Math Problem Statement

Work out 1 5/6 + 1 2/9. Give your answer as a mixed number in its lowest terms.

Solution

We are asked to solve 156+1291 \frac{5}{6} + 1 \frac{2}{9} and express the answer as a mixed number in its lowest terms.

Step 1: Convert the mixed numbers to improper fractions.

  1. 1561 \frac{5}{6}: 156=6×1+56=1161 \frac{5}{6} = \frac{6 \times 1 + 5}{6} = \frac{11}{6}

  2. 1291 \frac{2}{9}: 129=9×1+29=1191 \frac{2}{9} = \frac{9 \times 1 + 2}{9} = \frac{11}{9}

Step 2: Find a common denominator.

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

Convert the fractions to have the same denominator:

116=11×36×3=3318\frac{11}{6} = \frac{11 \times 3}{6 \times 3} = \frac{33}{18} 119=11×29×2=2218\frac{11}{9} = \frac{11 \times 2}{9 \times 2} = \frac{22}{18}

Step 3: Add the fractions.

Now, add the fractions: 3318+2218=33+2218=5518\frac{33}{18} + \frac{22}{18} = \frac{33 + 22}{18} = \frac{55}{18}

Step 4: Convert the improper fraction to a mixed number.

Divide 55 by 18: 55÷18=3 remainder 155 \div 18 = 3 \text{ remainder } 1

So, 5518=3118\frac{55}{18} = 3 \frac{1}{18}.

Thus, the answer is 31183 \frac{1}{18}, already in its lowest terms.

Would you like further details on any part of the solution?

Here are some related questions:

  1. How do you find the least common denominator?
  2. How do you convert a mixed number to an improper fraction?
  3. How do you simplify improper fractions?
  4. How do you convert improper fractions to mixed numbers?
  5. How can you check if your mixed number is in its lowest terms?

Tip: Always ensure that fractions are simplified by finding the greatest common divisor (GCD) of the numerator and denominator.

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Math Problem Analysis

Mathematical Concepts

Fractions
Mixed Numbers
Improper Fractions
Least Common Denominator

Formulas

Conversion of mixed number to improper fraction: a b/c = (c * a + b) / c
Finding the least common denominator
Adding fractions: a/b + c/b = (a + c) / b
Converting improper fraction to mixed number

Theorems

Least Common Denominator
Fraction Addition

Suitable Grade Level

Grades 5-7