Summary of Algebra 1 – Add, Subtract, Multiply, Divide
– In addition and subtraction, we only add or subtract coefficient, not powers.
– In multiplication, we multiply coefficients and add the powers of variables.
– In division, we divide coefficients and subtract powers of variables.
The previous post was about the basic Algebraic terms and normal mathematical operations.
This post is about how mathematical signs work in Algebra and how should students read them.
1- What are signs?
In Maths, numbers, terms and values are either negative ( – ) or positive ( + ).
2- How are plus and minus signs read in Algebra?
Any term with plus sign (+) is positive and minus sign (-) is negative. If sign is not written there, it means the term is positive.
+ 5a2 is positive five a square – a2 b2 is negative a square b square
Similarly, in, 2x2 – 3y2 , 2x2 is positive and 3y2 is negative
3- What are the results or answers of mathematical operations called?
– The answer of addition is called the ‘sum’.
– The answer of subtraction is called the ‘difference’.
– The answer of multiplication is called the ‘product’.
– The answer of division is called the ‘quotient’.
4- What are the rules for adding and subtracting like-terms?
There are some rules about using mathematical signs in Algebra.
1- The sum of two positive like-terms is always positive.
For example, 12x2 + 13x2 = 25x2
2- The sum of two negative like-terms is always negative.
For example, – 15a3 – 10a3 = – 25a3
3- The difference or result of one positive and one negative term carries the sign of bigger coefficient.
For example, 14x2 – 11x2 = 3x2 and 9x2 – 16x2 = – 7x2
4- The sum of one positive and one negative like terms with the same coefficient equals zero.
For example, 5a2 – 5a2 = 0
This is the same simple mathematical concept, you have 5 candies, you eat them all, you are left with nothing. So, having 5 candies is positive, eating 5 candies is negative and the result is zero.
5- What are the rules for multiplying and dividing terms?
1- The product of two positive terms is always positive.
For example, (14x2) (2x) = 28x3 coefficients are multiplied, powers are added
2- The product of two negative terms is positive too.
For example, (- 9y2) (- 4y5) = 36y7 coefficients are multiplied, powers are added
3- The product of one positive and one negative term is negative.
For example, (- 8b3) (7b) = – 56b4 coefficients are multiplied, powers are added
4- Like in Math, the product of any term multiplied by zero would be zero.
For example, (5a2 b2c2) ( 0 ) = 0
5– The quotient of two positive terms is always positive.
For example, 8a7 / 4a2 = 2a5 coefficients are divided and powers are subtracted
6– The quotient of two negative terms is positive.
For example, – 16x3 / – 4x = – 4x2
7– The quotient of one negative and one positive terms is negative.
For example, – 15c5 / 3c2 = – 5c3