**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:**

**Choose a letter for the unknown****Write the information of the equation in algebraic form****Make an equation****Solve the equation****Give the answer in written form.****check the results against the information given in the question.**

** **

**Example** :

**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 **

**John thinks of a number, he doubles it. His result is 58. What number does he think of?****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**** **

**A rectangle is 10m long and its perimeter is 26m. Find the breadth of the rectangle.****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**

**I subtract 8 from a certain number. I then multiply the result by 3. The final answer is 21. Find the original number.****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**** **

**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).****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 **

**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?****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**

**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?****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?****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.**

** **

**READING ASSIGNMENT **

**New General Mathematics pg 209-211**

** **

**WEEKEND ASSIGNMENT **

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

** **

**THEORY**

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

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