What Is the Order of Operations With Fractions?

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When dealing with fractions, the order of operations states that multiplication or division is performed first, moving from left to right, and is followed by addition or subtraction, also moving from left to right. Although addition and subtraction are the basic building blocks of arithmetic operations, they are used only after multiplication or division when solving fractions and other types of expressions.

The general rule of the order of operations holds true for most equations, provided they contain real numbers. With fractional equations, multiplication and division may be required to solve the problem. In that case, multiplication is performed first and is then followed by division. Similarly, addition and subtraction may be needed to balance an equation. With more complex mathematical expressions, the general rule governing the order of operations may change. When using expressions with exponents, for instance, the exponents precede multiplication and division in the order of operations. The same rule is true for equations with square roots.

When using the order of operations, it is generally helpful to organize symbols by grouping. Grouping symbols include parentheses, brackets, fraction bars and braces. Using grouping symbols to solve equations is common when dealing with long and complex equations. It is also frequently employed in certain mathematics disciplines, such as algebra.