Back to: MATHEMATICS JSS 2

**Welcome to Class !!**

*We are eager to have you join us !!*

*In today’s Mathematics class, We will be discussing Algebraic Fractions. We hope you enjoy the class!*

**CONTENTS **

- From words to algebra
- Word problems with brackets
- Word problems with fractions.
- 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

__$\frac{5n}{5}=\frac{85}{5}$__

__ __

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 =

$\frac{14}{2}$= 7

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.

I 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

$\frac{n+55}{3}$ ** **

The result is 4n

So,

$\frac{n+55}{3}=4n$………………..1

Multiply both sides by 3

__$3\times \frac{n+55}{3}=3\times 4n$__

__ …………………..2__

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

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**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.

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**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 triangle 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? A. 4b meters B. 5bmeters C. 8b meters D. 10bmeters
- What is the perimeter of a rectangle of length y meters and breadth 4m less than the length? A. 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?

*We have come to the end of this class. We do hope you enjoyed the class?*

*Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.*

*In our next class, we will be talking about Linear Inequalities. We are very much eager to meet you there.*

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