Fill in each blank with an integer (signed number). (a) -5 - 3 = -5 + ___ (b) -1 - (-7) = -1 + ___
Understand the Problem
The question is asking to fill in the blanks with integers to complete the equations provided in parts (a) and (b). Each equation involves operations with signed numbers.
Answer
(a) $-3$, (b) $7$
Answer for screen readers
(a) -3
(b) 7
Steps to Solve
- Solve equation (a)
Start with the equation: $$ -5 - 3 = -5 + \Box $$
Calculate the left-hand side: $$ -5 - 3 = -8 $$
Set up the equation: $$ -8 = -5 + \Box $$
Now, solve for the blank: $$ \Box = -8 + 5 $$ $$ \Box = -3 $$
- Solve equation (b)
Start with the equation: $$ -1 - (-7) = -1 + \Box $$
Calculate the left-hand side: $$ -1 - (-7) = -1 + 7 = 6 $$
Set up the equation: $$ 6 = -1 + \Box $$
Now, solve for the blank: $$ \Box = 6 + 1 $$ $$ \Box = 7 $$
(a) -3
(b) 7
More Information
In equation (a), when subtracting, we find that subtracting 3 from -5 gives us -8. To balance the equation, we need to add -3. In equation (b), subtracting a negative number is equivalent to adding its positive counterpart, hence -1 - (-7) equals 6.
Tips
- Confusing the operation of subtracting a negative number; remember that $-a - (-b) = -a + b$.
- Miscalculating the left-hand side of the equations. Always double-check arithmetic.
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