Percents — Free Pre-Algebra Review Games.

25% = 0.25, and 0.25 * 80 = 20.

Multiply by 100: 0.45 * 100 = 45%.

3/5 = 0.6 = 60%.

Divide by 100: 8/100 = 0.08.

10/50 = 0.2 = 20%.

Discount = 0.15 * 40 = $6. Sale price = $40 - $6 = $34.

Change = 10, percent = 10/50 = 0.2 = 20%.

0.30 * x = 24, so x = 24/0.30 = 80.

Tax = 0.06 * 25 = $1.50. Total = $25 + $1.50 = $26.50.

150% = 1.5, and 1.5 * 40 = 60.

Change = 1200, percent = 1200/8000 = 0.15 = 15%.

$56 = 80% of original. 56/0.80 = $70.

Sale: 200 * 0.90 = $180. Tax: 180 * 1.05 = $189.

Start at 100: 100 * 1.25 = 125, then 125 * 0.80 = 100. Net change is 0%.

Simple interest = P*r*t = 500 * 0.04 * 3 = $60.

To convert a fraction to a percent, multiply by \(100\), so \(\frac{7}{20} \times 100 = 35\%\). The choice \(7\%\) wrongly treats the numerator alone as the percent, ignoring the denominator entirely. Always remember that converting a fraction to a percent means finding its decimal equivalent first, then scaling by \(100\).

Multiplying a decimal by \(100\) shifts the decimal point two places right, so \(1.2 \times 100 = 120\%\). The distractor \(12\%\) mistakenly shifts the decimal only one place instead of two. Remember that percents greater than \(100\%\) correspond to decimals greater than \(1\).

Finding \(10\%\) of a number means multiplying by \(0.10\), so \(250 \times 0.10 = 25\). The choice \(10\) ignores the base number and just restates the percent value itself. A quick trick for \(10\%\) is to move the decimal point one place left in the original number.

Dividing the numerator by the denominator gives \(3 \div 4 = 0.75\), which is the decimal equivalent of the fraction. The distractor \(0.34\) confuses the fraction's digits with a decimal instead of actually performing the division. Always divide numerator by denominator to convert a fraction to a decimal.

To find what percent one number is of another, divide the part by the whole and multiply by \(100\): \(\frac{50}{200} \times 100 = 25\%\). The distractor \(50\%\) incorrectly assumes the part equals half of the whole without doing the actual division. This part-over-whole method works for any percent-of question.

Writing \(60\%\) as \(\frac{60}{100}\) and simplifying by dividing both terms by \(20\) gives \(\frac{3}{5}\). The choice \(\frac{6}{10}\) is a correct equivalent but not in simplest form, which the question specifically requires. Always reduce percent-to-fraction conversions to lowest terms unless told otherwise.

Since \(50\%\) equals one half, taking half of \(84\) gives \(42\). The distractor \(50\) mistakenly treats the percent value as the answer rather than applying it to the number. Recognizing \(50\%\) as a simple half-split can speed up mental math on the exam.

To convert a percent to a decimal, divide by \(100\), which moves the decimal point two places left, turning \(9\%\) into \(0.09\). The choice \(0.9\) moves the decimal only one place, a common error when converting single-digit percents. Always check that a percent under \(10\%\) becomes a decimal beginning with two zeros after the point.

Multiplying \(16\) by \(0.75\) gives \(12\), since \(75\%\) is equivalent to \(\frac{3}{4}\). The distractor \(4\) incorrectly calculates only \(25\%\) of the number instead of \(75\%\). Converting familiar percents like \(75\%\) to fractions can make mental calculations faster.

Any number divided by itself equals \(1\), and \(1 \times 100 = 100\%\), so \(40\) is \(100\%\) of \(40\). The distractor \(40\%\) confuses the given number with the percent value itself. Remember that a quantity is always \(100\%\) of itself.

Dividing \(1\) by \(8\) gives \(0.125\), and multiplying by \(100\) converts this to \(12.5\%\). The distractor \(8\%\) mistakenly uses the denominator as the percent instead of performing the division. This conversion process (divide then multiply by \(100\)) works for any fraction.

The discount amount is found by multiplying the original price by the discount rate: \(80 \times 0.25 = 20\). The distractor \(\\)60$ is actually the sale price after the discount, not the discount amount itself. Be careful to distinguish between the amount taken off and the final price remaining.

The discount amount is \(120 - 90 = 30\), and dividing this by the original price gives \(\frac{30}{120} = 0.25\), or \(25\%\). The distractor \(30\%\) mistakenly uses the dollar discount amount as the percent instead of dividing by the original price. Percent change always requires dividing the change by the original, not just reading off the raw difference.

The tax amount is \(60 \times 0.08 = 4.80\), and adding this to the original bill gives \(60 + 4.80 = \\)64.80$. The distractor \(\\)60.08$ incorrectly appends the tax percent as a decimal amount rather than calculating and adding the actual tax. Always compute the tax separately as a percentage of the pre-tax total before adding.

