Solve the Expression: 9:(3×2) Using Order of Operations

Order of Operations with Division Notation

9:(3×2)= 9:(3\times2)=

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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 write division as a fraction
00:08 Let's break down 9 into factors 3 and 3
00:14 Let's reduce what we can
00:20 Let's break down 3 into 2 plus 1
00:24 Let's split the fraction into two fractions
00:30 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

9:(3×2)= 9:(3\times2)=

2

Step-by-step solution

We rewrite the expression as a fraction:

93×2= \frac{9}{3\times2}=

We rewrite the numerator as a multiplication expression:

3×33×2= \frac{3\times3}{3\times2}=

We simplify the 3 in the numerator and denominator, obtaining:

32=112=1.5 \frac{3}{2}=1\frac{1}{2}=1.5

3

Final Answer

1.5 1.5

Key Points to Remember

Essential concepts to master this topic
  • Rule: Evaluate operations inside parentheses first, then division
  • Technique: Convert 9:(3×2) 9:(3\times2) to 96 \frac{9}{6} = 1.5
  • Check: Verify 3×2=6 3\times2 = 6 , then 9÷6=1.5 9÷6 = 1.5

Common Mistakes

Avoid these frequent errors
  • Dividing before multiplying inside parentheses
    Don't calculate 9÷3 first to get 3, then multiply by 2 = 6! This ignores the parentheses and order of operations. Always complete operations inside parentheses first, then divide by that result.

Practice Quiz

Test your knowledge with interactive questions

\( 100-(5+55)= \)

FAQ

Everything you need to know about this question

What does the colon (:) mean in math?

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The colon (:) is another way to write division, just like ÷. So 9:(3×2) 9:(3\times2) means 9 divided by (3×2).

Why do I have to do the multiplication first?

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Because of parentheses rules! Whatever is inside parentheses must be calculated first. So you need 3×2=6 3\times2 = 6 before you can divide 9 by that result.

Can I write the answer as a fraction instead of decimal?

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Absolutely! 1.5=32=112 1.5 = \frac{3}{2} = 1\frac{1}{2} are all correct ways to express the same answer. Use whichever form your teacher prefers!

What if I forgot PEMDAS and did it left to right?

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You'd get the wrong answer! Going left to right: 9÷3=3 9÷3 = 3 , then 3×2=6 3×2 = 6 . But the correct answer following PEMDAS is 1.5.

How do I remember to do parentheses first?

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  • Think of parentheses as "do me first!" signals
  • Use PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
  • Always scan for parentheses before starting any problem

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