Calculate the Sum: 4⅔ + 2⅖ + 3⅓ + 1⅗ Mixed Number Addition

Mixed Number Addition with Strategic Grouping

423+227+313+137=? 4\frac{2}{3}+2\frac{2}{7}+3\frac{1}{3}+1\frac{3}{7}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's arrange the equation so it will be easier to solve
00:15 Let's solve each addition separately and then sum up
00:24 Let's break down the addition into whole numbers addition and fractions addition
00:29 This is the result of the left-side addition
00:33 Now let's solve the right-side addition using the same method
00:39 Let's break down the addition into whole numbers addition and fractions addition
00:49 This is the result of the left-side addition
01:00 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

423+227+313+137=? 4\frac{2}{3}+2\frac{2}{7}+3\frac{1}{3}+1\frac{3}{7}=\text{?}

2

Step-by-step solution

Given that this is an exercise with only addition operation, we can change the order of the numbers.

We organize the exercise in a way that we can obtain a pair that gives us an integer.

Keep in mind that there is a pair of fractions that if we add them we will obtain an integer:

423+313+227+137= 4\frac{2}{3}+3\frac{1}{3}+2\frac{2}{7}+1\frac{3}{7}=

We solve the exercise from left to right:

423+313= 4\frac{2}{3}+3\frac{1}{3}=

4+3=7 4+3=7

23+13=33=1 \frac{2}{3}+\frac{1}{3}=\frac{3}{3}=1

7+1=8 7+1=8

Now we obtain the exercise:

8+227+137= 8+2\frac{2}{7}+1\frac{3}{7}=

We leave the 8 aside and add the rest of the exercise:

227+137= 2\frac{2}{7}+1\frac{3}{7}=

2+1=3 2+1=3

27+37=57 \frac{2}{7}+\frac{3}{7}=\frac{5}{7}

Now we obtain the exercise:

8+3+57=1157 8+3+\frac{5}{7}=11\frac{5}{7}

3

Final Answer

1157 11\frac{5}{7}

Key Points to Remember

Essential concepts to master this topic
  • Grouping Strategy: Pair fractions with same denominators for easier computation
  • Technique: Add whole parts separately: 4+3=7, then fractions 23+13=1 \frac{2}{3}+\frac{1}{3}=1
  • Check: Verify final answer substitutes correctly: 1157 11\frac{5}{7} equals original sum ✓

Common Mistakes

Avoid these frequent errors
  • Adding mixed numbers without strategic grouping
    Don't solve 423+227 4\frac{2}{3}+2\frac{2}{7} first = complex fraction arithmetic with different denominators! This creates unnecessary work with finding common denominators. Always group mixed numbers with same fractional denominators first to simplify calculations.

Practice Quiz

Test your knowledge with interactive questions

\( 74+32+6+4+4=\text{?} \)

FAQ

Everything you need to know about this question

Why should I rearrange the numbers before adding?

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Strategic grouping makes the problem much easier! When you pair 423+313 4\frac{2}{3}+3\frac{1}{3} , the fractions 23+13=1 \frac{2}{3}+\frac{1}{3}=1 create a whole number, avoiding complex fraction arithmetic.

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

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That's fine! Not all problems will have fractions that sum to 1. The key is still to group numbers with the same denominator first, then find a common denominator for any remaining different fractions.

Do I always add whole numbers and fractions separately?

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Yes! This is the standard method for mixed numbers. Add all whole parts together, add all fractional parts together, then combine. If the fractional sum is improper, convert it to a mixed number and add to your whole number total.

How do I know when I can group strategically?

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Look for matching denominators in your problem! In this case, we have two fractions with denominator 3 and two with denominator 7, making strategic pairing possible.

What if I get confused with the order of operations?

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Remember that addition is commutative - you can add in any order! Use this property to your advantage by rearranging terms to make calculations easier before you start adding.

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