To find the whole when given a part and percent, divide the part by the decimal form of the percent: \(45 \div 0.18 = 250\). The distractor \(81\) results from multiplying instead of dividing, a common inversion error. Whenever solving for the whole, isolate it by dividing the known part by the percent's decimal equivalent.

The increase is \(46{,}000 - 40{,}000 = 6{,}000\), and dividing by the original salary gives \(\frac{6000}{40000} = 0.15\), or \(15\%\). The distractor \(6\%\) mistakes the raw dollar increase's leading digit for the percent without dividing by the original value. Percent increase always compares the change to the original amount, never to the new amount.

The discount amount is \(45 \times 0.20 = 9\), and subtracting from the original price gives \(45 - 9 = \\)36$. The distractor \(\\)9$ is only the discount amount, not the actual sale price after the discount is applied. Always subtract the discount from the original price to find the final cost.

Dividing \(1\) by \(3\) produces the repeating decimal \(0.3333...\), and multiplying by \(100\) rounds to \(33.3\%\). The distractor \(30\%\) rounds too aggressively and loses the repeating decimal precision required by the question. Repeating decimals should be carried out at least to the requested rounding place before converting.

The tax amount is found by multiplying the price by the tax rate: \(150 \times 0.07 = 10.50\). The distractor \(\\)7.00$ mistakenly uses the tax rate's numeral as a dollar figure rather than calculating it as a percentage of the price. Tax is always a percentage applied to the pre-tax price, not a flat dollar amount matching the rate.

The increase is \(650 - 500 = 150\), and dividing by the original population gives \(\frac{150}{500} = 0.30\), or \(30\%\). The distractor \(25\%\) likely comes from dividing the increase by the new value instead of the original, a frequent mistake. Percent change formulas always use the original quantity as the denominator.

Multiplying \(75\) by \(1.20\) gives \(90\), since percents over \(100\%\) represent values greater than the original. The distractor \(75\) ignores the percent altogether and just restates the base number. Whenever a percent exceeds \(100\%\), the result must be larger than the original number.

The markup amount is \(25 \times 0.40 = 10\), and adding this to the original price gives \(25 + 10 = \\)35$. The distractor \(\\)15$ incorrectly subtracts the markup as if it were a discount rather than adding it. A markup increases price, while a discount decreases it, so always check the direction of the change.

Dividing the absent students by the total class size gives \(\frac{8}{32} = 0.25\), which converts to \(25\%\). The distractor \(8\%\) mistakenly uses the raw count of absent students as the percent without dividing by the total. Percent-of problems always require the part divided by the whole, expressed as a percent.

Dividing the discount amount by the original price gives \(\frac{15}{60} = 0.25\), or \(25\%\). The distractor \(15\%\) confuses the dollar amount of the discount with the percent discount itself. To convert a dollar discount into a percent, always divide by the original price, not the sale price.

The decrease is \(90 - 72 = 18\), and dividing by the original price gives \(\frac{18}{90} = 0.20\), or \(20\%\). The distractor \(18\%\) mistakes the raw dollar decrease for the percent without dividing by the original price. Always divide the amount of change by the starting value to find a true percent decrease.

The tax amount is \(34.56 - 32 = 2.56\), and dividing by the pre-tax price gives \(\frac{2.56}{32} = 0.08\), or \(8\%\). The distractor \(2.56\%\) mistakes the dollar amount of tax for the percent rate itself. To find a tax rate, always divide the tax charged by the original pre-tax price.

The discount amount is \(500 - 425 = 75\), and dividing by the original price gives \(\frac{75}{500} = 0.15\), or \(15\%\). The distractor \(85\%\) actually represents the percent of the original price remaining, not the percent discounted. Distinguish carefully between the percent taken off and the percent of price retained.

Multiplying the total students by the decimal form of the percent gives \(400 \times 0.65 = 260\). The distractor \(335\) likely comes from finding those who do not walk, a subtraction rather than the percent-of calculation requested. Percent-of-a-number problems always multiply the whole by the decimal equivalent of the percent.

The growth amount is \(800 \times 0.12 = 96\), and adding this to the original value gives \(800 + 96 = \\)896$. The distractor \(\\)812$ mistakenly adds only \(12\) dollars instead of \(12\%\) of the investment. Always calculate the percent of the original amount before adding it as growth.

The profit is \(150 - 120 = 30\), and dividing by the cost price gives \(\frac{30}{120} = 0.25\), or \(25\%\). The distractor \(20\%\) results from dividing the profit by the selling price instead of the cost price, giving a different ratio. Profit percent is conventionally measured relative to the original cost, not the final selling price.

After the first discount, the price is \(500 \times 0.90 = 450\), and applying the second \(10\%\) discount to this new price gives \(450 \times 0.90 = 405\). The distractor \(\\)400$ incorrectly assumes the two \(10\%\) discounts simply combine into a flat \(20\%\) off the original price. Successive percent discounts must always be applied one after another to the most recent price, not summed and applied once.

