Evaluate the Expression: (3+2-1):(1+3)-1+5 Using Order of Operations

Order of Operations with Division Notation

(3+21):(1+3)1+5= (3+2-1):(1+3)-1+5=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following expression
00:03 Always solve parentheses first
00:25 Division precedes subtraction
00:30 Continue to solve the expression according to the correct order of operations
00:35 This is the solution

Step-by-step written solution

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1

Understand the problem

(3+21):(1+3)1+5= (3+2-1):(1+3)-1+5=

2

Step-by-step solution

This simple rule is the order of operations which states that multiplication and division come before addition and subtraction, and operations enclosed in parentheses come first,

In the given example of division between two given numbers in parentheses, therefore according to the order of operations mentioned above, we start by calculating the values of each of the numbers within the parentheses, there is no prohibition against calculating the result of the addition operation in the given number, for the sake of proper order, this operation is performed later:

(3+21):(1+3)1+5=4:41+5 (3+2-1):(1+3)-1+5= \\ 4:4-1+5 In continuation of the principle that division comes before addition and subtraction the division operation is performed first and then the operations of subtraction and addition which were received in the given number and in the last stage:

4:41+5=11+5=5 4:4-1+5= \\ 1-1+5=\\ 5 Therefore the correct answer here is answer B.

3

Final Answer

5 5

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Parentheses first, then multiplication/division, finally addition/subtraction
  • Division Symbol: The colon (:) means divide, so 4:4 = 1
  • Check: Work left to right after parentheses: 1-1+5 = 5 ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring order of operations and working left to right
    Don't calculate (3+2-1):(1+3)-1+5 as 4:4-1+5 = 1-1+5 but then do 4-1 first = wrong result of 8! This skips the division step. Always do parentheses first, then division, then addition/subtraction from left to right.

Practice Quiz

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\( 0+0.2+0.6= \) ?

FAQ

Everything you need to know about this question

What does the colon symbol (:) mean in math?

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The colon (:) means division, just like ÷. So 4:4 4:4 is the same as 4÷4=1 4 ÷ 4 = 1 . It's commonly used in some countries instead of the division symbol.

Why do I solve parentheses before everything else?

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Parentheses have the highest priority in PEMDAS! They tell you exactly what to calculate first. Without solving (3+21) (3+2-1) and (1+3) (1+3) first, you can't do the division step.

Do I work from left to right for addition and subtraction?

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Yes! After handling parentheses and division, work addition and subtraction from left to right. So 11+5 1-1+5 becomes 0+5=5 0+5 = 5 , not 16=5 1-6 = -5 .

What if I get confused about the order?

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Remember PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Write each step clearly and double-check by substituting your final answer back into the original expression.

Can I use a different division symbol instead of the colon?

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Absolutely! You can write it as (3+21)÷(1+3)1+5 (3+2-1) ÷ (1+3) - 1 + 5 or even (3+21)(1+3)1+5 \frac{(3+2-1)}{(1+3)} - 1 + 5 . All three notations mean the same thing.

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