Solve the Fraction Addition: 2/5 + 1/6 Step-by-Step

Fraction Addition with Different Denominators

Solve the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this problem together.
00:08 First, multiply each fraction by the other fraction's denominator. This helps us find a common denominator.
00:15 Remember to multiply both the numerator and the denominator by this value.
00:21 Next, calculate the products of these fractions.
00:26 Now, add the fractions together using the common denominator.
00:30 And then, compute the numerator by adding.
00:34 Great job! That's how we find the solution to this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

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

2

Step-by-step solution

Let's try to find the lowest common denominator between 5 and 6

To find the lowest common denominator, we need to find a number that is divisible by both 5 and 6

In this case, the common denominator is 30

Now we'll multiply each fraction by the appropriate number to reach the denominator 30

We'll multiply the first fraction by 6

We'll multiply the second fraction by 5

2×65×6+1×56×5=1230+530 \frac{2\times6}{5\times6}+\frac{1\times5}{6\times5}=\frac{12}{30}+\frac{5}{30}

Now we'll combine and get:

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

3

Final Answer

1730 \frac{17}{30}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find LCD before adding fractions with different denominators
  • Technique: Convert 25 \frac{2}{5} to 1230 \frac{12}{30} and 16 \frac{1}{6} to 530 \frac{5}{30}
  • Check: Verify LCD: 30 ÷ 5 = 6 and 30 ÷ 6 = 5 ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 2+1=3 and 5+6=11 to get 311 \frac{3}{11} = wrong answer! This ignores that fractions represent parts of different-sized wholes. Always find the LCD first to make denominators the same.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 5:6= \)

FAQ

Everything you need to know about this question

How do I find the LCD of 5 and 6?

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List the multiples of each number: 5 → 5, 10, 15, 20, 25, 30... and 6 → 6, 12, 18, 24, 30... The first number that appears in both lists is your LCD!

Why can't I just add 2+1 and 5+6?

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Because 25 \frac{2}{5} means 2 pieces of something cut into 5 parts, while 16 \frac{1}{6} means 1 piece cut into 6 parts. You need same-sized pieces to add them!

What if the LCD is really big?

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Don't worry! Even if the LCD seems large, the math works the same way. Just multiply carefully and simplify your final answer if possible.

Do I need to simplify 17/30?

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Check if 17 and 30 share any common factors. Since 17 is prime and doesn't divide 30, 1730 \frac{17}{30} is already in simplest form!

Can I use a different common denominator?

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Yes, but using the LCD (30) keeps numbers smaller and easier to work with. Using 60 or 90 would also work, but creates unnecessary large numbers.

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