If the original price is \(P\), raising it \(30\%\) gives \(1.3P\), and then lowering that by \(30\%\) gives \(1.3P \times 0.70 = 0.91P\), which is a \(9\%\) decrease from the original. The distractor 'No change' assumes equal opposite percents cancel out, but they apply to different base amounts. Successive percent changes of equal magnitude but opposite direction never fully cancel because the base amount changes between steps.

Since the total equals the pre-tax price times \(1.15\), dividing gives \(92 \div 1.15 = \\)80$. The distractor \(\\)78.20$ comes from mistakenly subtracting \(15\%\) of the total instead of dividing to reverse the tax calculation. To reverse a tax or markup, always divide by \((1 + \text{rate})\) rather than subtracting a percent of the final amount.

Starting with revenue \(R\), a \(40\%\) decrease gives \(0.60R\), and a subsequent \(40\%\) increase on that gives \(0.60R \times 1.40 = 0.84R\), a net \(16\%\) decrease. The distractor 'No change' incorrectly assumes the percent decrease and increase apply to the same base and thus cancel exactly. This example reinforces that percent decreases followed by equal percent increases never return to the original value.

The discounted price is \(50 \times 0.80 = 40\), and applying the \(6\%\) tax to this discounted price gives \(40 \times 1.06 = \\)42.40$. The distractor \(\\)47.00$ incorrectly applies the \(6\%\) tax to the original price instead of the already-discounted price. Always apply tax after discounts to the current, reduced price, not the original price.

After one year, the value is \(20000 \times 0.85 = 17000\), and after the second year it becomes \(17000 \times 0.85 = 14450\). The distractor \(\\)14{,}000$ mistakenly applies a flat \(30\%\) total decrease to the original value instead of compounding the depreciation year by year. Repeated percent decreases must be applied successively to the most recent value, not combined into one flat percentage.

Since \(60\) represents \(75\%\) of the original price after a \(25\%\) discount, dividing gives \(60 \div 0.75 = \\)80$. The distractor \(\\)75$ incorrectly assumes the discount amount itself was \(\\)25$ rather than \(25\%\) of the unknown original price. To reverse a discount, divide the sale price by \((1 - \text{discount rate})\), never by the discount percent alone.

Multiplying \(100 \times 0.70 \times 1.30 = 91\) and \(100 \times 1.30 \times 0.70 = 91\) shows both orders produce the same final result because multiplication is commutative regardless of sequence. The distractor 'It cannot be determined' overlooks that the two operations are simple multiplicative factors that always yield the same product no matter the order applied. A key insight is that sequential percent multipliers commute, so the order of applying a percent increase and decrease does not affect the final value.

Working backward, the discounted price before tax is \(68 \div 1.06 \approx 64.15\), and dividing that by \(0.85\) to reverse the discount gives \(64.15 \div 0.85 \approx \\)75.47$. The distractor \(\\)64.15$ stops after reversing only the tax and forgets to also reverse the discount step. Reversing combined percent operations requires undoing each step in the opposite order it was applied.

After year one the fee is \(300 \times 1.10 = 330\), and after year two it becomes \(330 \times 1.10 = 363\), a total increase of \(\frac{363-300}{300} = 21\%\). The distractor \(20\%\) assumes the two \(10\%\) increases simply add together instead of compounding on each other. Compound percent increases always yield slightly more than the sum of the individual percents.

Since \(45\) represents \(75\%\) of the original listed price, dividing gives \(45 \div 0.75 = \\)60$. The distractor \(\\)56.25$ comes from incorrectly adding \(25\%\) of the sale price to itself instead of dividing by the remaining percentage. To find an original price from a discounted price, always divide by \((1 - \text{discount rate})\).

If the portfolio starts at value \(P\) and drops to \(0.5P\), it must double back to \(P\), which requires a \(100\%\) increase from the reduced value. The distractor \(50\%\) mistakenly assumes the recovery percent matches the loss percent, ignoring that the base for the increase is now smaller. Recovering from a percent loss always requires a larger percent gain because the base value has shrunk.

The marked-up price is \(40 \times 1.50 = 60\), and applying the \(50\%\) discount to this new price gives \(60 \times 0.50 = \\)30$. The distractor \(\\)40$ incorrectly assumes the equal-percent markup and discount cancel exactly and return to the original price. Equal percent increases and decreases never fully offset because each is calculated on a different base value.

Compounding the growth over three years gives \(10000 \times 1.08 \times 1.08 \times 1.08 \approx 12{,}597\), since each year's growth is calculated on the previous year's already-grown value. The distractor \(12{,}400\) likely results from simply tripling the \(8\%\) rate and applying it once, ignoring compounding effects. Repeated percent growth compounds multiplicatively across periods rather than adding up as simple percentages.

Subtracting the flat discount first gives \(150 - 20 = 130\), and then applying the \(10\%\) discount to this reduced amount gives \(130 \times 0.90 = \\)117$. The distractor \(\\)115$ likely comes from applying the \(10\%\) discount to the original price instead of the price after the flat discount was already subtracted. When combining a flat discount with a percent discount, always apply them in the given order to the running price, not independently to the original.