Solve Mixed Operations: 10:2 - 2² Step by Step

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

The colon (:) is another way to write division, just like the ÷ symbol. So $ 10:2 $ means $ 10 ÷ 2 = 5 $.

Q: Why do I calculate the exponent before division?

According to PEMDAS/BODMAS rules, exponents (powers) come before multiplication and division. This ensures everyone gets the same answer when solving math problems!

Q: What if I calculated left to right and got 9?

That's a common mistake! If you did $ 10:2 = 5 $, then $ 5-2 = 3 $, then $ 3^2 = 9 $, you ignored order of operations. Always calculate exponents first!

Q: How can I remember the correct order?

Use PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) or BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction). Both remind you that exponents come before other operations!

Q: Are there any parentheses in this problem?

No, there are no parentheses in $ 10:2-2^2 $. That's why we start with the exponent $ 2^2 $, which is the highest priority operation present.

Order of Operations with Division Notation

$10:2-2^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 Calculate the exponent

00:08 Always solve multiplication and division before addition and subtraction

00:16 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$10:2-2^2=$

Step-by-step solution

The given mathematical expression is $10:2-2^2$ .

According to the order of operations (often remembered by the acronym PEMDAS/BODMAS), we perform calculations in the following sequence:

Parentheses/Brackets
Exponents/Orders (i.e., powers and roots)
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

In this expression, there are no parentheses, but there is an exponent: $2^2$ . We calculate the exponent first:

$2^2 = 4$

Substituting back into the expression, we have:

$10:2-4$

Next, we perform the division from left to right. Here, $":"$ is interpreted as division:

$10 \div 2 = 5$

Now, substitute this back into the expression:

$5 - 4$

The final step is to perform the subtraction:

$5 - 4 = 1$

Therefore, the answer is $1$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Follow PEMDAS/BODMAS order: Exponents first, then Division, then Subtraction
Technique: Calculate $2^2 = 4$ , then $10:2 = 5$ , finally $5-4 = 1$
Check: Verify each step follows correct order: exponents → division → subtraction = 1 ✓

Common Mistakes

Avoid these frequent errors

Calculating operations from left to right without considering order
Don't solve $10:2-2^2$ as $5-2^2$ then $3^2 = 9$ ! This ignores that exponents must be calculated before subtraction. Always complete exponents first, then division, then subtraction following PEMDAS/BODMAS order.

Practice Quiz

Test your knowledge with interactive questions

What is the result of the following equation?

$36-4\div2$

FAQ

Everything you need to know about this question

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

The colon (:) is another way to write division, just like the ÷ symbol. So $10:2$ means $10 ÷ 2 = 5$ .

Why do I calculate the exponent before division?

According to PEMDAS/BODMAS rules, exponents (powers) come before multiplication and division. This ensures everyone gets the same answer when solving math problems!

What if I calculated left to right and got 9?

That's a common mistake! If you did $10:2 = 5$ , then $5-2 = 3$ , then $3^2 = 9$ , you ignored order of operations. Always calculate exponents first!

How can I remember the correct order?

Use PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) or BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction). Both remind you that exponents come before other operations!

Are there any parentheses in this problem?

No, there are no parentheses in $10:2-2^2$ . That's why we start with the exponent $2^2$ , which is the highest priority operation present.

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