $75.00 (correct answer)
2. $60.00
3. $65.50
4. $72.50

Explanation: Let the wholesale cost be $x$. After a 45% markup, the marked price is $1.45x$. After a 20% discount, the sale price is $0.80(1.45x) = 1.16x = 87$. Solving: $x = 87 ÷ 1.16 = 75$. Choice B ($60) would result if you incorrectly calculated the compound effect as 25$65.50) results from applying the discount to the wholesale cost instead of the marked price. Choice D ($72.50) comes from reversing the order of operations.

Question 11

1. $499.40$ (correct answer)
2. $510.00$
3. $500.60$
4. $504.40$

Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of $40$ = $40 \times 0.08 = 3.20$), increasing by percent (add: $40 + 3.20 = 43.20$, or multiply: $40 \times 1.08 = 43.20$ directly), decreasing (subtract or multiply by complement: 25% off $80$ = $80 \times 0.75 = 60$). Multi-step: fees (donations $520$, 3% fee: $520 \times 0.97 = 504.40$ after, then subtract $5$: $504.40 - 5 = 499.40$). For this problem, $520$ minus 3% fee ($520 \times 0.03 = 15.60$, $520 - 15.60 = 504.40$), then minus $5$: $504.40 - 5 = 499.40$. A common error is subtracting fees in wrong order or using 3% as addition instead of deduction, or forgetting the flat fee. Strategy: (1) identify operations needed (percent fee: $\times(1-\text{rate})$, flat fee: subtract), (2) sequence properly (percent then flat), (3) use decimal form of percents (3% = 0.03), (4) calculate step-by-step, (5) verify reasonable (fees total about $20.60$, $520 - 20.60 = 499.40$ yes). Common formulas: percent error = $|\text{estimate} - \text{actual}| / \text{actual} \times 100\%$; mistakes include wrong sequence or percent as whole number.

Question 12

1. \$$45.00
2. \$$47.25 (correct answer)
3. \$$47.50
4. \$$52.50

Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of $40$ = $40 \times 0.08 = 3.20$), increasing by percent (add: $40 + 3.20 = 43.20$, or multiply: $40 \times 1.08 = 43.20$), decreasing (subtract or multiply by complement: 25% off $80$ = $80 \times 0.75 = 60$). Multi-step: tax then tip (meal $45$, tax 7%: $45 \times 1.07 = 48.15$, tip 20% on total: $48.15 \times 1.20 \approx 57.78$, or combined: $45 \times 1.07 \times 1.20$). Simple interest I=Prt (principal×rate×time in years: $1000 \times 0.05 \times 2 = 100$). Percent change: $(new-old)/old \times 100\%$ (200→250: 50/200=25% increase). For example, $50$ item, 10% discount: $50 \times 0.90 = 45$, then 5% fee: $45 \times 1.05 = 47.25$. The correct calculation is 50×0.90=45 discounted, then 45×1.05=47.25 final. A common error is adding the fee before discount, like 50×1.05=52.50, then 52.50×0.90=47.25 (same here, but wrong sequence could differ in other cases). Strategy: (1) identify operations needed (tax: multiply by 1+rate, tip: multiply by 1+rate on appropriate base, interest: I=Prt), (2) sequence properly (tax before tip usually, markups before markdowns if both), (3) use decimal form of percents (8%=0.08, 20%=0.20), (4) multiply for efficiency (increase by 8% then 20%: ×1.08×1.20 in one calculation), (5) verify reasonable (total with tax and tip should be 30% more than meal: $45$→$58 reasonable✓). Common formulas: simple interest I=Prt (interest = principal × rate decimal × years), percent change = (new-old)/old (positive: increase, negative: decrease), percent error = |estimate-actual|/actual (absolute difference over actual). Mistakes: percent as whole number (most common: ×8 not ×0.08), wrong base for sequential percents (compounding error), order wrong (operations applied in wrong sequence), formula errors (I=Pr without t, or wrong denominator in percent change).

Question 13

1. \46.22$ (correct answer)
2. \45.36$
3. \43.20$
4. \46.08$

Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of $40 = 40×0.08=$3.20), increasing by percent (add: $40+$3.20=$43.20, or multiply: 40×1.08=43.20 directly), decreasing (subtract or multiply by complement: 25$80 = 80×0.75=$60). Multi-step: tax then tip (meal$45, tax 7%: 45×1.07=48.15, tip 20% on total: 48.15×1.20≈57.78, or combined: 45×1.07×1.20). For this problem, meal is $36 with 7$46.22). A common error is tipping on pre-tax amount instead of post-tax (tip on 36: 7.20, tax 2.52, total 36+2.52+7.20=45.72, wrong), or adding percents directly (7%+20%=27%, 36×1.27=45.72, ignores compounding). Strategy: (1) identify operations needed (tax: multiply by 1+rate, tip: multiply by 1+rate on appropriate base), (2) sequence properly (tax before tip usually), (3) use decimal form of percents (7%=0.07, 20%=0.20), (4) multiply for efficiency (×1.07×1.20 in one calculation), (5) verify reasonable (total with tax and tip should be ~27% more, but compounded to about 28.4%, $36→$46.22 reasonable). Common formulas: percent change = (new-old)/old×100%; mistakes include wrong base for sequential percents or order wrong.

