Fractions, Decimals & Percents Cheat Sheet

A printable reference covering fraction operations, decimal place value, percent conversions, equivalent forms, and comparison strategies for grades 4-6.

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Fractions, decimals, and percents are three ways to describe parts of a whole. Students need this cheat sheet because the same value can look different, such as $\frac{3}{4}$ , $0.75$ , and $75\%$ . These skills are used in measurement, money, data, recipes, and word problems. A clear reference helps students choose the right operation and convert between forms accurately. The most important ideas are equivalent values, place value, and using common denominators. A percent means a number out of $100$ , so $p\% = \frac{p}{100}$ . Decimals use place values such as tenths, hundredths, and thousandths. Fractions can be compared, added, subtracted, multiplied, and divided by following specific rules.

Key Facts

A fraction $\frac{a}{b}$ means $a$ parts out of $b$ equal parts, where $b \neq 0$ .
Equivalent fractions are made by multiplying or dividing the numerator and denominator by the same nonzero number: $\frac{a}{b} = \frac{a \times n}{b \times n}$ .
To add or subtract fractions with the same denominator, add or subtract only the numerators: $\frac{a}{b} + \frac{c}{b} = \frac{a+c}{b}$ .
To add or subtract fractions with different denominators, first rewrite them with a common denominator, such as $\frac{a}{b} + \frac{c}{d} = \frac{ad+bc}{bd}$ .
To multiply fractions, multiply across: $\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$ .
To divide fractions, multiply by the reciprocal: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$ , where $c \neq 0$ and $d \neq 0$ .
To convert a percent to a fraction, use $p\% = \frac{p}{100}$ , and to convert a decimal to a percent, multiply by $100$ and add $\%$ .
To compare fractions, decimals, and percents, convert them to the same form, such as changing $\frac{1}{2}$ , $0.5$ , and $50\%$ to matching values.

Vocabulary

Fraction: A number in the form $\frac{a}{b}$ that shows part of a whole or part of a set.
Numerator: The top number in a fraction that tells how many parts are being counted.
Denominator: The bottom number in a fraction that tells how many equal parts make one whole.
Decimal: A number written with a decimal point to show parts based on powers of $10$ , such as tenths or hundredths.
Percent: A number that means parts per $100$ , written with the symbol $\%$ .
Equivalent Forms: Different-looking numbers that have the same value, such as $\frac{1}{4}$ , $0.25$ , and $25\%$ .

Common Mistakes to Avoid

Adding denominators, such as writing $\frac{1}{4} + \frac{2}{4} = \frac{3}{8}$ , is wrong because the denominator names the size of the parts and stays $4$ when the parts are the same size.
Comparing fractions by only looking at numerators is wrong because $\frac{3}{8}$ is less than $\frac{2}{3}$ even though $3$ is greater than $2$ .
Moving the decimal the wrong direction when converting to percent gives the wrong value because $0.6 = 60\%$ , not $6\%$ .
Forgetting to use a common denominator before adding unlike fractions is wrong because $\frac{1}{2} + \frac{1}{3}$ cannot be added as $\frac{2}{5}$ .
Dividing fractions without using the reciprocal is wrong because $\frac{3}{4} \div \frac{1}{2}$ means how many halves fit in $\frac{3}{4}$ , so it becomes $\frac{3}{4} \times \frac{2}{1}$ .

Practice Questions

1 Convert $\frac{3}{5}$ to a decimal and a percent.
2 Find $\frac{2}{3} + \frac{1}{6}$ and write the answer in simplest form.
3 Order $0.4$ , $45\%$ , and $\frac{2}{5}$ from least to greatest.
4 Explain why $\frac{1}{2}$ , $0.50$ , and $50\%$ represent the same amount.

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