Solve the Fraction Addition: 2/5 + 1/4 Step-by-Step

Fraction Addition with Different Denominators

Solve the following exercise:

25+14= \frac{2}{5}+\frac{1}{4}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Multiply each fraction by the second denominator to find the common denominator
00:07 Make sure to multiply both numerator and denominator
00:14 Calculate the products
00:19 Add with the common denominator
00:23 Calculate the numerator
00:27 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

25+14= \frac{2}{5}+\frac{1}{4}=

2

Step-by-step solution

Let's try to find the lowest common denominator between 5 and 4

To find the lowest common denominator, we need to find a number that is divisible by both 5 and 4

In this case, the common denominator is 20

Now we'll multiply each fraction by the appropriate number to reach the denominator 20

We'll multiply the first fraction by 4

We'll multiply the second fraction by 5

2×45×4+1×54×5=820+520 \frac{2\times4}{5\times4}+\frac{1\times5}{4\times5}=\frac{8}{20}+\frac{5}{20}

Now we'll combine and get:

8+520=1320 \frac{8+5}{20}=\frac{13}{20}

3

Final Answer

1320 \frac{13}{20}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find the least common denominator before adding fractions
  • Technique: Convert 25 \frac{2}{5} to 820 \frac{8}{20} and 14 \frac{1}{4} to 520 \frac{5}{20}
  • Check: Verify LCD is correct by confirming 20 ÷ 5 = 4 and 20 ÷ 4 = 5 ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators together or adding numerators without common denominator
    Don't add 25+14 \frac{2}{5}+\frac{1}{4} as 39 \frac{3}{9} or 2+15 \frac{2+1}{5} ! This ignores that fractions represent different-sized pieces that can't be combined directly. Always find the LCD first to make equivalent fractions with the same denominator.

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 least common denominator of 5 and 4?

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List the multiples of each number: 5 (5, 10, 15, 20, 25...) and 4 (4, 8, 12, 16, 20, 24...). The smallest number that appears in both lists is your LCD - in this case, 20!

Why can't I just add the numerators and denominators separately?

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Because fractions represent parts of different-sized wholes! 25 \frac{2}{5} means 2 pieces out of 5, while 14 \frac{1}{4} means 1 piece out of 4. You need to make the pieces the same size first.

What if the LCD seems really big - did I do something wrong?

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Not necessarily! Sometimes the LCD is large, especially when the denominators don't share common factors. Double-check by ensuring your LCD is divisible by both original denominators.

Do I always need to simplify my final answer?

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Yes, when possible! Check if the numerator and denominator share any common factors. In this problem, 1320 \frac{13}{20} is already in simplest form since 13 and 20 share no common factors.

Can I use a different common denominator instead of the LCD?

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You can use any common denominator, but using the LCD makes the math easier with smaller numbers. Using 40 instead of 20 would work but create unnecessarily large fractions!

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