Solve the Division Chain: 21:(30:10) Step-by-Step Solution

Q: Why do I solve the parentheses first?

The order of operations (PEMDAS/BODMAS) requires you to solve parentheses first! In division chains like $ a:(b:c) $, the colon acts like division, so you must calculate $ (b:c) $ before dividing by a.

Q: What does the formula a:(b:c) = a:b×c mean?

This formula shows that division by a fraction equals multiplication by its reciprocal. When you have $ 21:(30:10) $, it becomes $ 21 \div \frac{30}{10} = 21 \times \frac{10}{30} $.

Q: Can I just work left to right like regular division?

No! Division chains with parentheses are different from simple left-to-right division. You must respect the parentheses. Think of it as $ 21 \div (30 \div 10) $, not $ (21 \div 30) \div 10 $.

Q: How do I know when to use fractions vs decimals?

Both work, but fractions often simplify more cleanly. In this problem, $ \frac{21}{30} = \frac{7}{10} $ makes the final multiplication $ \frac{7}{10} \times 10 = 7 $ very clear!

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

00:16 We will solve according to the order of operations from left to right

00:21 We'll divide by 3, and substitute in our exercise

00:28 We will reduce what we can

00:32 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

$21:(30:10)=$

2

Step-by-step solution

We will use the formula:

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

Therefore, we will get:

$21:30\times10=$

Let's write the division exercise as a fraction:

$\frac{21}{30}=\frac{7}{10}$

Now let's multiply by 10:

$\frac{7}{10}\times\frac{10}{1}=$

We'll reduce the 10 and get:

$\frac{7}{1}=7$

3

Final Answer

$7$

Key Points to Remember

Essential concepts to master this topic

Order Rule: Solve parentheses first, then work left to right
Technique: Convert $21:(30:10)$ to $21:30 \times 10$
Check: Verify $\frac{7}{10} \times 10 = 7$ gives whole number ✓

Common Mistakes

Avoid these frequent errors

Solving left to right without parentheses first
Don't calculate 21:30 = 0.7, then 0.7:10 = 0.07! This ignores the parentheses and gives a completely wrong decimal result. Always solve (30:10) = 3 first, then calculate 21:3 = 7.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I solve the parentheses first?

+

The order of operations (PEMDAS/BODMAS) requires you to solve parentheses first! In division chains like $a:(b:c)$ , the colon acts like division, so you must calculate $(b:c)$ before dividing by a.

What does the formula a:(b:c) = a:b×c mean?

+

This formula shows that division by a fraction equals multiplication by its reciprocal. When you have $21:(30:10)$ , it becomes $21 \div \frac{30}{10} = 21 \times \frac{10}{30}$ .

Can I just work left to right like regular division?

+

No! Division chains with parentheses are different from simple left-to-right division. You must respect the parentheses. Think of it as $21 \div (30 \div 10)$ , not $(21 \div 30) \div 10$ .

How do I know when to use fractions vs decimals?

+

Both work, but fractions often simplify more cleanly. In this problem, $\frac{21}{30} = \frac{7}{10}$ makes the final multiplication $\frac{7}{10} \times 10 = 7$ very clear!

What if I get a different answer than 7?

+

Double-check your order of operations! The most common mistake is calculating $21:30:10$ left to right instead of $21:(30:10)$ . Remember: parentheses first, always!

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Solve the Division Chain: 21:(30:10) Step-by-Step Solution

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