Solve Mixed Number Addition: 7⅚ + 6⅔ + ⅓

Mixed Number Addition with Strategic Grouping

756+623+13= ? 7\frac{5}{6}+6\frac{2}{3}+\frac{1}{3}=\text{ ?}

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Step-by-step written solution

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1

Understand the problem

756+623+13= ? 7\frac{5}{6}+6\frac{2}{3}+\frac{1}{3}=\text{ ?}

2

Step-by-step solution

Note that the right-hand side of the addition exercise between the fractions gives a result of a whole number, so we'll start with that:

623+13=7 6\frac{2}{3}+\frac{1}{3}=7

Giving us:

756+7=1456 7\frac{5}{6}+7=14\frac{5}{6}

3

Final Answer

1456 14\frac{5}{6}

Key Points to Remember

Essential concepts to master this topic
  • Strategy: Group fractions that add to whole numbers first
  • Technique: 623+13=7 6\frac{2}{3}+\frac{1}{3}=7 because 23+13=1 \frac{2}{3}+\frac{1}{3}=1
  • Check: Verify by adding all whole parts: 7+6+0=13, plus 56 \frac{5}{6} gives 1456 14\frac{5}{6}

Common Mistakes

Avoid these frequent errors
  • Adding all whole numbers first without considering strategic grouping
    Don't add 7+6=13 first and then struggle with 56+23+13 \frac{5}{6}+\frac{2}{3}+\frac{1}{3} = messy fraction work! This makes the problem much harder than needed. Always look for fractions that combine to make whole numbers first, like 23+13=1 \frac{2}{3}+\frac{1}{3}=1 .

Practice Quiz

Test your knowledge with interactive questions

\( 94+12+6= \)

FAQ

Everything you need to know about this question

Why should I group 623 6\frac{2}{3} and 13 \frac{1}{3} first?

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Because 23+13=1 \frac{2}{3}+\frac{1}{3}=1 ! When fractions add up to a whole number, it makes the problem much simpler. This turns 623+13 6\frac{2}{3}+\frac{1}{3} into just 7.

What if the fractions don't add up to a whole number?

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Then you'd need to find a common denominator for all the fractions. In this case, you got lucky because 23+13=33=1 \frac{2}{3}+\frac{1}{3}=\frac{3}{3}=1 .

How do I know which fractions to group together?

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Look for fractions with the same denominator or fractions that might add up to 1. For example, 14 \frac{1}{4} and 34 \frac{3}{4} would be perfect to group together!

Can I solve this problem a different way?

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Yes! You could convert everything to improper fractions first, then add. But the strategic grouping method is much faster and less prone to arithmetic errors.

What's the final answer again?

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The answer is 1456 14\frac{5}{6} . We got this by recognizing that 623+13=7 6\frac{2}{3}+\frac{1}{3}=7 , then adding 756+7=1456 7\frac{5}{6}+7=14\frac{5}{6} .

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