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
Simplify the following expression.
\(\left(\frac{7}{16} \div \frac{1}{2}\:of\: \frac{1}{5}\right)\times \frac{4}{5}-\frac{1}{3}\times\frac{5}{8}\div \frac{1}{2}+\frac{3}{4}\)
The value of \(\left( {2\frac{6}{7}of4\frac{1}{5} \div \frac{2}{3}} \right) \times 5\frac{1}{9} \div \left( {\frac{3}{4} \times 2\frac{2}{3}of\frac{1}{2} \div \frac{1}{4}} \right)\) is:
The value of \(\left[ {\frac{4}{7}\rm \;of\;2\frac{4}{5} \times 1\frac{2}{3} - \left( {3\frac{1}{2} - 2\frac{1}{6}} \right)} \right] \div \left( {3\frac{1}{5} \div 4\frac{1}{2}\;\rm of\;\;5\frac{1}{3}} \right)\) is:
The value of \(\frac{{0.0203 \times 2.92}}{{0.7 \times 0.0365 \times 2.9}} \div \frac{{{{\left( {12.12} \right)}^2} - {{\left( {8.12} \right)}^2}}}{{{{\left( {0.25} \right)}^2} + \left( {0.25} \right)\left( {19.99} \right)}}\) is:
The value of 4 ÷ 12 of [3 ÷ 4 of {(4 - 2) × 6 ÷ 2}] - 2 × 6 ÷ 8 + 3 is:
