Solve the Fraction Addition: 2/5 + 1/6

Question

25+16= \frac{2}{5}+\frac{1}{6}=

Video Solution

Solution Steps

00:00 Solve
00:03 We want to find the least common denominator
00:06 Multiply each fraction by the other denominator to find the common denominator
00:09 Remember to multiply both numerator and denominator
00:29 Calculate the multiplications
00:37 Add under the common denominator
00:43 Calculate the numerator
00:47 And this is the solution to the question

Step-by-Step Solution

To solve the problem of adding 25 \frac{2}{5} and 16 \frac{1}{6} , we need to find a common denominator. We do this by multiplying the denominators: 5×6=30 5 \times 6 = 30 . This is the smallest common multiple of the two denominators and ensures that each fraction can be represented with a common base, allowing addition.

Let's convert each fraction to an equivalent fraction with the common denominator of 30:

  • Convert 25 \frac{2}{5} : Multiply both the numerator and the denominator by 6 to get 2×65×6=1230 \frac{2 \times 6}{5 \times 6} = \frac{12}{30} .

  • Convert 16 \frac{1}{6} : Multiply both the numerator and the denominator by 5 to get 1×56×5=530 \frac{1 \times 5}{6 \times 5} = \frac{5}{30} .

Now, we add these equivalent fractions:

1230+530=12+530=1730 \frac{12}{30} + \frac{5}{30} = \frac{12 + 5}{30} = \frac{17}{30} .

The resulting fraction, 1730 \frac{17}{30} , is already in its simplest form because 17 is a prime number and does not share any common factors with 30 other than 1.

Thus, the sum of 25 \frac{2}{5} and 16 \frac{1}{6} is 1730 \frac{17}{30} .

Upon reviewing the given choices, the correct and matching choice is:

Choice 2: 1730 \frac{17}{30}

Answer

1730 \frac{17}{30}