Solve the Expression: 3+10-2:4+1 Using Order of Operations

Order of Operations with Mixed Numbers

3+10−2:4+1= 3+10-2:4+1=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Remember, multiplication and division come first, before addition and subtraction.
00:21 Now, we only have addition and subtraction left to solve.
00:25 Since addition and subtraction are equal in the order of operations, we solve them from left to right.
00:31 Let's break down the denominator of the fraction into multiplication.
00:40 Now, let's reduce the fraction.
00:45 Keep solving the addition and subtraction, moving from left to right.
00:53 And that's the solution! Great job!

Step-by-step written solution

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1

Understand the problem

3+10−2:4+1= 3+10-2:4+1=

2

Step-by-step solution

According to the order of arithmetic operations, multiplication and division precede addition and subtraction,

Therefore, let's start first with the division operation:

3+10−(2:4)+1=3+10−12+1 3+10-(2:4)+1=3+10-\frac{1}{2}+1

Now, as all remaining operations are at the same level (addition and subtraction),

let's start solving from left to right:

3+10−12+1=13−12+1 3+10-\frac{1}{2}+1=13-\frac{1}{2}+1

13−12+1=1212+1=1312 13-\frac{1}{2}+1=12\frac{1}{2}+1=13\frac{1}{2}

3

Final Answer

1312 13\frac{1}{2}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Division and multiplication operations are performed before addition and subtraction
  • Technique: Calculate 2÷4 = 1/2 first, then work left to right: 3+10-1/2+1
  • Check: Final result 13½ can be verified by converting to decimal: 13.5 ✓

Common Mistakes

Avoid these frequent errors
  • Working strictly from left to right without considering operation priority
    Don't calculate 3+10-2÷4+1 as ((3+10-2)÷4)+1 = 11÷4+1 = 3¾! This ignores PEMDAS rules and gives the wrong answer. Always perform division and multiplication first, then work left to right for addition and subtraction.

Practice Quiz

Test your knowledge with interactive questions

\( 8 + 3 \times 2 = \)

FAQ

Everything you need to know about this question

Why do I divide 2÷4 first instead of going left to right?

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The order of operations (PEMDAS) requires you to do multiplication and division before addition and subtraction. This ensures everyone gets the same answer when solving math problems.

How do I handle the fraction ½ with whole numbers?

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You can work with mixed numbers! 13−12=1212 13 - \frac{1}{2} = 12\frac{1}{2} , then 1212+1=1312 12\frac{1}{2} + 1 = 13\frac{1}{2} . Or convert everything to decimals: 13 - 0.5 + 1 = 13.5.

What does the colon (:) symbol mean in this problem?

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The colon (:) symbol means division, just like the ÷ symbol. So 2:4 is the same as 2÷4 = 12 \frac{1}{2} .

Can I convert everything to decimals instead of fractions?

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Yes! You can work with decimals: 3+10−0.5+1=13.5 3+10-0.5+1 = 13.5 . Just remember that 13.5=1312 13.5 = 13\frac{1}{2} - they're the same value!

How do I know which operations to do first?

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Remember PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). In this problem, division comes first!

What if I get confused with mixed numbers like 12½?

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Think of 1212 12\frac{1}{2} as 12+12 12 + \frac{1}{2} . When you add 1 more, you get 12+12+1=1312 12 + \frac{1}{2} + 1 = 13\frac{1}{2} .

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