AL1-L32 Algebra Practice : Notation, Algebraic Expression

(Part 1) TEACHING(15-20mins)                                         

1. Using a letter to represent a known no, notation, representation and interpretation

2. Simplify linear expression (excluding bracket)

3. Solving simple linear equation (whole number coefficient)

(Part2) Core PRACTICE (35-55mins)                 

State the algebraic expression for each of the following.

1.  Add 5 to K

2.  Y more than 8

3.  Subtract x from 12

4. 11 less than z

Find the value of each expression when p =6

5    10 p – 13

6.    12 – 4 p

                3

7.    3p + 1

         4      2

8.    7p + 9

            3

Simplify

9.    3y +4y – 2y

10.  8c + 5 – 2c -3

11.  5t + 8 – t

(II) Word Problems 

12. Find the value of 8𝑤− 3w if 𝑤= 4 (18/s/17)
                                           2

13.  What is the value of 21w – w +1 when w = 2? 

                                        10

14. *  What is the value of 10 + 3y  when y = 4?

                                                 2

For Question 15 and 16.
John has y sweet. Peter has 4 times as many sweets as John. Peter bought another 9 sweets.

15. Find the number of sweets Peter has more than John after he bought another 9 sweets in terms of y.

16. If John has 27 sweets. How many more sweet does John have than Peter?

Extra

1.  Mary had $4y. After buying some cloth at $7 per metre, she had $y left. How many metre of cloth did she buy?

2.   At a concert, there were X men and twice the number of women. During the interval, 4 men and 7 women left the concert.

(a)   How many people left during the interval?

(b)   How many people were there at the concert after the interval?

(c)   If X = 400, how many people were there at the convert after the interval?

3.*  Randy sold (4k + 1) tickets on Monday. He sold K more tickets on Tuesday than on Monday. How many tickets did he sell altogether? Give your answer in terms of k in the simplest form.

4.*  Three boys collected plastic bottles for recycling. Jona collected 2Y bottles which was half as many as what Zack collected. Zack collected 7 bottles more than Lionel. Hoe many bottle did they collect altogether? Give your answer in terms of Y in the simplest form.

5.*  Joyce had 4w apples. She ate 1 apple and gave w apples to her friend. Joyce’s sisters then ate half of the remaining apples. Hoe many apples had she left? Give your answer in terms of w in the simplest form.

6. Find the value of each expression when q = 2

a    11q – 13

b.   42 – 4q

                5

c.    9q + 27

         4

d.    14 p + 5
             7

7. State the algebraic expression.

a.  Add 2p to 10

b.  12 more than K

c. Subtract 8 from 3J

d. Y less than 4

8.  Simplify

a.  3y + 7 + y – 2

b.  4d - 5 – 2d - 3

TheMathbooklets Content Page 
Practice Content Page 

Algebra Answer Key

1.         k+5

2.         Y+8

3.         12 –x

4.         z-11

5.         47

6.         6

7.         5

8.         17

9.         5y

10.      6c + 2

11.      4t + 8

12.      26

13.      3.2

14.      60

15.      4y + 9

16.      117

AL1 Algebra : Algebraic Expression

ALGEBRA

where alphabets or other symbols are used to represent a value in a equation. They are also called variables.

Why do we use variables?

It is a symbol that we use to represent a value that we don’t know yet. 

            Example of symbols :  u, x, y, 𝛃, 𝛂

ALGEBRAIC EXPRESSIONS

Combining of numbers, variables and operators (+, -, ×, /) to form a representation.

In Algebra, multiplication of number and variables are represented without the x (multiply) sign.

                   (1) 5 x u = 5u

                   (2) y x 2 = 2y (number be 'in front' of the variable)

                   (3) 1 x z = z (does not need to write the 1)

Example

           3 x U + 1 => 3U + 1

                 3U + 1

 

- When a number is with a variable, the number is called the coefficient

- A number by itself is called a constant

When do we use algebraic expression?

Example 1

What is the algebraic expression of three more than z

How do we form the expression?

          Three more than z

Method

Step1:  What is given and required? 3, more than, z

              Three more than z => add 3 to z => + 3

            z + 3 <Step 2: Forming the expression> 

Example 2

           Four less than z

Step1:  What is given and required? z, 4, less than

            Four less than z => minus 4 from z => - 4

             z - 4 <Step 2 :Forming the expression> 

Example 3

           Five times of z

Step1: What is given and required? 5, x(times), z

            5z <Step 2: Forming the expression>

Example 4

           Sum of z and 8

Method

Step1:  What is given and required? z, 8 + (sum)

             z + 8   <Step 2 :Forming the expression> 

Replacing variables with a value

If z = 5, what are the values in the examples:

Example 1 : z + 3 

Step 1: 5 + 3 <Replace z with value given = 5>

Step 2 : 8      <Calculate>

Example 2 : z - 4

                   =  5 - 4 <Step 1: replace variable with value>

                   = 1 <Step 2 : calculate>         

Example 3 : 5z

                   = 5 x 5  <Step 1: replace variable with value>

                   = 25 <Step 2 : calculate>

Example 4 : z + 8

                   = 5 + 8 <Step 1: replace variable with value>

                   = 13 <Step 2 : calculate>

Practice:

1.         One-half of X

2.         Product of S and 6

3.         V divided by 5

SIMPLIFYING Algebraic Expression

Example

         Simplify 4f + 3g -2f +4g

Method

   Step1 CIRCLE different alphabets/numbers with +/- on left with different shapes

                   

   Step2 GROUP the different shapes together

             

  
   Step3 SIMPLIFY expression

               =   2f + 7g

Example

Simplify 4x + 9 – 3x -7

  

    Step3:    =   x - 2

Practices

Simplify:

  1.         4t + 5 + t – 2

  2.         5x – 2x + x

  3.         3m + 6 – 2m

  4.         3h + h

  5.         8p – 2k – k + 7

WORD PROBLEMS: Writing Algebraic Expression

Example 

Anna has 4u + 3 pens. She bought another 3u pens, and then gave 2u pens to Billy. How many pens does she have now?

Method:

   Step1: Who and their numbers/variables? Underline/Circle and write

            Anna        4u + 3

   Step2: What is the story? link and write expression

            Bought 3u pen => 4u + 5 + 3u

            Gave away 2u + 1 => 4u + 5 + 3u – 2u

   Step3: Solve

            4u + 5 + 3u – 2u 

            = 4u + 3u – 2u + 3

            = 5u + 3

Example

Jack has U number of apples. Mike has 2 apples more than Jack. How many apples does Mike have?

Method

  Step 1:  Who and their numbers/variables? Underline/Circle and write

W                 N

            Jack             U

            Mike

  Step 2: What is the story? link and write expression

           W                N

            Jack           U

            Mike           U      +2

  Step3: Solve: Form the expression

        Mike has U+2 apples

Example

Danny is U years old. His mother is 5 times as old as Danny. His father is 6 years older than his mother. Find his father’s age in terms of U.

   Step1: Who and their numbers/variables? Underline/Circle and write

            W                           N

            Danny                    U        

            Mother          

            Father           

  Step2: What is the story? link and write expression

           

  Step3: 

            His father is 5U + 6 years old.

Example

Harold had W bottles. He gave 8 bottles to his brother. How many bottles had he left?

Method

  Step1: 

            W                     N

            Harold              W

            brother

  Step2: 

           

  Step3: 
            Harold has W – 8 bottles left.

Example

Each of a square is K cm. What is the perimeter of the square?

Method

 Step1: 

            W                           N

            Side of Square       K        

            Perimeter

Step2: 

            W                           N

            Side of Square       K

            Perimeter               4 x K

Step3: 

            Perimeter is 4K

 

Example

Mary scored K marks for 5 subjects. What was her average marks for each subject?

Method

Step1: 

            W                           N

            Mary 5 subj            K                    

            Mary Avg

  Step2: 

            W                           N

            Mary 5 subj            K        

            Mary Average    = Total Value / Number of Data

  Step3: 

            Mary Average mark is K/5

Example

Alex sold (3k + 1) tickets on Saturday. He sold k more tickets on Sunday than on Saturday. How many tickets did he sell altogether?

Method

Step1: 

            W                       N

            Alex (Sat)     3k + 1

     Alex (Sun)  

  Step2: 

            W                           N

           

  Step3:             Alex sells 3K + 1 + 3K + 1 + K = 7K + 2 tickets

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Notes: Just in case...


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