Mixed Operations with Fractions and Decimals

Fractions and decimals stand together inside one expression. Three kinds of Calculation appear: expressions that only turn the decimal into a fraction and multiply, expressions mixing multiplication and division without parentheses, and expressions clearing what is inside the parentheses first, and the converted fractions are carried to the end.

At the point of turning a decimal into a fraction, a rewriting happens that puts the denominator at ten although two places stand below the point. Write 0.75 as 75 over 10 and it is ten times the original decimal. Divide the numerator of the converted fraction by its denominator, and a clean return to the first decimal means the denominator was taken correctly.

Settling the order runs as it did in Mixed Operations with Fractions, with one step, turning a decimal into a fraction, laid on top. That conversion also tells in Ratio Values and Simplifying Ratios, where a decimal ratio is matched into a whole-number ratio.