Question 14

1. \43.20$
2. \46.22$ (correct answer)
3. \45.36$
4. \46.08$

Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of $40 = 40×0.08=$3.20), increasing by percent (add: $40+$3.20=$43.20, or multiply: 40×1.08=43.20 directly), decreasing (subtract or multiply by complement: 25$80 = 80×0.75=$60). Multi-step: tax then tip (meal$45, tax 7%: 45×1.07=48.15, tip 20% on total: 48.15×1.20≈57.78, or combined: 45×1.07×1.20). For this problem, meal is $36 with 7$46.22). A common error is tipping on pre-tax amount instead of post-tax (tip on 36: 7.20, tax 2.52, total 36+2.52+7.20=45.72, wrong), or adding percents directly (7%+20%=27%, 36×1.27=45.72, ignores compounding). Strategy: (1) identify operations needed (tax: multiply by 1+rate, tip: multiply by 1+rate on appropriate base), (2) sequence properly (tax before tip usually), (3) use decimal form of percents (7%=0.07, 20%=0.20), (4) multiply for efficiency (×1.07×1.20 in one calculation), (5) verify reasonable (total with tax and tip should be ~27% more, but compounded to about 28.4%, $36→$46.22 reasonable). Common formulas: percent change = (new-old)/old×100%; mistakes include wrong base for sequential percents or order wrong.

Question 15

1. \504.40$
2. \499.40$ (correct answer)
3. \500.60$
4. \510.00$

Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of $40 = 40×0.08=$3.20), increasing by percent (add: $40+$3.20=$43.20, or multiply: 40×1.08=43.20 directly), decreasing (subtract or multiply by complement: 25$80 = 80×0.75=$60). Multi-step: fees (donations$520, 3% fee: 520×0.97=504.40 after, then subtract $5: 504.40-5=499.40). For this problem,$520 minus 3% fee (520×0.03=15.60, 520-15.60=504.40), then minus $5: 504.40-5=$499.40. A common error is subtracting fees in wrong order or using 3% as addition instead of deduction, or forgetting the flat fee. Strategy: (1) identify operations needed (percent fee: ×(1-rate), flat fee: subtract), (2) sequence properly (percent then flat), (3) use decimal form of percents (3%=0.03), (4) calculate step-by-step, (5) verify reasonable (fees total about $20.60,$520-$20.60=$499.40 yes). Common formulas: percent error = |estimate-actual|/actual×100%; mistakes include wrong sequence or percent as whole number.

Question 16

1. \43.20$
2. \44.22$
3. \46.22$ (correct answer)
4. \45.36$

Explanation: This problem tests multi-step problems with percents, requiring calculation of tax then tip on the after-tax total. First, we calculate the bill with tax: $36.00 × 1.07 =$38.52. Then we calculate the tip on this total: $38.52 × 1.20 =$46.224, which rounds to $46.22. Alternatively, we can combine the multipliers:$36.00 × 1.07 × 1.20 = $46.224. The correct calculation gives us$46.22. A common error would be calculating tip on the pre-tax amount ($36 × 0.20 =$7.20) then adding both tax and tip to the original, which would give a different result. Strategy: (1) apply tax first to get after-tax total, (2) calculate tip on the after-tax amount as specified, (3) use decimal forms (7% = 0.07, 20% = 0.20), (4) multiply efficiently using 1.07 and 1.20, (5) verify reasonableness (roughly 30% more than original: $36 → ~$47 is reasonable✓).

Question 17

1. \6$
2. \460$
3. \20$
4. \60$ (correct answer)

Explanation: This problem tests multi-step problems with percents, specifically simple interest calculation using the formula I = Prt. We have principal P = $400, rate r = 0.05 (5$400 × 0.05 × 3 = $60. The interest earned is$60. A common error would be forgetting to multiply by time (calculating just $400 × 0.05 =$20 for one year) or using the percent as a whole number ($400 × 5 × 3 =$6,000). Strategy: (1) identify the three components: principal ($400), rate (5$400 = $60✓). Simple interest accumulates linearly, not compounded.

