Adding and Subtracting Fractions and Decimals

If every value converts to an exact decimal, converting to decimals is usually faster. If any fraction produces a repeating decimal, such as one third or one seventh, the decimal method requires rounding. Converting everything to fractions instead gives an exact answer. Choose the method that avoids approximation.

Fractions and decimals are two ways of writing the same value. Whether you convert three fifths to 0.6 or convert 0.75 to three quarters, the underlying amounts stay equal. The final answer is the same regardless of which form you choose.

Some fractions, such as one third and one seventh, produce long repeating decimals that cannot be written exactly. If you round these decimals before calculating, your answer will only be an approximation. Converting to fractions instead avoids this rounding problem entirely.

When an expression contains decimals you can combine in one step, simplify those first. This reduces the number of conversions you need to make. For example, subtracting 0.3 from 0.55 gives 0.25, leaving a simpler expression to convert and solve.

A common denominator is a shared denominator that lets you add or subtract fractions directly. You find it by identifying the lowest common multiple of the denominators. Then you convert each fraction so both share that denominator before you calculate.