Expressions using Letter-Numbers
Taking one expression away from another
Learn how to subtract one expression from another, using a furniture rental shop.
A shop rents out chairs and tables for a day. You pay ₹40 per chair and ₹75 per table at the start. When you return them, you get back ₹6 per chair and ₹10 per table.
For x chairs and y tables:
- paid at the start: 40x + 75y
- paid back: 6x + 10y
- actually paid: (40x + 75y) − (6x + 10y)
Simplify it step by step:
- The second bracket has a minus in front, so remove it and flip both signs: 40x + 75y − 6x − 10y.
- Put like terms together: (40x − 6x) + (75y − 10y).
- Add each group: 34x + 65y.
So you really pay ₹34 for each chair and ₹65 for each table.
Another way to see it: taking away an expression is the same as adding the opposite of each of its terms: (40x + 75y) + (−6x − 10y).
To subtract one expression from another, change the sign of every term inside the bracket, then collect like terms.
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