Math Problem Statement

1/5-4/15+8/10-11/15+107/19

Solution

Let's solve the expression step by step:

15415+8101115+10719\frac{1}{5} - \frac{4}{15} + \frac{8}{10} - \frac{11}{15} + \frac{107}{19}

Step 1: Convert to Common Denominators

  • The denominators are 5, 15, 10, 15, and 19.

  • The least common multiple (LCM) for 5, 15, and 10 is 30 (ignoring 19 for now, since it’s a prime).

  • Convert fractions to have denominator 30:

    15=630,415=830,810=2430,1115=2230\frac{1}{5} = \frac{6}{30}, \quad \frac{4}{15} = \frac{8}{30}, \quad \frac{8}{10} = \frac{24}{30}, \quad \frac{11}{15} = \frac{22}{30}

Now the expression becomes:

630830+24302230+10719\frac{6}{30} - \frac{8}{30} + \frac{24}{30} - \frac{22}{30} + \frac{107}{19}

Step 2: Simplify the Fractions

(630830+24302230)+10719\left( \frac{6}{30} - \frac{8}{30} + \frac{24}{30} - \frac{22}{30} \right) + \frac{107}{19}

68+242230+10719\frac{6 - 8 + 24 - 22}{30} + \frac{107}{19}

030+10719\frac{0}{30} + \frac{107}{19}

0+10719=107190 + \frac{107}{19} = \frac{107}{19}

Final Answer:

10719or5.63 (approx.)\frac{107}{19} \quad \text{or} \quad 5.63 \text{ (approx.)}

Let me know if you need a detailed breakdown of any step!

Related Questions:

  1. How do you find the least common denominator for multiple fractions?
  2. What is the process for adding and subtracting fractions with different denominators?
  3. How do you convert an improper fraction to a mixed number?
  4. Why is it useful to simplify fractions before performing operations?
  5. How do you handle fractions when they involve prime denominators?

Tip:

When adding or subtracting fractions, always simplify common terms first—it can make calculations much easier!

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Math Problem Analysis

Mathematical Concepts

Fraction Addition
Fraction Subtraction
LCM (Least Common Multiple)
Simplification of Fractions

Formulas

LCM of denominators
Simplification of fractions

Theorems

Fraction addition and subtraction rules

Suitable Grade Level

Grades 5-7