Solve the Sequential Division: 10:(10:5) Step-by-Step Solution

Order of Operations with Nested Division

10:(10:5)= 10:(10:5)=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Division is also multiplication by the reciprocal
00:07 Therefore when opening the parentheses, it will end up multiplied by C
00:11 We will use this formula in our exercise
00:17 A number divided by itself is always equal to 1
00:21 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

10:(10:5)= 10:(10:5)=

2

Step-by-step solution

To solve the expression 10:(10:5) 10 : (10 : 5) , we will apply the order of operations systematically.

Step 1: Evaluate the inner division 10:5 10 : 5 .
When we compute 10:5 10 : 5 , we are finding how many times 5 fits into 10. This calculation can be expressed as:
105=2 \frac{10}{5} = 2 .

Step 2: Substitute the result from step 1 into the outer division.
Now, we substitute 10:(10:5) 10 : (10 : 5) with 10:2 10 : 2 . Once again, we apply division:
102=5 \frac{10}{2} = 5 .

Therefore, the solution to the expression 10:(10:5) 10 : (10 : 5) is 5 5 .

3

Final Answer

5 5

Key Points to Remember

Essential concepts to master this topic
  • Parentheses First: Always solve operations inside parentheses before outside operations
  • Technique: Calculate 10:5=2 10 : 5 = 2 , then 10:2=5 10 : 2 = 5
  • Check: Substitute back: 10:(2)=5 10 : (2) = 5 matches our answer ✓

Common Mistakes

Avoid these frequent errors
  • Calculating from left to right without considering parentheses
    Don't solve 10 : 10 : 5 left to right = 0.2! This ignores the parentheses which change the order completely. Always solve what's in parentheses first, then work outward.

Practice Quiz

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

FAQ

Everything you need to know about this question

Why can't I just solve 10 : 10 : 5 from left to right?

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The parentheses change everything! 10:(10:5) 10:(10:5) means you must solve 10:5 10:5 first, then divide 10 by that result. Without parentheses, you'd get a completely different answer.

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

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The colon (:) is another way to write division, just like the ÷ symbol. So 10:5 10:5 means the same as 10÷5 10 ÷ 5 or 105 \frac{10}{5} .

How do I remember to do parentheses first?

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Think PEMDAS (Please Excuse My Dear Aunt Sally)! Parentheses always come first, before any other operations like multiplication or division.

What if there are multiple sets of parentheses?

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Work from the innermost parentheses outward. Solve the deepest nested operations first, then gradually work your way to the outside operations.

Can I rewrite this using fraction notation?

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Absolutely! 10:(10:5) 10:(10:5) becomes 10105 \frac{10}{\frac{10}{5}} . When dividing by a fraction, multiply by its reciprocal: 10×510=5 10 \times \frac{5}{10} = 5 .

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