Solve 3 + (3/3 × 2/3) - 2: Mixed Operations Practice

Order of Operations with Mixed Fractions

3+33×23−2= 3+\frac{3}{3}\times\frac{2}{3}-2=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:10 Remember, multiply and divide come first before adding and subtracting.
00:16 When adding fractions, multiply top with top, and bottom with bottom.
00:21 You can reduce by finding common factors in the numerator and denominator.
00:28 Addition and subtraction are equal. Solve them from left to right.
00:35 Now, we're left with an easy subtraction.
00:39 And that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

3+33×23−2= 3+\frac{3}{3}\times\frac{2}{3}-2=

2

Step-by-step solution

According to the rules of the order of arithmetic operations, we first place the multiplication exercise inside of parentheses:

3+(33×23)−2= 3+(\frac{3}{3}\times\frac{2}{3})-2=

We then solve the exercise in the parentheses, combining the multiplication into a single exercise:

(33×23)=3×23×3=69=23 (\frac{3}{3}\times\frac{2}{3})=\frac{3\times2}{3\times3}=\frac{6}{9}=\frac{2}{3}

We obtain the following exercise:

3+23−2= 3+\frac{2}{3}-2=

Lastly we solve the exercise from left to right:

3+23=323 3+\frac{2}{3}=3\frac{2}{3}

323−2=123 3\frac{2}{3}-2=1\frac{2}{3}

3

Final Answer

123 1\frac{2}{3}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Follow PEMDAS: parentheses, multiplication/division, then addition/subtraction left to right
  • Technique: Multiply fractions first: 33×23=69=23 \frac{3}{3} \times \frac{2}{3} = \frac{6}{9} = \frac{2}{3}
  • Check: Verify final calculation: 3+23−2=123 3 + \frac{2}{3} - 2 = 1\frac{2}{3} ✓

Common Mistakes

Avoid these frequent errors
  • Adding and subtracting before multiplying fractions
    Don't solve 3+33×23−2 3 + \frac{3}{3} \times \frac{2}{3} - 2 from left to right = wrong answer of 83 \frac{8}{3} ! This ignores order of operations and puts addition before multiplication. Always complete all multiplication and division first, then work left to right for addition and subtraction.

Practice Quiz

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\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why do I multiply the fractions first instead of going left to right?

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The order of operations (PEMDAS) tells us to do multiplication and division before addition and subtraction. Even though 33×23 \frac{3}{3} \times \frac{2}{3} comes after the addition sign, you must solve it first!

How do I multiply fractions like 3/3 × 2/3?

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Multiply the numerators together and denominators together: 3×23×3=69 \frac{3 \times 2}{3 \times 3} = \frac{6}{9} . Then simplify by dividing both top and bottom by 3 to get 23 \frac{2}{3} .

What's the easiest way to add 3 + 2/3?

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Convert the whole number to a mixed number: 3=233 3 = 2\frac{3}{3} , so 3+23=233+23=323 3 + \frac{2}{3} = 2\frac{3}{3} + \frac{2}{3} = 3\frac{2}{3} . Or convert to improper fractions first!

How do I subtract 2 from 3⅔?

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Think of it as 323−2=323−203 3\frac{2}{3} - 2 = 3\frac{2}{3} - 2\frac{0}{3} . Subtract the whole numbers: 3−2=1 3 - 2 = 1 , and keep the fraction: 123 1\frac{2}{3} .

What if I get a different answer when I check my work?

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Double-check each step! Make sure you multiplied the fractions correctly, simplified properly, and followed the order of operations. The most common error is doing addition before multiplication.

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