Word Problems Leading to Simple Algebraic Fractions - JSS2 Mathematics Lesson Note

Word problems often involve real-life scenarios that can be translated into algebraic fractions.

Example 1:

Problem: Sarah has 3 more apples than twice the number of apples that John has. If John has 

𝑥 apples, how many apples does Sarah have?

Solution: The number of apples Sarah has can be expressed as: 2𝑥+3

If this number of apples is divided equally among 5 people, the number of apples each person gets can be represented by the algebraic fraction:

2𝑥+3/5

Example 2:

Problem: A car travels at a speed of 𝑥 miles per hour. If it covers a distance of 100 miles, how long does it take?

Solution: The time taken can be found using the formula:

Time=Distance/Speed

So, the algebraic expression for the time taken is:

100𝑥

Example 3:

Problem: A rectangle's length is 4 units more than three times its width. If the width is 𝑤, what is the length?

Solution: The length 

𝐿 can be expressed as:

𝐿=3𝑤+4

If the perimeter of the rectangle is given by the formula 

𝑃=2𝐿+2𝑤, substituting the expression for 𝐿 gives:

𝑃=2(3𝑤+4)+2𝑤

=6𝑤+8+2𝑤

=8𝑤+8