When we see a minus sign before parentheses, we need to change the sign of every number inside the parentheses. This is an important mathematical rule. For example, 8 minus the quantity 3 plus 2 is not 8 minus 3 plus 2 equals 7. The correct way is 8 minus 3 minus 2 equals 3. Remember: subtract parentheses, change all signs!
Why do we need to change signs? The essence of subtraction is adding the opposite. When we subtract parentheses, we distribute the negative sign to every term inside. Let's see step by step: 9 minus the quantity 4 plus 2. This equals 9 plus the opposite of 4 plus 2. Which becomes 9 plus negative 4 minus 2. Finally, 9 minus 4 minus 2 equals 3.
Here are the sign change rules when subtracting parentheses: plus becomes minus, minus becomes plus, and every number must change! Let's see examples. 7 minus the quantity 3 plus 5 becomes 7 minus 3 minus 5 equals negative 1. Next, 10 minus the quantity 6 minus 2 becomes 10 minus 6 plus 2 equals 6. Finally, 5 minus the quantity negative 3 plus 1 becomes 5 plus 3 minus 1 equals 7.
Let's practice with some problems to see if you've mastered the rule of changing signs when subtracting parentheses. First: 12 minus the quantity 4 plus 5. We change signs: 12 minus 4 minus 5 equals 3. Second: 15 minus the quantity 8 minus 3. We get 15 minus 8 plus 3 equals 10. Third: 6 minus the quantity negative 2 plus 4. This becomes 6 plus 2 minus 4 equals 4. Finally: 20 minus the quantity 7 minus 3 plus 1. We get 20 minus 7 plus 3 minus 1 equals 15.
Let's summarize with a memory chant. When subtracting parentheses, change the signs. Positive becomes negative, negative becomes positive. Every term must change. Calculate carefully to avoid mistakes. Here's our final example: 18 minus the quantity 5 minus 2 plus 3. This becomes 18 minus 5 plus 2 minus 3 equals 12. Remember: practice makes perfect!