Fractions, decimals, and percents for the GED

Three ways to write the same amount

One half can be written as 1/2, 0.5, or 50%. A percent means “per hundred,” so 50% is 50 out of 100. Switching forms quickly lets you use whichever is easiest for the problem in front of you, and it helps you compare answer choices written in different forms.

A few equivalents are worth memorizing because they come up often: 1/4 = 0.25 = 25%, 1/5 = 0.2 = 20%, 1/8 = 0.125 = 12.5%, 3/4 = 0.75 = 75%, and 1/3 ≈ 0.333, or 33 1/3%.

• Fraction to decimal: divide the top by the bottom. 3/8 = 3 ÷ 8 = 0.375.
• Decimal to percent: move the decimal point two places right. 0.375 = 37.5%.
• Percent to decimal: move the decimal point two places left. 6% = 0.06, not 0.6.
• Decimal to fraction: read the place value, then simplify. 0.45 = 45/100 = 9/20.
• Percent to fraction: write it over 100 and simplify. 120% = 120/100 = 6/5.

Working with fractions

To add or subtract fractions, you need a common denominator. Find the least common multiple of the denominators, rewrite each fraction, then add or subtract the numerators. Turn mixed numbers into improper fractions first: 2 3/4 = 11/4.

To multiply fractions, multiply the tops and multiply the bottoms. To divide, keep the first fraction, flip the second, and multiply. Canceling a common factor from a top and a bottom before you multiply keeps the numbers small.

Decimals and place value

Decimal mistakes almost always come from a misplaced decimal point. When adding or subtracting, line up the decimal points and fill empty places with zeros: 12.5 − 3.75 becomes 12.50 − 3.75 = 8.75.

When multiplying, ignore the decimal points, multiply, then count the total number of decimal places in both factors and place the point that many places from the right. For 0.6 × 0.04, multiply 6 × 4 = 24, then count three places to get 0.024. When dividing by a decimal, move the point in both numbers the same number of places until the divisor is a whole number: 7.2 ÷ 0.3 becomes 72 ÷ 3 = 24.

To compare decimals, compare place by place from the left. 0.6 is greater than 0.58 because 6 tenths is more than 5 tenths, even though 58 looks larger than 6. Adding a zero makes it clear: 0.60 versus 0.58.

Solving percent problems

Nearly every percent problem has three parts: the part, the whole, and the percent. The relationship is part = percent × whole. If you know any two, you can find the third. Writing the problem as a short equation keeps you from guessing whether to multiply or divide.

For mental math, start from 10%. Moving the decimal point one place left gives 10%, half of that is 5%, and you can combine them. A 15% tip on $46 is $4.60 + $2.30 = $6.90.

• Find the part: what is 18% of $250? 0.18 × 250 = $45.
• Find the percent: 27 is what percent of 60? 27 ÷ 60 = 0.45, so 45%.
• Find the whole: 36 is 15% of what number? 36 ÷ 0.15 = 240.

Common traps and quick checks

Estimation is the best check. If you need 3/8 of a $96 bill, the answer must be less than half, or $48 (it is $36). If a 6% tax on $40 comes out to $24, the decimal point is in the wrong place; the tax is $2.40.

• Treating 0.5% as 0.5. Half a percent is 0.005 as a decimal.
• Adding fractions by adding tops and bottoms: 1/3 + 1/4 is 7/12, not 2/7.
• Combining two discounts by adding them: 20% off and then 10% off is 28% off, not 30%.
• Forgetting that percents can exceed 100: a price that doubles has risen by 100% and is 200% of the original.
• Leaving an answer in a different form from the choices, such as a decimal when every choice is a fraction.