Solve Sequential Division: 500÷(2000÷25) Step-by-Step

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

Mathematical expressions follow the order of operations (PEMDAS)! Operations in parentheses must be calculated first. Solving left to right would give $ \frac{1}{100} $ instead of $ 6\frac{1}{4} $.

Q: How do I convert 6.25 to a mixed number?

Since 6.25 = 6 + 0.25, and 0.25 = $ \frac{1}{4} $, we get $ 6\frac{1}{4} $. Remember that 0.25 always equals one-fourth!

Q: What if I get confused by the division symbols?

The colon (:) means the same as ÷. Think of it as 500 ÷ (2000 ÷ 25). The parentheses show you exactly what to calculate first.

Q: Can I use a calculator for this?

Yes! But be careful with the order of operations. Calculate 2000÷25=80 first, then 500÷80. Don't try to enter the whole expression at once unless you're sure about parentheses.

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, in the end it will be multiplied by C

00:11 We will use this formula in our exercise

00:15 We will solve according to the order of mathematical operations from left to right

00:22 We will write division as a fraction

00:25 We will reduce zeros and calculate

00:34 We will substitute in our exercise and continue solving

00:38 Make sure to multiply numerator by numerator and denominator by denominator

00:44 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

$500:(2000:25)=$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Calculate $2000 \div 25$ .
Step 2: Calculate $500 \div (\text{result from Step 1})$ .

Let's work through each step:

Step 1: Calculate $2000 \div 25$ .

$2000 \div 25$ can be calculated as follows:

Divide 2000 by 25:

$2000 \div 25 = 80$

Step 2: Use the result from Step 1 to perform the division with 500.

Now, calculate $500 \div 80$ .

$500 \div 80 = \frac{500}{80} = \frac{25}{4} = 6.25$

Finally, $6.25$ can be expressed as a mixed number:

$6\frac{1}{4}$

Therefore, the solution to the problem is $6\frac{1}{4}$ .

3

Final Answer

$6\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Order Rule: Always solve operations inside parentheses first
Technique: Calculate 2000÷25=80, then 500÷80=6.25
Check: Verify 80×6.25=500 and 25×80=2000 ✓

Common Mistakes

Avoid these frequent errors

Solving from left to right without parentheses
Don't calculate 500÷2000 first = 0.25, then divide by 25 = 0.01! This ignores order of operations and gives completely wrong results. Always solve the parentheses (2000÷25) first, then use that result.

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 solve from left to right?

+

Mathematical expressions follow the order of operations (PEMDAS)! Operations in parentheses must be calculated first. Solving left to right would give $\frac{1}{100}$ instead of $6\frac{1}{4}$ .

How do I convert 6.25 to a mixed number?

+

Since 6.25 = 6 + 0.25, and 0.25 = $\frac{1}{4}$ , we get $6\frac{1}{4}$ . Remember that 0.25 always equals one-fourth!

What if I get confused by the division symbols?

+

The colon (:) means the same as ÷. Think of it as 500 ÷ (2000 ÷ 25). The parentheses show you exactly what to calculate first.

Can I use a calculator for this?

+

Yes! But be careful with the order of operations. Calculate 2000÷25=80 first, then 500÷80. Don't try to enter the whole expression at once unless you're sure about parentheses.

Why is my answer different from the choices?

+

Double-check that you solved the parentheses first! The most common error is calculating $500÷2000$ first, which leads to wrong answers like $\frac{1}{100}$ .

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Solve Sequential Division: 500÷(2000÷25) Step-by-Step

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