Solve the Fraction Addition: 1/4 + 6/8 Step-by-Step

Fraction Addition with Common Denominators

Solve the following exercise:

14+68= \frac{1}{4}+\frac{6}{8}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's solve this problem step by step.
00:09 We'll multiply the fraction by two, to get the same denominator.
00:14 Remember to multiply both the top number, and the bottom number.
00:18 Now, let's figure out the products we get.
00:24 Next, let's add with our common denominator.
00:28 Time to calculate the result for the top number.
00:31 Remember, any number divided by itself is always one.
00:36 And that's the solution to our question. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

14+68= \frac{1}{4}+\frac{6}{8}=

2

Step-by-step solution

Let's try to find the least common denominator between 4 and 8

To find the least common denominator, we need to find a number that is divisible by both 4 and 8

In this case, the common denominator is 8

Now we'll multiply each fraction by the appropriate number to reach the denominator 8

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

1×24×2+6×18×1=28+68 \frac{1\times2}{4\times2}+\frac{6\times1}{8\times1}=\frac{2}{8}+\frac{6}{8}

Now we'll combine and get:

2+68=88=1 \frac{2+6}{8}=\frac{8}{8}=1

3

Final Answer

1 1

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find common denominator before adding fractions together
  • Technique: Convert 14 \frac{1}{4} to 28 \frac{2}{8} by multiplying by 22 \frac{2}{2}
  • Check: Simplify final answer: 88=1 \frac{8}{8} = 1

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 14+68=712 \frac{1}{4} + \frac{6}{8} = \frac{7}{12} ! This treats fractions like separate numbers instead of parts of wholes. Always find a common denominator first, 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 can't I just add 1+6 and 4+8 directly?

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Because fractions represent parts of different-sized wholes. Adding 14+68 \frac{1}{4} + \frac{6}{8} is like adding 1 quarter to 6 eighths - you need the same size pieces first!

How do I find the least common denominator?

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Look for the smallest number both denominators divide into evenly. Since 8 ÷ 4 = 2 and 8 ÷ 8 = 1, the LCD of 4 and 8 is 8.

Do I always multiply the whole fraction?

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Yes! When converting 14 \frac{1}{4} to eighths, multiply both numerator and denominator: 1×24×2=28 \frac{1 \times 2}{4 \times 2} = \frac{2}{8} . This keeps the fraction's value the same.

What if my answer is greater than 1?

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That's perfectly normal! When adding fractions, you can get improper fractions (numerator larger than denominator) or whole numbers like we got here: 88=1 \frac{8}{8} = 1 .

Should I always simplify my final answer?

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Always! Check if your answer can be reduced. Here, 88=1 \frac{8}{8} = 1 is already in simplest form since any number divided by itself equals 1.

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