Solve the Fraction Addition: 4/10 + 2/6 Step by Step

Question

Solve the following exercise:

410+26=? \frac{4}{10}+\frac{2}{6}=\text{?}

Video Solution

Solution Steps

00:00 Solve
00:03 We want to find the least common denominator
00:06 Therefore we'll multiply by 3 and 5 respectively for the common denominator 30
00:09 Remember to multiply both numerator and denominator
00:21 Let's calculate the multiplications
00:26 Add under common denominator
00:31 Calculate the numerator
00:36 And this is the solution to the question

Step-by-Step Solution

To solve for the sum of 410+26 \frac{4}{10} + \frac{2}{6} , we will proceed with the following steps:

  • Step 1: Identify the least common denominator (LCD)
  • Step 2: Convert each fraction to an equivalent fraction with this common denominator
  • Step 3: Add the numerators

Let's begin:

Step 1: Identify the least common denominator (LCD)
The denominators are 10 and 6. The least common multiple (LCM) of 10 and 6 can be found by evaluating their prime factors:
10 = 2 × 5
6 = 2 × 3
The LCM is found by taking the highest power of each prime that appears:
LCM = 2 × 3 × 5 = 30.
Thus, the common denominator is 30.

Step 2: Convert each fraction to an equivalent fraction with the common denominator of 30
For 410 \frac{4}{10} :
Multiply both the numerator and the denominator by 3 to make the denominator 30:
410=4×310×3=1230 \frac{4}{10} = \frac{4 \times 3}{10 \times 3} = \frac{12}{30} .
For 26 \frac{2}{6} :
Multiply both the numerator and the denominator by 5 to make the denominator 30:
26=2×56×5=1030 \frac{2}{6} = \frac{2 \times 5}{6 \times 5} = \frac{10}{30} .

Step 3: Add the numerators
Now that the fractions have the same denominator, add the numerators:
1230+1030=12+1030=2230 \frac{12}{30} + \frac{10}{30} = \frac{12 + 10}{30} = \frac{22}{30} .
This fraction cannot be simplified further as 22 and 30 have no common factors besides 1.

Therefore, the sum of 410+26 \frac{4}{10} + \frac{2}{6} is 2230 \frac{22}{30} .

Answer

2230 \frac{22}{30}