Solve: -4/9 + 5 + (-2) + 5/9 Mixed Number Operations

Fraction Operations with Regrouping Terms

49+5+(2)+59= -\frac{4}{9}+5+(-2)+\frac{5}{9}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:05 We'll use the commutative law and arrange the exercise
00:10 Positive times negative always equals negative
00:16 Let's add the fractions
00:22 Let's calculate the difference
00:26 Let's calculate the numerator
00:35 Let's convert from a whole number to a fraction with a common denominator
00:47 Let's add the fractions together
00:56 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

49+5+(2)+59= -\frac{4}{9}+5+(-2)+\frac{5}{9}=

2

Step-by-step solution

To solve this problem, we'll perform operations involving both fractions and whole numbers:

  • Step 1: Combine the fractional parts 49-\frac{4}{9} and 59\frac{5}{9}.

  • Step 2: Add the remaining whole numbers 55 and 2-2.

  • Step 3: Sum the results from Step 1 and Step 2.

Let's start:
Step 1: Work with the fractions together. - We have 49-\frac{4}{9} and 59\frac{5}{9}, both have the same denominator, thus can be directly added: 49+59=4+59=19 -\frac{4}{9} + \frac{5}{9} = \frac{-4+5}{9} = \frac{1}{9}

Step 2: Add the integer components 55 and 2-2: 5+(2)=52=3. 5 + (-2) = 5 - 2 = 3.

Step 3: Combine results from Step 1 and Step 2: 3+19=279+19=289 3+\frac{1}{9}=\frac{27}{9}+\frac{1}{9}=\frac{28}{9} .

Therefore, the final result of the expression is 289\frac{28}{9}.

3

Final Answer

289 \frac{28}{9}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Group terms with same denominators to simplify calculations
  • Technique: Combine 49+59=19 -\frac{4}{9} + \frac{5}{9} = \frac{1}{9} first
  • Check: Convert final answer: 289=319 \frac{28}{9} = 3\frac{1}{9} matches work ✓

Common Mistakes

Avoid these frequent errors
  • Adding all terms left to right without grouping
    Don't calculate 49+5=419 -\frac{4}{9} + 5 = \frac{41}{9} first = creates complex fractions unnecessarily! This makes the problem much harder and leads to calculation errors. Always group like terms first: fractions with fractions, whole numbers with whole numbers.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{2}{4}+\frac{1}{4}= \)\( \)

FAQ

Everything you need to know about this question

Why should I group the fractions together first?

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Grouping like terms makes calculations easier! When you combine 49 -\frac{4}{9} and 59 \frac{5}{9} first, you get 19 \frac{1}{9} - much simpler than working with mixed numbers throughout.

How do I add fractions with the same denominator?

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Keep the denominator the same and just add the numerators! So 49+59=4+59=19 -\frac{4}{9} + \frac{5}{9} = \frac{-4+5}{9} = \frac{1}{9} . Think of it like having pieces of the same pie.

What if I get confused with positive and negative signs?

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Write it as subtraction when you see negative signs: 5+(2) 5 + (-2) becomes 52=3 5 - 2 = 3 . This makes the arithmetic clearer!

How do I convert the whole number to a fraction?

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To add 3+19 3 + \frac{1}{9} , write 3 as 279 \frac{27}{9} (multiply by 99 \frac{9}{9} ). Then 279+19=289 \frac{27}{9} + \frac{1}{9} = \frac{28}{9} .

Can I leave my answer as an improper fraction?

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Yes! 289 \frac{28}{9} is perfectly acceptable. You could also write it as the mixed number 319 3\frac{1}{9} - both forms are correct!

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