Final answer:
Comparing the expressions 40÷4 and 40÷8 without calculating the actual values involves understanding that a larger divisor yields a smaller quotient, meaning 40÷8 will be smaller than 40÷4.
Step-by-step explanation:
To compare the expressions 40÷4 and 40÷8 without computing the exact results, you can analyze the relationship between division and multiplication. Dividing by a larger number results in a smaller quotient. So, because 8 is larger than 4, dividing 40 by 8 will yield a smaller result than dividing 40 by 4. Recognizing the reciprocal nature of division and multiplication is beneficial here, as it tells us that dividing by 8 (40÷8) is the same as multiplying by 1/8, which is less than multiplying by 1/4 (40÷4).