Lesson
Title: Word Problem Leading to Fraction.
Objective:
At the end of this lesson, you will be able to solve word problems that lead to fractions.
What you should know:
=> BODMAS precedence, Multiplication, Addition, and Subtraction of fractions.
Introduction:
Word problem that lead to fractions is often featured in internal and external examinations, it is expected of students to be able to translate the problem into mathematical terms and solve it accordingly.
Presentation/Steps:
=> Mrs. Maureen spent 1/4 of her monthly income at a shopping mall, 1/3 at an open market, and 2/5 of the remaining amount at a mechanic workshop. If she had #225,000.00 left, find (i) Her monthly income, and (ii) the amount spent at the open market.
Steps: Solution
=> let x = monthly income.
=> Amount left after spending = #225,000.00.
=> Spent 1/4 of monthly income = 1/4x.
=> Spent 1/3 of monthly income at an open market = 1/3x.
=> Therefore, 1/4x + 1/3x = 7/12x, money spent at a shopping mall and an open market. N.B. addition of fraction procedure is used to arrive at 7/12x.
=> Monthly income left after spending,
x - 7/12x = 5/12x, N.B subtraction of fraction procedure is used to arrive at 5/12x.
=> 2/5 of the remaining amount 5/12x spent at the mechanic workshop, 2/5 * 5/12x = x/6, N.B multiplication of fraction is used to arrive at x/6.
=> New fraction left after the last spending 5x/12 - x/6 = x/4.
=> To get her monthly income x, equate all her spending results x/4 with what is left #225,000.00,
x/4 = #225,000.00.
=> Make X the subject of the formula by multiplying both sides by 4.
4 * x/4 = 225,000.00 * 4 => x = #900,000.00.
=> Therefore, her monthly income X = #900,000.00.
=>The amount spent at the open market, i.e. 1/3 of #900,000.00 (her income).
=> 1/3 * 900000 = #300,000.00
Summary/ Conclusion:
It is important to understand the word problem as it will ease the translation to fractions.
Exercise:
A woman spent 1/3 of her money at the market, 1/4 at the chemist's, 1/6 at the electric shop, and had #555 left. How much money did she have to start with?