# Simple Algebra 1 – Add, Subtract, Multiply, Divide

April 27, 2012 4 Comments

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**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.

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1- **What is a consonant constant?**

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

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**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*

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**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*

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**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

*and*

*x**3*

*y*are terms.

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**5- What is an expression?**

Two or more terms make up an expression.

For example, 2 *a* + 3*b* – c or *xy* – 5*xy* + 4

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**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, *x ^{2 }y^{2 }*

*x*

^{3 }y^{3 }*x*

^{4 }y^{4 }*x*— 2, 3, 4, 5 on top of x and

^{5 }y^{5 }*y*are the exponent or power of x and y.

*x ^{2 }*= (

*x*) (

*x*) – read as

*x*square (means

*x*is multiplied twice)

*y ^{3}* = (

*y*) (

*y*) (

*y*) – read as

*y*cube (means

*y*is multiplied three times)

*2 ^{5}* = (

*2*) (

*2*) (

*2*) (

*2*) (

*2*) – read as 2 to the power of 5 (means 2 is multiplied 5 times)

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**7- How should students read powers?**

*x y* – *x* and *y* – their power is 1 (which is not written or read as 1)

*x ^{2 }y^{2}* – x square, y square (reading this term as

*x2*is wrong)

*x ^{3 }y^{3}* – x cube, y cube (reading this term as

*x*3 or

*y*3 is wrong)

*x ^{4 }y^{4}* –

*x*4 or

*y*4)

*x ^{10 }y^{10}* –

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**8a- What is a term?**

A term is a constant or a variable written separate or together.

For example, 5 *a*^{2} *b*^{2}*c*^{2 }– 2*a*^{3} *b*^{2}*c*

**8b- What is an expression?**

An expression is a combination of two or more terms.

For example, 2*x*^{2} + 2*y*^{2} *a*^{2} – *b*^{2 } 3*a*^{2} + *b*^{2} – 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.

For example,

*a*^{2} + 4*a*^{2} 2*ab*^{3} + 8a*b*^{3} 5*a*^{2} *b*^{2}*c*^{2 }– *a*^{2} *b*^{2}*c*^{2} – are like terms

so they can be added or subtracted,

*a*^{2} + 4*a*^{2} = 5*a*^{2} 2*ab*^{3} + 8a*b*^{3 }= 10a*b*^{3} 5*a*^{2} *b*^{2}*c*^{2 }– *a*^{2} *b*^{2}*c*^{2 }= 4*a*^{2} *b*^{2}*c*^{2}

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**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.

*a*^{3} + 4*a*^{2} = ~~5~~ terms are not like because variables are same but powers are different*a*^{2}

2*ab*^{3}c + 8a*b*^{3 }=~~ 10a~~ terms are not like because variables are different*b*^{3}c

5*a*^{3} *b*^{2}*c*^{ }– *a*^{2} *b* + *c*^{2 }= not possible because powers and variables are different

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**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.

For example,

MULTIPLICATION:

(*x ^{2}* ) (

*x*) = (

^{3}*x*) =

^{2+3}*x*

*(*

^{5}*x*

^{2}*y*) (

^{2}*x*

^{4}*y*

^{5}*z*) = (

^{3}*x*

^{2+4 }*y*

^{2+5 }*z*) =

^{3}*x*

^{6 }*y*

^{7 }*z*

^{3}(3*x ^{2}* ) (4

*x*) = (12

^{3}*x*) = 12

^{2+3}*x*

*— 3 and 4 are multiplied while the powers of*

^{5}*x*are added

(*x ^{2}* ) (

*y*) = (

^{3}*xy*) =

^{2+3}*xy*

^{5}DIVISION:

(*x ^{5}* /

*) = (*

^{3}*x*) =

^{5 – 3}*x*

*(*

^{2}*x*

^{6}*y*/

^{9}*x*

^{4}*y*

^{5}*z*) = (

^{3}*x*

^{6- 4 }*y*

^{9 – 5 }*z*) =

^{3}*x*

^{2 }*y*

^{4 }*z*

^{3}(15*x ^{4}* / 3

*x*) = (5

^{3}*x*) = 5

^{4 – 3}*x*— 15 is divided by 3 while the powers of

*x*are subtracted

(*x ^{5}* ) (

*y*) = (

^{3}*xy*) =

^{5 – 3}*xy*

^{2}.

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**READING, EXPLAINING AND RE-WRITING ALGEBRAIC TERMS**

**Reading terms:**

8^{2} read as eight square m^{2} read as m sqaure (not m two) 4*a*^{2} read as four a square (not 4 a two)

*x*^{2} + *y*^{2} read as x square plus y square (not as x two and y two or x square and y square)

3*a*^{4} – 2*b*^{3} read as three a to the power of four minus two b cube

(*x ^{2}*) (

*y*

*) read as x square multiplied by y square*

^{2}(*x ^{3}*

*y*/

^{3}*x*

^{3}*y*

^{5}*z*) read as x cube y cube divided by x cube, y to the power of 5, z cube

^{3}**Explaining terms:**

8^{2} – 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)

m^{3} – 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)

4*a*^{2} – 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.

*x*^{2} + *y*^{2} This is an algebraic expression in which, the first term x square is added to the second term y square.

3*a*^{4} – 2*b*^{3} 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.

(*x ^{2}*) (

*y*

*) – This is an algebraic expression in which, x square is multiplied to y square.*

^{2}(*x ^{3}*

*y*/

^{3}*x*

^{3}*y*

^{5}*z*) – This is an algebraic expression in which, x cube y cube are divided by x cube, y to the power of 5, z cube.

^{3}**Re-writing Algebraic Terms:**

1) *a*^{-2} —— any power with minus sign shows that the term is a denominator, it is written as 1/*a*^{2}

2) *x*^{a+1} —— a+1 as power shows that the two terms *x*^{a} and *x* are multiplied together,

so they can be written as *x*(*x*^{a}) or (*x*) (*x*^{a})

similarly, *x*^{4+2} = *( x^{4}) (x^{2}) *

3) *x*^{a-1} —— a – 1 as power shows that the two terms *x*^{a} and x are divided and can be written as *x*^{a}/*x*

similarly, *w*^{7 – 5} = *w*^{7} / *w*^{5}

4) *x*^{0} —— zero as a power shows that two like-terms are being divided,

it can be written as *x */*x* because *x*/*x = x^{1-1 = 0}*

The answer of *x*^{0}* * or* **x*/*x* is 1. Any number or variable with zero power equals 1.

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https://rubikh.wordpress.com/2012/05/08/simple-algebra-2-signs/

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I can see some mistake right from the beginning :-P. Its a CONSTANT not CONSONANT. Also your read the power incorrectly, you should have said y to the power of 10, instead you said, 10 to the power of y. I couldn’t read any further, sorry :-P.

That’s because Algeblah confuzes me 🙂

please correct the whole post 🙂

I love Algebra. It is difficult but is quite interesting.

https://rubikh.wordpress.com/2012/05/08/simple-algebra-2-signs/