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The sum of two rational numbers is −4. If one of them is 25−13, then the other is:
25−87
25−67
25−37
25−47
25−87
Express -4 as a fraction with denominator 25: -4 = -100/25. Then subtract the known number: -100/25 - (-13/25) = (-100 + 13)/25 = -87/25.
Sum of two rational numbers = -4, one number = -13/25
x+y=S⟹y=S−x
Express -4 as a fraction with denominator 25: -4 = -100/25. Then subtract the known number: -100/25 - (-13/25) = (-100 + 13)/25 = -87/25.
Sign errors during subtraction: failing to account for the double negative when subtracting a negative number, i.e., -4 - (-13/25) becomes -4 + 13/25.
Define the equation
Let the unknown number be y. We are given the sum of two numbers, x and y, as −4.
−4=y+(25−13)
Isolate the variable
To find y, move 25−13 to the other side by adding it to −4.
y=−4+2513
Convert to common denominator
Convert −4 into a fraction with denominator 25 by multiplying the numerator and denominator by 25.
−4=25−4×25=25−100
Perform final subtraction
Add the fractions 25−100 and 2513.
y=25−100+13=25−87
A is correct because calculating −4−(−13/25) results in 25−100+13=−87/25.
This concept of finding a missing addend is foundational for basic algebra and solving linear equations in one variable.
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