Math Problem Statement

Add: Write in simplest form: 5 5/7 + 3 1/2.

Solution

The expression in the image is the sum of two mixed numbers: 557+3125 \frac{5}{7} + 3 \frac{1}{2}.

Steps to solve:

  1. Convert mixed numbers to improper fractions:

    • 557=(5×7)+57=35+57=4075 \frac{5}{7} = \frac{(5 \times 7) + 5}{7} = \frac{35 + 5}{7} = \frac{40}{7}
    • 312=(3×2)+12=6+12=723 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}
  2. Find a common denominator:

    • The denominators are 7 and 2. The least common denominator (LCD) is 14.
    • Convert both fractions:
      • 407=40×27×2=8014\frac{40}{7} = \frac{40 \times 2}{7 \times 2} = \frac{80}{14}
      • 72=7×72×7=4914\frac{7}{2} = \frac{7 \times 7}{2 \times 7} = \frac{49}{14}
  3. Add the fractions: 8014+4914=80+4914=12914\frac{80}{14} + \frac{49}{14} = \frac{80 + 49}{14} = \frac{129}{14}

  4. Simplify or convert back to a mixed number:

    • 12914\frac{129}{14} can be written as a mixed number.
    • Divide 129÷14=9129 \div 14 = 9 remainder 33, so: 12914=9314\frac{129}{14} = 9 \frac{3}{14}

Thus, the sum is 93149 \frac{3}{14}.

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

Here are 5 related questions:

  1. How do you subtract mixed numbers?
  2. What is the method to find the least common denominator?
  3. How do you simplify improper fractions?
  4. How can you multiply mixed numbers?
  5. What are the steps to convert an improper fraction back to a mixed number?

Tip: Always check for common factors between the numerator and denominator when simplifying fractions!

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Math Problem Analysis

Mathematical Concepts

Fractions
Mixed Numbers
Improper Fractions
Addition of Fractions

Formulas

a b/c = (a * c + b)/c
LCD for fractions
Sum of fractions: a/b + c/d = (a*d + b*c)/(b*d)

Theorems

Least Common Denominator
Addition of Improper Fractions

Suitable Grade Level

Grades 6-8