Solve: 210 ÷ (5.25 × 4) - Complete Order of Operations Challenge

Q: Why do I have to do the multiplication first if division comes before multiplication in PEMDAS?

Great question! The parentheses change everything. PEMDAS says parentheses come first, so you must calculate $ 5.25 \times 4 $ before any division. Without parentheses, you'd work left to right.

Q: How do I multiply 5.25 × 4 without a calculator?

Think of 5.25 as 5¼! You can calculate: $ 5 \times 4 = 20 $ and $ 0.25 \times 4 = 1 $, then add: $ 20 + 1 = 21 $.

Q: What if I forgot the parentheses and worked left to right?

Without parentheses, $ 210 ÷ 5.25 \times 4 $ would equal 160 (working left to right). But the parentheses are there for a reason - they completely change the order!

Q: How can I check if 10 is the right answer?

Substitute back! If the answer is 10, then $ 10 \times (5.25 \times 4) $ should equal 210. Calculate: $ 10 \times 21 = 210 $ ✓

Q: Is there a trick to remember the order of operations?

Use PEMDAS: Please Excuse My Dear Aunt Sally. Parentheses first, then Exponents, then Multiplication/Division (left to right), then Addition/Subtraction (left to right).

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 divided by C

00:11 We will use this formula in our exercise

00:15 We'll solve according to the order of operations from left to right

00:27 We'll convert from number to number and fraction

00:33 We'll convert to fraction

00:40 Division is also multiplication by the reciprocal

00:45 Divide 210 by 21

00:50 We'll substitute in our exercise and continue solving

00:53 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

$210:(5.25\times4)=$

2

Step-by-step solution

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

Step 1: Calculate the product of 5.25 and 4.
Step 2: Divide 210 by the result from Step 1.

Now, let's work through each step:
Step 1: Calculate $5.25 \times 4$ .
$5.25 \times 4 = 21$

Step 2: Divide 210 by the result from Step 1.
$\frac{210}{21} = 10$

Therefore, the solution to the problem is $10$ .

3

Final Answer

10

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Always solve expressions inside parentheses first
Technique: Calculate $5.25 \times 4 = 21$ before dividing
Check: Verify $210 \div 21 = 10$ by multiplying $10 \times 21 = 210$ ✓

Common Mistakes

Avoid these frequent errors

Dividing 210 by 5.25 first instead of following order of operations
Don't calculate 210 ÷ 5.25 first = 40, then multiply by 4 = 160! This ignores the parentheses which must be solved first. Always complete operations inside parentheses before any other calculations.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why do I have to do the multiplication first if division comes before multiplication in PEMDAS?

+

Great question! The parentheses change everything. PEMDAS says parentheses come first, so you must calculate $5.25 \times 4$ before any division. Without parentheses, you'd work left to right.

How do I multiply 5.25 × 4 without a calculator?

+

Think of 5.25 as 5¼! You can calculate: $5 \times 4 = 20$ and $0.25 \times 4 = 1$ , then add: $20 + 1 = 21$ .

What if I forgot the parentheses and worked left to right?

+

Without parentheses, $210 ÷ 5.25 \times 4$ would equal 160 (working left to right). But the parentheses are there for a reason - they completely change the order!

How can I check if 10 is the right answer?

+

Substitute back! If the answer is 10, then $10 \times (5.25 \times 4)$ should equal 210. Calculate: $10 \times 21 = 210$ ✓

Is there a trick to remember the order of operations?

+

Use PEMDAS: Please Excuse My Dear Aunt Sally. Parentheses first, then Exponents, then Multiplication/Division (left to right), then Addition/Subtraction (left to right).

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Solve: 210 ÷ (5.25 × 4) - Complete Order of Operations Challenge

Order of Operations with Decimal Multiplication

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