Order of Operations with Fractions
Fractions with denominators up to 12. Every answer is given in lowest terms.
The same order, with fractions
Grouping first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. With fractions, students also have to find common denominators and simplify, so problems are shorter: two or three operations.
Dividing by a fraction means multiplying by its reciprocal. The answer key writes the division step and its simplified result; it does not show the common-denominator working.
Worked examples
- 12 × 3 + (13 + 56) = 83
- Parentheses: 1⁄3 + 5⁄6 = 7⁄612 × 3 + 76
- Multiply: 1⁄2 × 3 = 3⁄232 + 76
- Add: 3⁄2 + 7⁄6 = 8⁄383
- (2 − 14) × 34 = 2116
- Parentheses: 2 − 1⁄4 = 7⁄474 × 34
- Multiply: 7⁄4 × 3⁄4 = 21⁄162116
Two more, answers only
- 110 ÷ (35 + 34) = 227
- (14 ÷ 78) × 23 = 421
More worksheets
Questions
Are fraction answers simplified?
Yes. Every result in the key, including the steps, is in lowest terms. Whole-number results are written as whole numbers.
How big do the denominators get?
Fractions on the sheet have denominators of 12 or less. Answers and in-between results stay at or below 72, so common denominators can be found by hand.
What can I do for free?
Make 3 new worksheets a day with up to 20 problems each, print them, save them as PDF or download them as HTML. Free sheets carry a small footer line, and the answer key shows every final answer plus step-by-step work for the first 3 problems. No account is needed.
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