Let's solve the given mathematical expression step-by-step, ensuring clarity at each stage.
The expression is:
[tex]\[ 4 + 7 \div 7 + 8 \div 2^2 - 10 \][/tex]
We will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
1. Evaluate the division and exponentiation first:
[tex]\[ 7 \div 7 = 1 \][/tex]
[tex]\[ 2^2 = 4 \][/tex]
[tex]\[ 8 \div 4 = 2 \][/tex]
2. Substitute these values back into the expression:
[tex]\[ 4 + 1 + 2 - 10 \][/tex]
3. Perform the addition and subtraction from left to right:
[tex]\[ 4 + 1 = 5 \][/tex]
[tex]\[ 5 + 2 = 7 \][/tex]
[tex]\[ 7 - 10 = -3 \][/tex]
Therefore, the final result of the expression [tex]\( 4 + 7 \div 7 + 8 \div 2^2 - 10 \)[/tex] is:
[tex]\[ \boxed{-3} \][/tex]
