Solve Mixed Number Addition: 4⅚ + 1 1/12

Mixed Number Addition with Different Denominators

456+1112= 4\frac{5}{6}+1\frac{1}{12}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 The formula for converting a mixed fraction to a fraction
00:11 We'll use this formula in our exercise and convert to fractions
00:30 Multiply to find the common denominator
00:41 Add with the common denominator
00:51 Now we'll convert back to a mixed fraction
00:55 Break down 71 into 60 plus 11
00:59 Break down the fraction into whole number and remainder
01:03 Convert from improper fraction to whole number and combine into mixed fraction
01:09 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

456+1112= 4\frac{5}{6}+1\frac{1}{12}=

2

Step-by-step solution

To solve the addition of the mixed numbers 456 4\frac{5}{6} and 1112 1\frac{1}{12} , follow these steps:

  • Step 1: Add the whole numbers.
    The whole numbers are 4 and 1, so we add these together:
    4+1=5 4 + 1 = 5 .
  • Step 2: Add the fractional parts.
    First, find a common denominator for the fractions 56\frac{5}{6} and 112\frac{1}{12}. The least common denominator of 6 and 12 is 12.
    Convert 56\frac{5}{6} to twelfths: 56=5×26×2=1012\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}.
    Now add the fractions: 1012+112=1112\frac{10}{12} + \frac{1}{12} = \frac{11}{12}.
  • Step 3: Combine the results.
    Add the whole number and the sum of the fractions:
    5+1112=511125 + \frac{11}{12} = 5\frac{11}{12}.

Thus, the sum of 456+1112 4\frac{5}{6} + 1\frac{1}{12} is 51112 5\frac{11}{12} .

3

Final Answer

51112 5\frac{11}{12}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Add whole numbers separately, then add fractional parts
  • Technique: Convert 56 \frac{5}{6} to 1012 \frac{10}{12} using common denominator 12
  • Check: Verify 51112 5\frac{11}{12} equals 4+1+1012+112 4 + 1 + \frac{10}{12} + \frac{1}{12}

Common Mistakes

Avoid these frequent errors
  • Adding denominators instead of finding common denominator
    Don't add 6 + 12 = 18 and get 618 \frac{6}{18} ! This creates a completely wrong fraction with no mathematical basis. Always find the least common denominator first, then convert both fractions.

Practice Quiz

Test your knowledge with interactive questions

\( 2\frac{2}{5}+2\frac{2}{5}= \)

FAQ

Everything you need to know about this question

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

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You can only add fractions when they have the same denominator. Think of it like adding different units - you can't add 3 apples + 2 oranges and get 5 apples!

How do I know what common denominator to use?

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Find the least common multiple (LCM) of the denominators. For 6 and 12, since 12 is already a multiple of 6, the LCD is 12.

What if my answer has an improper fraction?

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Convert it to a mixed number! For example, if you get 51312 5\frac{13}{12} , change it to 6112 6\frac{1}{12} by taking out the whole number.

Do I always need to simplify my final answer?

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Yes! Always check if your fraction can be reduced. In this problem, 1112 \frac{11}{12} is already in simplest form since 11 and 12 share no common factors.

Can I convert everything to improper fractions instead?

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Absolutely! You could convert to 296+1312 \frac{29}{6} + \frac{13}{12} , find the sum, then convert back. Both methods work - choose what feels easier!

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