Compute 140 000 Divided by 12
The phrase 140 000 divided by 12 means the quotient \(140{,}000 \div 12\). In math algebra, division can be expressed as a fraction, simplified to an exact form, and then written as a decimal when needed.
Goal: Find the exact value of \(\dfrac{140{,}000}{12}\) and its decimal form.
Step 1: Write the division as a fraction
\[ 140{,}000 \div 12 = \frac{140{,}000}{12} \]
Step 2: Simplify the fraction
Since \(12 = 4 \cdot 3\), divide numerator and denominator by 4:
\[ \frac{140{,}000}{12} = \frac{140{,}000 \div 4}{12 \div 4} = \frac{35{,}000}{3} \]
Exact value: \(\displaystyle \frac{35{,}000}{3}\).
Step 3: Convert to a repeating decimal
Dividing by 3 produces a repeating decimal:
\[ \frac{35{,}000}{3} = 11{,}666.\overline{6} \]
The bar indicates the digit 6 repeats forever.
Step 4: Quotient and remainder form (verification)
Compute a whole-number quotient:
\[ 12 \cdot 11{,}666 = 139{,}992 \]
Subtract to find the remainder:
\[ 140{,}000 - 139{,}992 = 8 \]
Therefore:
\[ 140{,}000 \div 12 = 11{,}666 + \frac{8}{12} = 11{,}666 + \frac{2}{3} = 11{,}666.\overline{6} \]
Summary table
| Form | Value | Notes |
|---|---|---|
| Original division | \(140{,}000 \div 12\) | Given expression |
| Exact fraction | \(\dfrac{35{,}000}{3}\) | Simplified exactly |
| Decimal | \(11{,}666.\overline{6}\) | Repeating decimal |
| Quotient + remainder | \(11{,}666\) remainder \(8\) | \(8/12 = 2/3\) |
Visualization: Division as groups plus remainder
Final answer
\[ 140{,}000 \div 12 = \frac{35{,}000}{3} = 11{,}666.\overline{6} \approx 11{,}666.6667 \]