Math Problem Statement

5 7/18+9 5/12

Solution

Let's break down the addition step by step:

You are adding two mixed numbers: 57185 \frac{7}{18} and 95129 \frac{5}{12}.

Step 1: Convert the mixed numbers to improper fractions.

For 57185 \frac{7}{18}: 5718=5×18+718=90+718=97185 \frac{7}{18} = \frac{5 \times 18 + 7}{18} = \frac{90 + 7}{18} = \frac{97}{18}

For 95129 \frac{5}{12}: 9512=9×12+512=108+512=113129 \frac{5}{12} = \frac{9 \times 12 + 5}{12} = \frac{108 + 5}{12} = \frac{113}{12}

Step 2: Find a common denominator.

The denominators are 18 and 12. The least common denominator (LCD) of 18 and 12 is 36.

  • Convert 9718\frac{97}{18} to have a denominator of 36: 9718=97×218×2=19436\frac{97}{18} = \frac{97 \times 2}{18 \times 2} = \frac{194}{36}

  • Convert 11312\frac{113}{12} to have a denominator of 36: 11312=113×312×3=33936\frac{113}{12} = \frac{113 \times 3}{12 \times 3} = \frac{339}{36}

Step 3: Add the fractions.

Now we can add the fractions: 19436+33936=194+33936=53336\frac{194}{36} + \frac{339}{36} = \frac{194 + 339}{36} = \frac{533}{36}

Step 4: Simplify the result.

53336\frac{533}{36} is an improper fraction. To convert it back to a mixed number:

  • Divide 533 by 36: 533÷36=14533 \div 36 = 14 (quotient) with a remainder of 53336×14=533504=29533 - 36 \times 14 = 533 - 504 = 29.
  • So, 53336=142936\frac{533}{36} = 14 \frac{29}{36}.

Final Answer:

5718+9512=1429365 \frac{7}{18} + 9 \frac{5}{12} = 14 \frac{29}{36}

Let me know if you'd like more details or further clarification!

Here are some related questions for practice:

  1. How do you convert mixed numbers to improper fractions?
  2. What is the least common denominator (LCD) and how do you find it?
  3. How do you simplify improper fractions to mixed numbers?
  4. Can you add two fractions with different denominators without finding the LCD?
  5. How do you subtract fractions with different denominators?

Tip: When adding or subtracting fractions, always make sure to find a common denominator before combining them!

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Math Problem Analysis

Mathematical Concepts

Mixed Numbers
Improper Fractions
Fraction Addition

Formulas

Mixed Number to Improper Fraction: a b/c = (a * c + b)/c
Adding Fractions: (a/c + b/d) = (a * d + b * c) / (c * d)
Improper Fraction to Mixed Number: a/b = quotient remainder

Theorems

Least Common Denominator (LCD)

Suitable Grade Level

Grades 4-6