Determine the value for $m$ in the equation $1.7 m=0.85$.
The problem asks us to solve for the variable \(m\) in the linear equation \(1.7m = 0.85\). We are given a set of options and need to determine which value satisfies the equation. Our objective is to isolate \(m\) by performing algebraic operations.
To isolate the variable \(m\), we divide both sides of the equation by the coefficient of \(m\), which is 1.7. This gives us:
\[m = \frac{0.85}{1.7}\]
To simplify this division, we can multiply both the numerator and the denominator by 100 to remove the decimals:
\[m = \frac{0.85 \times 100}{1.7 \times 100} = \frac{85}{170}\]
We can further simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 85:
\[m = \frac{85 \div 85}{170 \div 85} = \frac{1}{2}\]
Thus, the value of \(m\) is 0.5, which is equivalent to 0.50.
The calculated value \(m = 0.50\) corresponds to the second option provided in the problem. Therefore, the correct value for \(m\) is \(\boxed{0.50}\).
Imagine you are buying specialized fasteners for a home repair project. Each fastener costs \(\$1.70\), and you have a total budget of \(\$0.85\) left in your wallet. By setting up the equation \(1.7m = 0.85\), where \(m\) represents the fraction of a fastener you can afford, you find that \(m = 0.50\). This means you have exactly enough money to buy half of a fastener! This type of simple division is fundamental to managing small budgets and scaling quantities in everyday shopping.