Solve the Fraction Addition: 3/7 + 1/3 Step by Step

Question

Solve the following exercise:

37+13=? \frac{3}{7}+\frac{1}{3}=\text{?}

Video Solution

Solution Steps

00:00 Solve
00:03 Multiply each fraction by the second denominator to find a common denominator
00:09 Remember to multiply both numerator and denominator
00:20 Calculate the multiplications
00:30 Add under common denominator
00:35 Calculate the numerator
00:38 And this is the solution to the question

Step-by-Step Solution

To solve the problem of adding the fractions 37 \frac{3}{7} and 13 \frac{1}{3} , we follow these steps:

  • Step 1: Find a common denominator for the fractions. The denominators are 77 and 33. By multiplying 77 and 33, we find the common denominator is 2121.
  • Step 2: Convert each fraction to an equivalent fraction with this common denominator.
    • The first fraction: 37 \frac{3}{7} . We multiply both the numerator and the denominator by 33 (since 7×3=217 \times 3 = 21): 3×37×3=921. \frac{3 \times 3}{7 \times 3} = \frac{9}{21}.
    • The second fraction: 13 \frac{1}{3} . We multiply both the numerator and the denominator by 77 (since 3×7=213 \times 7 = 21): 1×73×7=721. \frac{1 \times 7}{3 \times 7} = \frac{7}{21}.
  • Step 3: Add the fractions. Now that both fractions have the same denominator, we can add them: 921+721=9+721=1621. \frac{9}{21} + \frac{7}{21} = \frac{9 + 7}{21} = \frac{16}{21}.
  • Step 4: Simplify the resulting fraction if necessary. In this case, 1621 \frac{16}{21} is already in its simplest form.

Therefore, the final solution to the problem is 1621\frac{16}{21}.

Answer

1621 \frac{16}{21}