To evaluate the expression 3 5 + 1 5 ÷ 1 2, we will follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here are the steps:
- Convert Mixed Numbers to Improper Fractions:
- The mixed number 3 5 can be converted to an improper fraction. This involves multiplying the whole number (3) by the denominator (5), then adding the numerator (5). This gives us:
3 5 = (3 × 5 + 5)/5 = (15 + 5)/5 = 20/5 = 4.
So, 3 5 = 4. - The mixed number 1 5 converts to:
1 5 = (1 × 5 + 1)/5 = (5 + 1)/5 = 6/5. - Rewrite the Expression: Now the expression looks like this:
4 + (6/5) ÷ (1/2) - Perform Division: We need to divide 6/5 by 1/2. Dividing fractions involves multiplying by the reciprocal:
(6/5) ÷ (1/2) = (6/5) × (2/1) = 12/5. - Add the Results: Now, we add 4 (which we can write as 20/5 to have a common denominator) to 12/5:
20/5 + 12/5 = (20 + 12)/5 = 32/5.
The final result expressed as a mixed number is:
32/5 = 6 2/5.
Therefore, the answer to the expression 3 5 + 1 5 ÷ 1 2 is: