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summary of this topic

Algebra: Variables and Expressions

Algebra: Variables and Expressions

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Algebraic Expressions


 »  numerical expression
    →  a quantity represented with numbers and arithmetic operations between them
    →  eg: `(32-23)+43xx2 - 4`


 »  algebraic expression
    →  a quantity represented with variables, numbers and arithmetic operations between them
    →  eg: `3x-4y+2`


 »  Parts of Algebraic Expressions.
    →  considering an expression of `2` variables. eg: `3x-4y+2`
    →  term: Part of the algebraic expression that is added. eg: `3x`, `2`, `-4y` are `3` terms
    →  coefficient: the constant in a term is called the coefficient of the term. eg: `3` is the coefficient of `x` and `-4` is the coefficient of `y`.

Algebraic Expressions

plain and simple summary

nub

plain and simple summary

nub

dummy

Algebraic Expression is a collection of variables, numbers, and arithmetic operations between them representing a quantity.

A term is a part of the expression which is added to the rest of the expression.

A coefficient of a term is the number part multiplied to the variables of the term.

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In this page, algebraic expression is introduced as a collection of variables, numbers, and arithmetic operations between them representing a quantity. The terms and coefficients of algebraic expression is explained.


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Starting on learning "Algebraic Expressions". ;; In this page, algebraic expression is introduced as a collection of variables, numbers, and arithmetic operations between them, representing a quantity. The terms and coefficients of algebraic expression is explained.

As part of numerical arithmetic, students are introduced to numerical expressions. Let us just recall what we know already. Which of the following is an example of numerical expression?

  • `2+2+84-2`
  • `23 xx 123 + 8`
  • `(32-23)+43xx2 - 4`
  • all the above

The answer is 'all the above'

What is a numerical expression?

  • a collection of numbers and arithmetic operations between them forming a quantity
  • a statement of a quantity with numbers and arithmetic operations
  • both the above

The answer is 'both the above'

Algebraic expressions are similar to numerical expressions. Let us see some examples to understand algebraic expressions.

How many squares are made in the figure?square using crayons one row

  • `3`
  • `1`

The answer is '`3`'. There are `3` squared made using crayons.

How many crayons are used in the figure?square using crayons one row

  • `3`
  • `10`

The answer is '`10`'. There are `3` squared made using `10` crayons

In this pattern of squares using crayons, if the number of squares in a row is `2`, how many crayons are required?square using crayons one row Note: the figure shows `3` squares, but the question asks about `2` squares.

  • `4`
  • `7`

The answer is '`7`'

In this pattern of squares using crayons, if the number of squares in a row is `10`, how many crayons are required?square using crayons one row Note: the figure shows `3` squares, but the question asks about `10` squares.

  • cannot figure this out
  • `3xx10 + 1`

The answer is '`3xx10 + 1`'. This is an example of numerical expression.

In this pattern of squares using crayons, if the number of squares in a row is `x`, how many crayons are required?illustration of square using crayons one row Note: the figure shows `3` squares, but the question asks about `x` squares.

  • `3xx x + 1`
  • `4xx x`

The answer is '`3xx x + 1`'. This expression involves a variable `x`, and this is an example of algebraic expression.

The figure shows the how the formula is arrived at. For each of `3` columns, `3` crayons are used -- shown by shaded regions. There is an additional `1` on the left side.illustration of square using crayons one row For `x` columns, there will be `x` shaded regions with `3x` crayons and `1` additional crayon.

Number of crayons required for `x` columns = `3x+1`

`3x+1` is an example of algebraic expression.

How many squares are made in the figure?square using crayons two rows

  • `3`
  • `6`

The answer is '`6`'. There are `6` squared made using crayons.

How many crayons are used in the figure?square using crayons two rows

  • `17`
  • `10`

The answer is '`17`'. There are `6` squared made using `17` crayons

In this pattern of squares using crayons, the figure shows `2` rows and `3` columns. If the number of rows and columns are changed to `4` and `5`, how many crayons are required?square using crayons two rows

  • `4+5+2xx4xx5`
  • `3xx5+1`

The answer is '`4+5+2xx4xx5`'. Derivation of this formula is explained in the next page.

