Consider the expression 4 – (-10).
a. Write the expression as an unknown addend equation.
b. What must be added to 10 to get a sum of 4?
c. What is the value of the subtraction expression 4-(-10)? Explain how you know
The correct answer and explanation is:
a. Write the expression as an unknown addend equation:
The expression 4−(−10)4 – (-10) can be written as an unknown addend equation as follows:
4+10=x4 + 10 = x
This is because subtracting a negative number is equivalent to adding the positive of that number. Therefore, 4−(−10)4 – (-10) becomes 4+104 + 10, and the result is represented by xx.
b. What must be added to 10 to get a sum of 4?
To solve this, the equation is:
10+unknown number=410 + \text{unknown number} = 4
To find the unknown number, subtract 10 from both sides:
unknown number=4−10\text{unknown number} = 4 – 10
Thus, the unknown number is −6-6. Therefore, −6-6 must be added to 10 to get a sum of 4.
c. What is the value of the subtraction expression 4−(−10)4 – (-10)? Explain how you know.
The value of the expression 4−(−10)4 – (-10) can be simplified by recognizing that subtracting a negative number is the same as adding the positive of that number.
So, 4−(−10)=4+10=144 – (-10) = 4 + 10 = 14
Thus, the value of 4−(−10)4 – (-10) is 14. This is because subtracting a negative number effectively changes the operation to addition. Therefore, 4+104 + 10 equals 14, and that is the result.