Solve 15÷(2×5): Order of Operations Division Problem

Q: Why can't I just divide 15÷2÷5 from left to right?

The parentheses change everything! They tell you to multiply 2×5 first. Without parentheses, 15÷2÷5 would equal 1.5, but with parentheses, $ 15÷(2×5) = 1\frac{1}{2} $.

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

The colon (:) is another way to write division, just like ÷. So $ 15:(2×5) $ means the same as $ 15÷(2×5) $.

Q: How do I convert my decimal answer to a mixed number?

Since 15÷10 = 1.5, and 0.5 = $ \frac{1}{2} $, your answer becomes $ 1\frac{1}{2} $. The whole number part is 1, and the fractional part is $ \frac{1}{2} $.

Q: Can I write this as a single fraction instead?

Absolutely! You can write $ 1\frac{1}{2} $ as the improper fraction $ \frac{3}{2} $. Both answers are correct - it depends on what format the question asks for.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiplication is also division by reciprocal

00:07 Therefore when opening the parentheses, it will end up as divided by C

00:11 We will use this formula in our exercise

00:17 We will solve according to the order of operations from left to right

00:20 We will write division as a fraction

00:28 Division is also multiplication by reciprocal

00:32 We will make sure to multiply numerator by numerator and denominator by denominator

00:40 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

$15:(2\times5)=$ ?

2

Step-by-step solution

First we need to apply the following formula:

$a:(b\times c)=a:b:c$

Therefore, we get:

$15:2:5=$

Now, let's rewrite the exercise as a fraction:

$\frac{\frac{15}{2}}{5}=$

Then we'll convert it to a multiplication of two fractions:

$\frac{15}{2}\times\frac{1}{5}=$

Finally, we multiply numerator by numerator and denominator by denominator, leaving us with:

$\frac{15}{10}=1\frac{5}{10}=1\frac{1}{2}$

3

Final Answer

$1\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Always solve operations inside parentheses first, then divide
Technique: Calculate 2×5 = 10, then 15÷10 = 1.5
Check: Verify parentheses were handled first: 15÷(2×5) = 15÷10 = 1½ ✓

Common Mistakes

Avoid these frequent errors

Ignoring parentheses and dividing from left to right
Don't calculate 15÷2÷5 = 1.5 by working left to right! This ignores the parentheses and gives the wrong answer. Always solve what's inside parentheses first: 15÷(2×5) = 15÷10 = 1½.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why can't I just divide 15÷2÷5 from left to right?

+

The parentheses change everything! They tell you to multiply 2×5 first. Without parentheses, 15÷2÷5 would equal 1.5, but with parentheses, $15÷(2×5) = 1\frac{1}{2}$ .

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

+

The colon (:) is another way to write division, just like ÷. So $15:(2×5)$ means the same as $15÷(2×5)$ .

How do I convert my decimal answer to a mixed number?

+

Since 15÷10 = 1.5, and 0.5 = $\frac{1}{2}$ , your answer becomes $1\frac{1}{2}$ . The whole number part is 1, and the fractional part is $\frac{1}{2}$ .

Can I write this as a single fraction instead?

+

Absolutely! You can write $1\frac{1}{2}$ as the improper fraction $\frac{3}{2}$ . Both answers are correct - it depends on what format the question asks for.

What if I forgot PEMDAS and got 37½ as my answer?

+

This happens when you multiply 15×2 first, getting 30, then add 5 to get 35, then divide by something. Remember PEMDAS - parentheses come first, so calculate 2×5 = 10 before dividing.

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Solve 15÷(2×5): Order of Operations Division Problem

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