Math Problem Statement

Add. Simplify the answer and write the answer as a mixed number if appropriate: 1/9 + 5/6.

Solution

The problem is asking to add 19+56\frac{1}{9} + \frac{5}{6}, simplify the result, and express it as a mixed number if appropriate.

Step 1: Find a common denominator.

The least common denominator (LCD) of 9 and 6 is 18.

  • Convert 19\frac{1}{9} to a fraction with denominator 18: 19=218\frac{1}{9} = \frac{2}{18}

  • Convert 56\frac{5}{6} to a fraction with denominator 18: 56=1518\frac{5}{6} = \frac{15}{18}

Step 2: Add the fractions.

Now that both fractions have the same denominator, we can add them: 218+1518=1718\frac{2}{18} + \frac{15}{18} = \frac{17}{18}

Step 3: Check if the result can be simplified or written as a mixed number.

The fraction 1718\frac{17}{18} is already in its simplest form and cannot be converted into a mixed number, as the numerator is less than the denominator.

Final Answer:

The sum is 1718\frac{17}{18}, so the correct option is the first one: 1718\frac{17}{18}.

Would you like any further details on the steps? Here are some follow-up questions:

  1. How do you find the least common denominator (LCD)?
  2. Why is 1718\frac{17}{18} in its simplest form?
  3. What is the process for converting improper fractions into mixed numbers?
  4. Can 56\frac{5}{6} be simplified before adding it to 19\frac{1}{9}?
  5. What are the rules for adding fractions with different denominators?

Tip: Always simplify fractions before finalizing your answer—it makes calculations easier!

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Math Problem Analysis

Mathematical Concepts

Addition of Fractions
Least Common Denominator (LCD)
Simplification

Formulas

LCD of two fractions: LCD(a, b)
Adding fractions: (a/b) + (c/d) = (ad + bc) / bd

Theorems

Simplification of fractions

Suitable Grade Level

Grade 6-8