The figure shows the pattern with `2` rows and `3` columns.

 •  The crayons highlighted with blue background on the left equals number of rows `2`.

 •  The crayons highlighted with red background at the bottom equals number of columns `3`.

 •  The crayons highlighted with green and yellow backgrounds are repeated the number of squares `2xx2xx3`.

Total number of crayons `= 2+3+2xx2xx3 =17` square using crayons two rows `2+3+2xx2xx3` is an example of numerical expression. It evaluates to `17`.

square using crayons two rows Generalizing this for `x` rows and `y` columns.

 •  The crayons on the left equals number of rows `x`.

 •  The crayons at the bottom equals number of columns `y`.

 •  The crayons on squares are repeated the number of squares `2xx x xx y`.

The total number of crayons `=x+y+2xy`.

The result `x+y+2xy` is an example of an algebraic expression. The following are noted for this expression.

 •  there are `3` terms: x, y, and 2xy

 •  there are `2` variables : x, and y

 •  the constant in the term `2xy`, is `2` and it is called coefficient of that term.

Which of the following is a meaning for the word 'expression'?

  • a collection that jointly represent a quantity
  • something that is moving very fast

The answer is 'a collection that jointly represent a quantity'.

Which of the following is a meaning for the word 'term'?

  • one smaller part of quantity
  • year by year

The answer is 'one smaller part of quantity'.

Which of the following is a meaning for the word 'coefficient'?

  • being together to produce a result
  • very efficient

The answer is 'being together to produce a result'. coefficient is co (together) + effect (root word for producing a result).

What is the word or phrase used to refer a quantity that is given by collection of variables, numbers, and arithmetic between them?

  • Practice Saying the Answer

The answer is 'algebraic expression'.

What is the word or phrase used to refer to parts of an algebraic expression?

  • Practice Saying the Answer

The answer is 'algebraic term or term'.

What is the word used to refer the number part in a term?

  • Practice Saying the Answer

The answer is 'coefficient of the term'.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Algebraic Expression : A quantity represented by collection of variables, numbers, and arithmetic operations between them is an algebraic expression.

Algebraic Term : A part of an algebraic expression which is added to the rest of the expression in forming the expression.

Coefficient : The constant part of a term is called the coefficient of the term.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

A rectangle is made by joining two squares of side `x`. What is the outer perimeter of the rectangle?

  • `4 x`
  • `6 x`

The answer is '`6 x`'

A person covers 5000 steps to commute to office. In the evening, she walks 40 steps per minute during the free time available every day. How many steps she walks in a day in which free time was `t` minutes?

  • `4t`
  • `40 t + 5000`

The answer is '`40 t + 5000`'