Question 18

1. $11.1\%$
2. $6.3\%$
3. $2\%$
4. $12.5\%$ (correct answer)

Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of $40 = 40×0.08=$3.20), increasing by percent (add: $40+$3.20=$43.20, or multiply: 40×1.08=43.20 directly), decreasing (subtract or multiply by complement: 25$80 = 80×0.75=$60). Multi-step: tax then tip (meal$45, tax 7%: 45×1.07=48.15, tip 20% on total: 48.15×1.20≈57.78, or combined: 45×1.07×1.20). Simple interest I=Prt (principal×rate×time in years: $1000×0.05×2=$100). Percent change: (new-old)/old×100% (200→250: 50/200=25% increase). For example, estimate 20 cm, actual 18 cm: |20-18|/18×100%≈11.1%, but note formula uses actual in denominator. The correct calculation is |18-16|/16×100%=2/16×100%=12.5%. A common error is using estimate in denominator: |18-16|/18×100%≈11.1%, or forgetting absolute value and getting negative. Strategy: (1) identify operations needed (tax: multiply by 1+rate, tip: multiply by 1+rate on appropriate base, interest: I=Prt), (2) sequence properly (tax before tip usually, markups before markdowns if both), (3) use decimal form of percents (8%=0.08, 20%=0.20), (4) multiply for efficiency (increase by 8% then 20%: ×1.08×1.20 in one calculation), (5) verify reasonable (total with tax and tip should be ~30% more than meal: $45→~$58 reasonable✓). Common formulas: simple interest I=Prt (interest = principal × rate decimal × years), percent change = (new-old)/old (positive: increase, negative: decrease), percent error = |estimate-actual|/actual (absolute difference over actual). Mistakes: percent as whole number (most common: ×8 not ×0.08), wrong base for sequential percents (compounding error), order wrong (operations applied in wrong sequence), formula errors (I=Pr without t, or wrong denominator in percent change).

Question 19

1. \265$
2. \150$
3. \14$
4. \15$ (correct answer)

Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of $40 = 40×0.08=$3.20), increasing by percent (add: $40+$3.20=$43.20, or multiply: 40×1.08=43.20 directly), decreasing (subtract or multiply by complement: 25$80 = 80×0.75=$60). Multi-step: tax then tip (meal$45, tax 7%: 45×1.07=48.15, tip 20% on total: 48.15×1.20≈57.78, or combined: 45×1.07×1.20). Simple interest I=Prt (principal×rate×time in years: $1000×0.05×2=$100). Percent change: (new-old)/old×100% (200→250: 50/200=25% increase). For example, 6% commission on $200 sales: 200×0.06=12. The correct calculation is 250×0.06=15. A common error is using 6 instead of 0.06, getting 250×6=1500, or adding to sales like 250+15=265. Strategy: (1) identify operations needed (tax: multiply by 1+rate, tip: multiply by 1+rate on appropriate base, interest: I=Prt), (2) sequence properly (tax before tip usually, markups before markdowns if both), (3) use decimal form of percents (8$45→~$58 reasonable✓). Common formulas: simple interest I=Prt (interest = principal × rate decimal × years), percent change = (new-old)/old (positive: increase, negative: decrease), percent error = |estimate-actual|/actual (absolute difference over actual). Mistakes: percent as whole number (most common: ×8 not ×0.08), wrong base for sequential percents (compounding error), order wrong (operations applied in wrong sequence), formula errors (I=Pr without t, or wrong denominator in percent change).

Question 20

1. \10.20$
2. \13.50$
3. \12.15$
4. \13.80$ (correct answer)

Explanation: This question tests multi-step problems with percents, ratios, proportions: tax, tip, markup, markdown, commission, simple interest, percent change, percent error—calculating percent of amounts and combining operations. Percent operations: finding percent of amount (8% of $40 = 40×0.08=$3.20), increasing by percent (add: $40+$3.20=$43.20, or multiply: 40×1.08=43.20 directly), decreasing (subtract or multiply by complement: 25$80 = 80×0.75=$60). Multi-step: tax then tip (meal$45, tax 7%: 45×1.07=48.15, tip 20% on total: 48.15×1.20≈57.78, or combined: 45×1.07×1.20). Simple interest I=Prt (principal×rate×time in years: $1000×0.05×2=$100). Percent change: (new-old)/old×100% (200→250: 50/200=25% increase). For example, $10 price increases by 15$45→~$58 reasonable✓). Common formulas: simple interest I=Prt (interest = principal × rate decimal × years), percent change = (new-old)/old (positive: increase, negative: decrease), percent error = |estimate-actual|/actual (absolute difference over actual). Mistakes: percent as whole number (most common: ×8 not ×0.08), wrong base for sequential percents (compounding error), order wrong (operations applied in wrong sequence), formula errors (I=Pr without t, or wrong denominator in percent change).