Calculate 19170 ÷ 54 ÷ 5. A. 17 B. 1775 C. 71 D. 1757
C
Understanding the Division Problem
The question asks us to perform a sequence of division operations: calculate $19170 \div 54 \div 5$. When multiple divisions are presented in a row like this, we perform them from left to right.
So, the calculation will involve two steps:
- First, divide $19170$ by $54$.
- Then, divide the result of the first step by $5$.
Step-by-Step Calculation: Dividing 19170 by 54
Let's start by dividing $19170$ by $54$. We can use long division for this step.
Performing the division $19170 \div 54$:
\begin{align*} 54 &\overline{|19170} \\ &-162 \downarrow \quad (54 \times 3 = 162) \\ &\quad \overline{0297} \\ &\quad -270 \downarrow \quad (54 \times 5 = 270) \\ &\quad \overline{0270} \\ &\quad -270 \quad (54 \times 5 = 270) \\ &\quad \overline{0000} \end{align*}
So, $19170 \div 54 = 355$.
Second Step: Dividing the Result by 5
Now we take the result from the first step, which is $355$, and divide it by $5$.
$355 \div 5$
We can perform this division:
- $3$ divided by $5$ is $0$ with a remainder of $3$.
- Combine the remainder $3$ with the next digit $5$ to get $35$.
- $35$ divided by $5$ is $7$.
- Now, divide the last digit $5$ by $5$.
- $5$ divided by $5$ is $1$.
Putting the results together, $355 \div 5 = 71$.
Alternatively, thinking about the structure of $355$:
$355 = 350 + 5$
$(350 + 5) \div 5 = (350 \div 5) + (5 \div 5)$
$350 \div 5 = 70$
$5 \div 5 = 1$
$70 + 1 = 71$.
Final Answer
After performing both divisions, the final result of $19170 \div 54 \div 5$ is $71$.
Comparing this result with the given options:
| Option | Value |
|---|---|
| A | 17 |
| B | 1775 |
| C | 71 |
| D | 1757 |
The calculated value $71$ matches Option C.
Revision Table: Key Concepts in Division
Understanding the order of operations is crucial in mathematics. For a sequence of divisions, work from left to right.
| Concept | Description | Example |
|---|---|---|
| Division | Splitting a number into equal parts. The inverse of multiplication. | $10 \div 2 = 5$ |
| Sequential Division | Performing division operations one after the other from left to right. | $100 \div 10 \div 2 = (100 \div 10) \div 2 = 10 \div 2 = 5$ |
| Dividend | The number being divided. | In $10 \div 2$, $10$ is the dividend. |
| Divisor | The number by which the dividend is divided. | In $10 \div 2$, $2$ is the divisor. |
| Quotient | The result of the division. | In $10 \div 2$, $5$ is the quotient. |
Additional Information: Order of Operations
While division and multiplication are performed from left to right, remember the overall order of operations (often remembered by acronyms like BODMAS or PEMDAS).
- Brackets (or Parentheses)
- Orders (or Exponents)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
In this specific problem, we only have division, so the left-to-right rule is the primary concept applied after identifying there are no brackets or exponents.
Important Questions from Simplification
If P = 0.3 × 0.3 + 0.03 × 0.03 - 0.6 × 0.03 and Q = 0.54, then \(\rm \frac{P}{Q}\) is equal to:
The value of \(\left(\frac{1}{2}\right)^{−2} \times\left(\frac{1}{3}\right)^{−2} \times\left(\frac{1}{4}\right)^{−2} \) is
The solution of the equation \(\frac{2}{3 x-4}+\frac{2}{2 x-6}=0 \) is:
What will come in the place of question mark (?) in the given expression?
\(\sqrt{21+\sqrt{49}+\sqrt{64}} \space {\%\:of\:5000}=?\)
There are 5 tasks and 5 persons. Task-1 cannot be assigned to either person-1 or person-2. Task-2 must be assigned to either person-3 or person-4. Every person is to be assigned one task. In how many ways can the assignment be done?