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As part of numerical arithmetic, students are introduced to numerical expressions. Let us just recall what we know already. Which of the following is an example of numerical expression?
1
2
3
4
The answer is 'all the above'
What is a numerical expression?
collection;numbers
a collection of numbers and arithmetic operations between them forming a quantity
statement;quantity;arithmetic
a statement of a quantity with numbers and arithmetic operations
both;above
both the above
The answer is 'both the above'
Algebraic expressions are similar to numerical expressions. Let us see some examples to understand algebraic expressions.
How many squares are made in the figure?
3
3
1
1
The answer is ' 3 '. There are 3 squared made using crayons.
How many crayons are used in the figure?
3
3
10
10
The answer is ' 10 '. There are 3 squared made using 10 crayons
In this pattern of squares using crayons, if the number of squares in a row is 2, how many crayons are required? Note: the figure shows 3 squares, but the question asks about 2 squares.
4
4
7
7
The answer is "7"
In this pattern of squares using crayons, if the number of squares in a row is 10, how many crayons are required? Note: the figure shows 3 squares, but the question asks about 10 squares.
cannot figure this out
cannot figure this out
3;times;10;plus;1
3 times 10 plus 1
The answer is "3 times 10 plus 1". This is an example of numerical expression.
In this pattern of squares using crayons, if the number of squares in a row is x, how many crayons are required? Note: the figure shows 3 squares, but the question asks about x squares.
3;1
3 times x plus 1
4
4 times x
The answer is "3 times x plus 1". This expression involves a variable x, and this is an example of algebraic expression.
The figure shows the how the formula is arrived at. For each of 3 columns, 3 crayons are used -- shown by shaded regions. There is an additional 1 on the left side. For x columns, there will be x shaded regions with 3x crayons and 1 additional crayon. ;; Number of crayons required for x columns = 3x+1 ;; 3x + 1 is an example of algebraic expression.
How many squares are made in the figure?
3
3
6
6
The answer is ' 6 '. There are 6 squared made using crayons.
How many crayons are used in the figure?
17
17
10
10
The answer is ' 17 '. There are 6 squared made using 17 crayons
In this pattern of squares using crayons, the figure shows 2 rows and 3 columns. If the number of rows and columns are changed to 4 and 5, how many crayons are required?
4;2
4+5+2 multiplied 4 multiplied 5
3;1
3 times 5 plus 1
The answer is "4+5+2 multiplied 4 multiplied 5". Derivation of this formula is explained in the next page.
The figure shows the pattern with 2 rows and 3 columns. ;; The crayons highlighted with blue background on the left equals number of rows 2. ;; The crayons highlighted with red background at the bottom equals number of columns 3. ;; The crayons highlighted with green and yellow backgrounds are repeated the number of squares 2 crayons per square multiplies 2 rows multiplied 3 columns ;; Total number of crayons = 2+3+2 times 2 times 3 = 17. ;; This provides an example for numerical expression.
Generalizing this for x rows and y columns. ;; The crayons on the left equals number of rows x. ;; The crayons at the bottom equals number of columns y. ;; The crayons on squares are repeated the number of squares 2 times x times y. ;; The total number of crayons =x+y+2 x y.
The result x + y + 2 x y is an example of an algebraic expression. The following are noted for this expression. ;; there are 3 terms x, y, and 2 x y. ;; There are 2 variables: x and y. ;; the constant in the term 2 x y is 2. It is called coefficient of that term.
Which of the following is a meaning for the word 'expression'?
collection;jointly;represent;quantity
a collection that jointly represent a quantity
something;moving;very;fast
something that is moving very fast
The answer is 'a collection that jointly represent a quantity'.
Which of the following is a meaning for the word 'term'?
1;smaller;part
one smaller part of quantity
year;by
year by year
The answer is 'one smaller part of quantity'.
Which of the following is a meaning for the word 'coefficient'?
being;together;produce;result
being together to produce a result
very;efficient
very efficient
The answer is 'being together to produce a result'. coefficient is co (together) + effect (root word for producing a result).
What is the word or phrase used to refer a quantity that is given by collection of variables, numbers, and arithmetic between them?
expression
The answer is 'algebraic expression'.
What is the word or phrase used to refer to parts of an algebraic expression?
term
The answer is 'algebraic term or term'.
What is the word used to refer the number part in a term?
coefficient
The answer is 'coefficient of the term'.
Algebraic Expression is a collection of variables, numbers, and arithmetic operations between them representing a quantity. ;; A term is a part of the expression which is added to the rest of the expression. ;; A coefficient of a term is the number part multiplied to the variables of the term.
Algebraic Expression: A quantity represented by collection of variables, numbers, and arithmetic operations between them is an algebraic expression.;; Algebraic term: A part of an algebraic expression which is added to the rest of the expression in forming the expression ;; coefficient : the constant part of any term is called the coefficient of the term.
A rectangle is made by joining two squares of side x . What is the outer perimeter of the rectangle?
4
4 x
6
6 x
The answer is ' 6 x '
A person covers 5000 steps to commute to office. In the evening, she walks 40 steps per minute during the free time available every day. How many steps she walks in a day in which free time was t minutes?
4
4t
40;5000;thousand;2
40 t + 5000
The answer is ' 40 t + 5000 '

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