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In today’s Mathematics class, We will be discussing Algebraic Fractions. We hope you enjoy the class!
- 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.
- 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
n = 17
Check: 17 x 5 = 85 + 15 = 100
- 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.
A rectangle is 8m long and its perimeter is 30m. Find the breadth of the rectangle.
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 = = 7
The breadth of the rectangle is 7 meters
Check: 8m + 7m + 8 + 7m = 30m
- 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.
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.
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
5x – 15 + 9 = 54……………….2
Collect like terms
5x = 54 + 15 – 9 =60
x = 60 ÷ 5 = 12
The original number is 12
- 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?
Find two consecutive even number such that seven times the smaller number subtracted from nine times the greater number makes 46.
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.
- 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
The result is 4n
Multiply both sides by 3
n + 55 = 12 n ………………………………3
55 = 12n – n
55 = 11n
So, n = 5
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
- 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.
- 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.
New General Mathematics pg. 209-211
- 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
- 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?
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In our next class, we will be talking about Linear Inequalities. We are very much eager to meet you there.
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