# Lesson Notes By Weeks and Term - Junior Secondary School 2

WORD PROBLEMS ON ALGEBRAIC FRACTIONS

SUBJECT: MATHEMATICS

CLASS:  JSS 2

DATE:

TERM: 2nd TERM

WEEK TWO                                            Date: ___________

TOPIC: WORD PROBLEMS ON ALGEBRAIC FRACTIONS

CONTENTS

• From words to algebra
• Word problems with brackets
• Word problems with fraction.
• From words to Algebra

When solving word problems:

1.   Choose a letter for the unknown
2.   Write the information of the equation in algebraic form
3. Make an equation
4. Solve the equation
5. Give the answer in written form.
6. check the results against the information given in the question.

Example :

1. I think of a number. Multiply it by 5 and add 15. The result is 100. What is the number I thought of?

Let the number be n

I multiply n by 5:5n

I add 15: 5n + 15

The result is 100:5n + 15 = 100 …………   ( i)

Subtract 15 from both sides

5n + 15 -15 = 100 – 15

5n = 85 …………………..  2

Divide  both sides by 5

5n   =   85

5         5

n = 17

Check:  17 x 5 = 85 + 15 = 100

EVALUATION

1. John thinks of a number, he doubles it.  His result is 58.  What number does he think of?
2. A number is multiplied by 6 and then 4 is added.  The result is 34.  Find the  number .

Example

A rectangle is 8m long and its perimeter is 30m. find the breadth of the rectangle .

Solution

Let the breadth of the rectangle be ‘b’ meters.

Perimeter = 8 + b + 8 + b meters

=  16  + 2b = 30

Subtract 16 from both sides

2b = 30 -16 = 14

Divide both sides by 2

B =  14   = 7

2

The breadth of the rectangle is 7 meters

Check : 8m + 7m + 8 + 7m = 30m

EVALUATION

1. A rectangle is 10m long and its perimeter is 26m. Find the breadth of the rectangle.
2. A square has a perimeter of 32m. Find the length of one side of the square.

Word problems with brackets.

Example

I subtract 3 from a certain number, multiply the result by 5 and then add 9.  If the final result is 54, find the original number.

Solution

Let the original number be x.

1 subtract 3 , this gives x – 3.

I multiply by 5 this gives 5(x- 3)

I add 9 this gives 5 ( x – 3 )` + 9

The result is 54.

So, 5 ( x – 3) + 9 = 54 ……………………..1

Clear brackets

5x – 15 + 9 = 54 ………………………..2

Collect like terms

5x = 54 + 15 – 9 =60

x = 60 ÷ 5 = 12

The original number is 12

Evaluation

1. I subtract 8 from a certain number. I then multiply the result by 3.  The final answer is 21. Find the original number.
2. I thought of a number, I multiplied it by 5. I then subtracted 19. Finally, I doubled the result, the result was 22. What number did I think of?

Worked Examples

Find two consecutive even number such that seven times the smaller number subtracted from nine times the greater number makes 46.

Solution

Note : 1, 2, 3, 4,5 ……………are consecutive whole numbers

2,4,6,8,10 ……………………are consecutive even numbers

1,3,4,7,9 ……………………are consecutive odd numbers.

Let the number be x and ( x + 2)

Multiply  x by 7, gives 7x

Multiply ( x + 2) by 9 gives 9 ( x + 2)

The result is 46.

9(x+2) – 7x = 46 ……………………………1

9x + 18 – 7x = 46 …………………………..2

9x – 7x = 46 – 18 ………………………….3

2x = 28 ………………………………………4

X = 28/2  = 14

If x = 14

( x+ 2) = 14 + 2 = 16

The numbers are 14 and 16.

EVALUATION

1. Find the consecutive whole numbers such that five times the smaller number added to three times greater number makes 59. ( hint let the numbers be x and (x +1).
2. Find two consecutive odd numbers such that six times the smaller added to four times the greater comes to 138. ( hint: let the number is x and x + 2)

Word problems with Fractions

Examples: I add 55 to a certain number and then divide the sum by 3.  The result is four times the first number, find the

number.

Let the number be n

I add 55 to n this gives n + 55

I divide the sum by 3 : this gives   n _ + 55

3

The result is 4n

So,  n + 55   = 4n …………………………….1

3

Multiply both sides by 3

3 ( n + 55)    =  3 x 4n …………………….2

3

n + 55 = 12 n ……………………………..3

Collect terms

55 = 12n – n

55 = 11n

So, n = 5

EVALUATION

I think of a number . I double it. I divide the result by 5. My answer is 6. What number did I think of?

New General Mathematics, UBE Edition chapter 13 pgs 114-118

Essential Mathematics by  AJS Oluwasanmi, chapter 19pgs 205-207

GENERAL EVALUATION

1. A woman is 7 times as old as her daughter in 2 years time, she will be 5 times as old as her daughter. How old are they now?
2. If 60 is added to a number, and the sum is divided by 3, the result is 7 times the same number. Find the number.

REVISION QUESTION

1. I  think of  a  number. I add  7  to  it  and  then  divide  the  sum  by  4.The  result  is  5.What  is  the  number?
2. A  man  spent  two  third  of  his  monthly  wages  on  his  car  and  one  quarter  on  food. If he  spent  #5500 altogether,how  much  does  earn  in  a  month?
3. If  18  is  added  to  a  number  to  a  number,  and  the  sum  is  divided  by  2,the  result  is  5 times  the  number. Find  the  number.

New General Mathematics pg 209-211

WEEKEND ASSIGNMENT

1. What is the perimeter of an equilateral triangles of side 2b meters.? A. 4b B.  5b C. 6b D. 8b
2. How many altogether if a number is 3 less than a? A. a -3 B. – a + 3 C. 3 – a D. 3 + a
3. How many altogether if a number is doubled and then 5 is taken away? A. 5 – 2y B. 2y – 5 C. 5y – 2 D. 2 – 5y
4. What is the perimeter of a rectangle of breadth b meters and length three times as long?
5. 4b meters         B. 5bmeters        C. 8b meters        D. 10bmeters
6. What is the perimeter of a rectangle of length y meters and breath 4m less than the length?
7. 4(y -2)meters         B. 2 ( y – 4)meters    C. 4 ( 2-y)        D. 2 ( 4- y )meter

THEORY

1. A rectangle is such that its breadth is 2m less than its length. Find the length of the rectangle if the perimeter is 8m.
2. I am thinking of a number. I take away 5, the result is 14. What number did it think of?