Fractions, Decimals & Percents formulas

All 16 formulas in this topic

Adding Fractionsab+cd=ad+bcbd\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}Add fractions with different denominators by finding a common denominator, then combining the numerators to get your answer.Subtracting Fractionsab−cd=ad−bcbd\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}Subtracting fractions with different denominators requires a common denominator to combine the numerators into a single fraction.Multiplying Fractionsab⋅cd=acbd\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}Multiplying fractions gives you a single fraction when you multiply two fractions together, used whenever you need part of a part.Dividing Fractionsab÷cd=ab⋅dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}Dividing fractions means flipping the second fraction and multiplying instead — it lets you split quantities into equal groups.Simplifying Fractionsab=a÷gcd⁡(a,b)b÷gcd⁡(a,b)\frac{a}{b} = \frac{a \div \gcd(a,b)}{b \div \gcd(a,b)}Simplifying Fractions reduces a fraction to lowest terms by dividing the numerator and denominator by their greatest common factor.Equivalent Fractionsab=akbk,k≠0\frac{a}{b} = \frac{ak}{bk}, \quad k \neq 0Multiply or divide both parts of a fraction by the same non-zero number to create an equivalent fraction with the same value.Comparing Fractionsab>cd  ⟺  ad>bc(b,d>0)\frac{a}{b} > \frac{c}{d} \iff ad > bc \quad (b, d > 0)Compare two fractions to find which is larger or smaller without finding a common denominator—use when you need a quick size comparison.Mixed Number to Improper Fractionwab=wb+abw\frac{a}{b} = \frac{wb + a}{b}Convert a mixed number into an improper fraction so you can multiply, divide, or compare it with other fractions in calculations.Reciprocalab⋅ba=1\frac{a}{b} \cdot \frac{b}{a} = 1A reciprocal flips a fraction—multiply a number by its reciprocal and you always get 1, helping you solve fraction equations.Complex Fractions;ab;cd=adbc\frac{;\frac{a}{b};}{\frac{c}{d}} = \frac{ad}{bc}Learn to simplify complex fractions where the numerator and denominator are themselves fractions using the multiply-by-reciprocal rule.Fraction to Decimalab=a÷b\frac{a}{b} = a \div bConvert a fraction to its decimal form by dividing the numerator by the denominator, useful for comparing fractions directly.Repeating Decimal to Fraction0.d1⋯dn‾=d1⋯dn10n−10.\overline{d_1 \cdots d_n} = \frac{d_1 \cdots d_n}{10^n - 1}Convert repeating decimals to fractions when you need to express infinite decimals like 0.333... as exact fractions for calculation and comparison.Fraction to Percentp%=ab×100%p\% = \frac{a}{b} \times 100\%Converting a fraction to a percentage tells you what proportion out of 100 you represent, making it easier to compare quantities on a standard scale.Percent Change% change=new−oldold×100%\%\,\text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100\%Percent change calculates how much a quantity has increased or decreased, expressed as a percentage of its original value.Percent Error% error=∣measured−actualactual∣×100%\%\,\text{error} = \left| \frac{\text{measured} - \text{actual}}{\text{actual}} \right| \times 100\%Percent Error measures how far off a measurement is from the true value, as a percentage — use it to check accuracy of lab work or approximations.Simple InterestI=PrtI = PrtSimple Interest calculates the total earnings or charges on borrowed or invested money using principal, rate, and time, without compounding effects.

Other topics