Solve Mixed Number Division: 10(70/560) Step-by-Step

To solve the problem of converting $10 \frac{70}{560}$ to a decimal, follow these steps:

• Step 1: Simplify the fraction $\frac{70}{560}$.
• Step 2: Convert the simplified fraction to a decimal.
• Step 3: Combine the result with the integer part 10.

Now, let's work through each step:

Step 1: Simplify $\frac{70}{560}$.
To simplify, find the greatest common divisor (GCD) of 70 and 560, which is 70.
Divide both the numerator and the denominator by 70:
$\frac{70}{560} = \frac{70 \div 70}{560 \div 70} = \frac{1}{8}$

Step 2: Convert $\frac{1}{8}$ to a decimal.
$\frac{1}{8} = 0.125$

Step 3: Add 10 to the decimal fraction obtained.
Therefore, $10 + 0.125 = 10.125$.

The decimal representation of $10 \frac{70}{560}$ is $\textbf{10.125}$.