First algebra and simple equations · Usually met around P5
Terms, coefficients and simplifying
Like terms: add the coefficients, keep the letter.
How to do it
Method
Like terms: add the coefficients, keep the letter
y + y + y = 3y; 2a + 3 + 4a + 1 = 6a + 4
Another way
Check with a number
a = 2: 2a + 4a = 12, 6a = 12
In full
In an algebraic expression, each part separated by + or − is a term: 3a + 5 has two terms, 3a and 5. The number in front of a letter is its coefficient: in 3a the coefficient of a is 3, and a on its own has coefficient 1. Terms with the same letter are like terms and can be combined: y + y + y is 3 lots of y, written 3y; 5b + 2b = 7b and 6m − m = 5m. Add or take away the coefficients and keep the letter. Number terms are combined on their own: 2a + 3 + 4a + 1 = 6a + 4. Terms with different letters can't be combined: 2a + 3b is already as simple as it gets. Another way: check by putting in a number. When a = 2, 2a + 4a = 4 + 8 = 12 and 6a = 6 × 2 = 12, the same.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
3 lots of y added: y + y + … + y = □y
Show the answer and working
Answer: 3
Each y has coefficient 1; 3 lots of y is 3 × y, written 3y.
Example 2
In the expression 11m + 11, the coefficient of m is □.
Show the answer and working
Answer: 11
The number in front of the letter is its coefficient: in 11m it is 11. 11 is a number term.
Example 3
9y + 2 + 5y simplifies to 16y + 2.
True or false?
Show the answer and working
Answer: False
The y terms: 9y + 5y = 14y. The number term 2 can't join them: 14y + 2.
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