Adding Fractions: Solve 1/5 + 2/15 Step by Step

Fraction Addition with Different Denominators

Solve the following exercise:

15+215= \frac{1}{5}+\frac{2}{15}=

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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 step by step.
00:08 First, we'll multiply the fraction by 3 to get a common denominator. This will help us add the fractions easily.
00:16 Remember, when we multiply a fraction, we need to multiply both the top number (numerator) and bottom number (denominator).
00:24 Now, let's carefully calculate these products.
00:28 Great! Now we can add the fractions since they have the same denominator.
00:34 Let's add the numbers in the numerator while keeping the same denominator.
00:38 And there we have it! We've successfully solved this problem by following each step carefully.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

15+215= \frac{1}{5}+\frac{2}{15}=

2

Step-by-step solution

Let's try to find the lowest common denominator between 5 and 15

To find the lowest common denominator, we need to find a number that is divisible by both 5 and 15

In this case, the common denominator is 15

Now we'll multiply each fraction by the appropriate number to reach the denominator 15

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

1×35×3+2×115×1=315+215 \frac{1\times3}{5\times3}+\frac{2\times1}{15\times1}=\frac{3}{15}+\frac{2}{15}

Now we'll combine and get:

3+215=515 \frac{3+2}{15}=\frac{5}{15}

3

Final Answer

515 \frac{5}{15}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find the LCD to make denominators the same
  • Technique: Convert 15 \frac{1}{5} to 315 \frac{3}{15} by multiplying by 3
  • Check: Verify 315+215=515 \frac{3}{15} + \frac{2}{15} = \frac{5}{15} by adding numerators ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators together
    Don't add denominators like 5 + 15 = 20 and get 320 \frac{3}{20} ! This creates a fraction with the wrong denominator. Always find the LCD first, convert both fractions to the same denominator, then add only the numerators.

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

Why is 15 the LCD and not 75?

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The LCD is the smallest number that both denominators divide into evenly. Since 15 ÷ 5 = 3 and 15 ÷ 15 = 1, we know 15 works perfectly without going to larger numbers like 75.

How do I know what to multiply each fraction by?

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Divide the LCD by each denominator: 15 ÷ 5 = 3, so multiply 15 \frac{1}{5} by 3. And 15 ÷ 15 = 1, so 215 \frac{2}{15} stays the same.

Can I simplify my final answer?

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Yes! 515 \frac{5}{15} can be simplified to 13 \frac{1}{3} by dividing both numerator and denominator by 5. Always check if your answer can be reduced to lowest terms.

What if the denominators don't divide evenly?

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That's okay! Sometimes you need to find multiples. List multiples of both denominators until you find the smallest common one. For example: 5, 10, 15, 20... and 15, 30, 45...

Do I always need to convert both fractions?

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Not always! In this problem, 215 \frac{2}{15} already has the LCD as its denominator, so it doesn't change. Only convert fractions that don't already have the LCD.

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