Simple Algebra 1 – Add, Subtract, Multiply, Divide
April 27, 2012 4 Comments
SIMPLE ALGEBRAIC TERMS AND EXPRESSIONS
Give a week or two to students to learn and understand Algebraic terminology. Must avoid teaching signs until students are able to read and explain Algebraic terms and expressions properly.
1- What is a
consonant constant in Algebra is a known value, a quantity that does not change unless a mathematical operation is applied. Any number, fraction, pi π are consonants constants.
For example, 1, 2, 3/4, 2/5, π
2 – What is a variable?
A variable is a symbol, which is represented by any small letter, that stands for an unknown value.
For example, a b x y z
3- What is a Coefficient?
A number right before a variable is called a coefficient. Any variable with no number has 1 as a coefficient.
For example, in 2 x, 2 is the coefficient of variable x
4- What is an Algebraic term?
A term could be a
consonant constant or a variable that is a part of an Algebraic expression.
For example, 2 x + 3 y is an Algebraic expression and 2 x and 3 y are terms.
5- What is an expression?
Two or more terms make up an expression.
For example, 2 a + 3b – c or xy – 5xy + 4
6- What is an exponent?
An exponent is the power of a
consonant constant or a variable. It is represented by a small number on top side of a consonant constant or a variable. This number as an exponent shows that the consonant constant or variable is multiplied to itself that many times.
For example, x2 y2 x3 y3 x4 y4 x5 y5 — 2, 3, 4, 5 on top of x and y are the exponent or power of x and y.
x2 = (x) (x) – read as x square (means x is multiplied twice)
y3 = (y) (y) (y) – read as y cube (means y is multiplied three times)
25 = (2) (2) (2) (2) (2) – read as 2 to the power of 5 (means 2 is multiplied 5 times)
7- How should students read powers?
x y – x and y – their power is 1 (which is not written or read as 1)
x2 y2 – x square, y square (reading this term as x2 is wrong)
x3 y3 – x cube, y cube (reading this term as x3 or y3 is wrong)
x4 y4 –
4 to the power of x x to the power of 4 and 4 to the power of y y to the power of 4 (shouldn’t be read as x4 or y4)
x10 y10 –
10 to the power of x x to the power of 10 and 10 to the power of y y to the power of 10
8a- What is a term?
A term is a constant or a variable written separate or together.
For example, 5 a2 b2c2 – 2a3 b2c
8b- What is an expression?
An expression is a combination of two or more terms.
For example, 2x2 + 2y2 a2 – b2 3a2 + b2 – 1
8c- What are like terms?
Same variables having same powers in an expression are called “like-terms”. Like terms can have different co-efficient. Only like terms can be added or subtracted. Adding or subtracting terms means their coefficients are added or subtracted, not powers.
a2 + 4a2 2ab3 + 8ab3 5a2 b2c2 – a2 b2c2 – are like terms
so they can be added or subtracted,
a2 + 4a2 = 5a2 2ab3 + 8ab3 = 10ab3 5a2 b2c2 – a2 b2c2 = 4a2 b2c2
9- What happens when the terms are not like-terms?
Terms that are not like (have different variable or powers) cannot be added or subtracted.
a3 + 4a2 =
5a2 terms are not like because variables are same but powers are different
2ab3c + 8ab3 =
10ab3c terms are not like because variables are different
5a3 b2c – a2 b + c2 = not possible because powers and variables are different
10- When are powers added or subtracted?
Powers of a number or a variable are added in multiplication and subtracted in division. The parenthesis ) and ( are used as a sign of multiplication. Slash / is used as a sign of division. Only the powers of same variables are added or subtracted. The coefficients of same variables are multiplied or divided beside adding or subtracting powers. The coefficients of different variables cannot be multiplied or divided.
(x2 ) (x3 ) = (x2+3) = x5 (x2y2) (x4y5z3) = (x2+4 y2+5 z3) = x6 y7 z3
(3x2 ) (4x3 ) = (12x2+3) = 12 x5 — 3 and 4 are multiplied while the powers of x are added
(x2 ) (y3 ) = (xy2+3) =
xy5 powers of two different variables cannot be added
(x5 / 3 ) = (x5 – 3) = x2 (x6y9/ x4y5z3) = (x6- 4 y9 – 5 z3) = x2 y4 z3
(15x4 / 3x3 ) = (5x4 – 3) = 5x — 15 is divided by 3 while the powers of x are subtracted
(x5 ) (y3 ) = (xy5 – 3) =
xy2 powers of two different variables cannot be subtracted
READING, EXPLAINING AND RE-WRITING ALGEBRAIC TERMS
82 read as eight square m2 read as m sqaure (not m two) 4a2 read as four a square (not 4 a two)
x2 + y2 read as x square plus y square (not as x two and y two or x square and y square)
3a4 – 2b3 read as three a to the power of four minus two b cube
(x2) (y2) read as x square multiplied by y square
(x3y3/ x3y5z3) read as x cube y cube divided by x cube, y to the power of 5, z cube
82 – This is an algebraic term in which, 8 is the number, two is it’s exponent or power, which shows that 8 is being multiplied two times (8 x 8)
m3 – This is an algebraic term in which, m is the variable, 3 is it’s power, which shows that m is being multiplied three times (m x m x m)
4a2 – This is an algebraic term in which, 4 is coefficient, a is the variable and 2 is the power of a, which shows that a is being multiplied twice.
x2 + y2 This is an algebraic expression in which, the first term x square is added to the second term y square.
3a4 – 2b3 This is an algebraic expression in which, the first term has 3 as a coefficient, a as a variable and 4 as it’s power and the second term has 2 as coefficient, b as a variable and 3 as it’s power. Two b cube is to be subtracted from three a to the power of 4.
(x2) (y2) – This is an algebraic expression in which, x square is multiplied to y square.
(x3y3/ x3y5z3) – This is an algebraic expression in which, x cube y cube are divided by x cube, y to the power of 5, z cube.
Re-writing Algebraic Terms:
1) a-2 —— any power with minus sign shows that the term is a denominator, it is written as 1/a2
2) xa+1 —— a+1 as power shows that the two terms xa and x are multiplied together,
so they can be written as x(xa) or (x) (xa)
similarly, x4+2 = (x4) (x2)
3) xa-1 —— a – 1 as power shows that the two terms xa and x are divided and can be written as xa/x
similarly, w7 – 5 = w7 / w5
4) x0 —— zero as a power shows that two like-terms are being divided,
it can be written as x /x because x/x = x1-1 = 0
The answer of x0 or x/x is 1. Any number or variable with zero power equals 1.