Solve the Division Chain: 90÷(139.5÷15.5) Step-by-Step Solution

Q: Why can't I just divide 90 by 139.5 first?

The parentheses tell you the order! You must do $ 139.5 \div 15.5 $ first because it's in parentheses, then use that result to divide 90.

Q: How do I divide decimals like 139.5 ÷ 15.5?

You can use long division or notice that $ 139.5 = 15.5 \times 9 $. Both 139.5 and 15.5 can be thought of as multiples of 15.5 to make the division easier.

Q: Is there a shortcut for this type of problem?

Yes! Remember that $ a \div (b \div c) = a \times \frac{c}{b} $. So $ 90 \div (139.5 \div 15.5) = 90 \times \frac{15.5}{139.5} $, but the step-by-step method is usually clearer.

Q: Why does 139.5 ÷ 15.5 equal exactly 9?

Because $ 15.5 \times 9 = 139.5 $! You can verify: 15.5 × 9 = 15.5 × (10 - 1) = 155 - 15.5 = 139.5.

Step-by-step video solution

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Step-by-step written solution

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1

Understand the problem

$90:(139.5:15.5)=$

2

Step-by-step solution

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

Step 1: Evaluate the expression inside the parentheses: $139.5:15.5$ .
Step 2: Use the result from Step 1 in the outer division operation $90 \div (\text{result from Step 1})$ .

Let's work through each step:

**Step 1:** Compute $139.5 \div 15.5$ .
To divide 139.5 by 15.5, you perform the division as follows: $139.5 \div 15.5 = 9$ This is confirmed through straightforward calculation (or using a calculator for precision).

**Step 2:** Now substitute this result into the next operation.
So, $90 \div 9 = 10$ .

Thus, the solution to the problem $90:(139.5:15.5)$ is $10$ .

3

Final Answer

10

Key Points to Remember

Essential concepts to master this topic

Rule: Always evaluate operations inside parentheses first before outer operations
Technique: Calculate $139.5 \div 15.5 = 9$ then $90 \div 9 = 10$
Check: Verify that $90 \div (139.5 \div 15.5) = 90 \div 9 = 10$ ✓

Common Mistakes

Avoid these frequent errors

Solving from left to right without parentheses
Don't calculate 90 ÷ 139.5 first = 0.645! This ignores the parentheses and gives completely wrong results. Always solve what's inside parentheses first, then use that result in the outer operation.

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 90 by 139.5 first?

+

The parentheses tell you the order! You must do $139.5 \div 15.5$ first because it's in parentheses, then use that result to divide 90.

How do I divide decimals like 139.5 ÷ 15.5?

+

You can use long division or notice that $139.5 = 15.5 \times 9$ . Both 139.5 and 15.5 can be thought of as multiples of 15.5 to make the division easier.

What if I get a different answer using a calculator?

+

Double-check that you're entering the parentheses correctly! Many calculators require you to explicitly show the grouping: 90 ÷ (139.5 ÷ 15.5).

Is there a shortcut for this type of problem?

+

Yes! Remember that $a \div (b \div c) = a \times \frac{c}{b}$ . So $90 \div (139.5 \div 15.5) = 90 \times \frac{15.5}{139.5}$ , but the step-by-step method is usually clearer.

Why does 139.5 ÷ 15.5 equal exactly 9?

+

Because $15.5 \times 9 = 139.5$ ! You can verify: 15.5 × 9 = 15.5 × (10 - 1) = 155 - 15.5 = 139.5.

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Solve the Division Chain: 90÷(139.5÷15.5) Step-by-Step Solution

Order of Operations with Nested Division

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