Consider the following expressions
`10-\frac{2}{5}\cdot35-4\ \frac{2}{5}`______`\frac{3}{5}+8\cdot7-1`
To evaluate the expressions, we need to follow the order of operations (also known as PEMDAS - Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
For the first expression:
1. Simplify the multiplication: $\frac{2}{5} \cdot 35 = 14$
2. Simplify the subtraction: $10 - 14 = -4$
3. Convert the mixed number to an improper fraction: $4\ \frac{2}{5} = \frac{22}{5}$
4. Simplify the subtraction: $-4 - \frac{22}{5} = -\frac{42}{5}$
So, the first expression simplifies to $-\frac{42}{5}$.
For the second expression:
1. Simplify the multiplication: $8 \cdot 7 = 56$
2. Simplify the addition: $\frac{3}{5} + 56 = \frac{3+280}{5} = \frac{283}{5}$
So, the second expression simplifies to $\frac{283}{5}$.
Therefore, the simplified expressions are:
$10-\frac{2}{5}\cdot35-4\ \frac{2}{5}$ simplifies to $-\frac{42}{5}$.
$\frac{3}{5}+8\cdot7-1$ simplifies to $\frac{283}{5}$.