Your friend evaluates the expression. Is your friend correct? Explain your reasoning.
$- 4.25 \div 1.7 = 2.5$

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Solution

Step 1: Simplify the given expression
Given $- 4.25 \div 1.7$
Changing the division sign into multiplication,
$\begin{array}{rcl} - 4.25 \div 1.7 & = & - 4.25 \times \frac{1}{1.7} [∵ a \div b = a \times \frac{1}{b}] \end{array}$
Removing the decimals by multiplying with multiple of $10$
$\begin{array}{rcl} \Rightarrow & - 4.25 \div 1.7 = \frac{- 4.25 \times 100}{1.7 \times 100} \\ \Rightarrow & - 4.25 \div 1.7 = \frac{- 425}{170} \end{array}$
Step 2: Use long division method
$170 2.5 425 - 340 850 - 850 0$
The quotient of two integers of opposite signs is negative.
$- 4.25 \div 1.7 = - 2.5$
So, The given calculation by my friend is not correct because he has given a positive quotient $2.5$ .
Although we got the quotient as negative $- 2.5$
Hence, the calculation done by friend is incorrect.

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