Yes, your friend is correct. The relationship between addition and subtraction allows us to use the known addition fact 4+7=11 to find 11−3. These operations are inverses of each other, and exploiting this relationship can simplify problem-solving.
To understand this, consider the fact that addition and subtraction are opposite operations. When you add a number to another and then subtract the same number, you return to the original value. In this case, 4+7=11, and if you subtract 3 from 11 (11−3), you are essentially undoing the addition of 3. It's like saying, "I had 11, and then I took away 3."
This concept aligns with the associative property of addition, which states that the way in which numbers are grouped in an addition expression does not affect the sum. Therefore, 4+(7−3) is equivalent to (4+7)−3.
So, using the fact 4+7=11, you can think of 11−3 as 4+7−3, which is equal to 11. Therefore, your friend is correct in using the addition fact 4+7=11 to help find 11−3. This understanding not only demonstrates mathematical proficiency but also highlights the interconnected nature of mathematical operations.
Complete question
Your friend says he can use the addition fact 4+7=11 to help find 11-3. is your friend correct? Explain your answer.