Simplify 2 1/2 + 2 2/3 ÷ 2 1/3 - Order of Operations with Mixed Numbers

Published on September 27, 2026

Pre-Algebra

Learn how to evaluate the expression 2 1/2 + 2 2/3 ÷ 2 1/3 by converting mixed numbers to improper fractions, applying the order of operations to divide first, and then adding the fractions.

Question

Answer

To solve the expression

, follow the order of operations (division before addition).

Step 1: Convert the mixed numbers to improper fractions

The expression becomes:

Step 2: Perform the division
To divide fractions, multiply by the reciprocal of the divisor:

The expression now is:

Step 3: Perform the addition
Find a common denominator, which is

Step 4: Convert to a mixed number

Final Answer:

Theorems

• Order of Operations

A rule that specifies the sequence in which calculations should be performed, prioritizing division and multiplication before addition and subtraction:

• Fraction Division

To divide one fraction by another, multiply the first fraction by the reciprocal of the second:

• Fraction Addition

To add two fractions, find a common denominator so their numerators can be combined:

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