Math Problem Statement

Add 2/5 and 3/4, following the steps to find a common denominator.

Solution

Let's solve the fraction addition problem:

25+34\frac{2}{5} + \frac{3}{4}

Step 1: Find the common denominator

We need to find the least common denominator (LCD) between 5 and 4. The least common multiple (LCM) of 5 and 4 is 20.

Step 2: Convert the fractions

Now, we rewrite the fractions with the denominator of 20.

  • For 25\frac{2}{5}, we multiply both the numerator and the denominator by 4: 25=2×45×4=820\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}

  • For 34\frac{3}{4}, we multiply both the numerator and the denominator by 5: 34=3×54×5=1520\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}

Step 3: Add the fractions

Now that both fractions have the same denominator, we can add them: 820+1520=8+1520=2320\frac{8}{20} + \frac{15}{20} = \frac{8 + 15}{20} = \frac{23}{20}

Step 4: Simplify the result

Since 2320\frac{23}{20} is an improper fraction, we can convert it to a mixed number: 2320=1320\frac{23}{20} = 1 \frac{3}{20}

Thus, the result is:

25+34=1320\frac{2}{5} + \frac{3}{4} = 1 \frac{3}{20}

Would you like further details or have any questions?

Here are 5 related questions for practice:

  1. What is 37+25\frac{3}{7} + \frac{2}{5}?
  2. How do you subtract 4913\frac{4}{9} - \frac{1}{3}?
  3. What is the sum of 56+29\frac{5}{6} + \frac{2}{9}?
  4. Can you simplify 1115+310\frac{11}{15} + \frac{3}{10}?
  5. How would you solve 7814\frac{7}{8} - \frac{1}{4}?

Tip: Always find the least common denominator to make adding and subtracting fractions easier!

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Math Problem Analysis

Mathematical Concepts

Fractions
Addition of Fractions
Least Common Denominator

Formulas

(a/b) + (c/d) = (a*d + b*c) / (b*d)
Least Common Multiple (LCM)

Theorems

Equivalent Fractions

Suitable Grade Level

Grades 5-7