Solve the Fraction Addition: 1/10 + 1/3 Step by Step

Question

Solve the following exercise:

110+13=? \frac{1}{10}+\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
00:22 Calculate the multiplications
00:28 Add under common denominator
00:34 Calculate the numerator
00:38 And this is the solution to the question

Step-by-Step Solution

To solve the addition of fractions 110+13 \frac{1}{10} + \frac{1}{3} , we must first find a common denominator.

  • Step 1: Find the Least Common Multiple (LCM) of the denominators, 10 and 3. By multiplying these denominators, the LCM is 10×3=30 10 \times 3 = 30 .

  • Step 2: Rewrite each fraction with the common denominator of 30:
    - Convert 110 \frac{1}{10} to an equivalent fraction with a denominator of 30. Multiply both numerator and denominator by 3: 110=1×310×3=330 \frac{1}{10} = \frac{1 \times 3}{10 \times 3} = \frac{3}{30}
    - Convert 13 \frac{1}{3} to an equivalent fraction with a denominator of 30. Multiply both numerator and denominator by 10: 13=1×103×10=1030 \frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30}

  • Step 3: Add the equivalent fractions: 330+1030=3+1030=1330 \frac{3}{30} + \frac{10}{30} = \frac{3 + 10}{30} = \frac{13}{30}

  • Step 4: Simplify the resulting fraction. Since 13 is a prime number and does not divide 30, 1330\frac{13}{30} is already in its simplest form.

Thus, the sum of 110 \frac{1}{10} and 13 \frac{1}{3} is 1330 \frac{13}{30} .

The correct answer is 1330 \frac{13}{30} , which corresponds to choice 4.

Answer

1330 \frac{13}{30}