Study S1 Mathematics Maths - Percentage - Geniebook

Percentage

In this chapter, we will be discussing the below-mentioned topics in detail:

  • Fractions, Ratio, Decimals and Percentage
  • Convert a non-integer percentage to fraction/ decimal and vice versa
  • Percentages greater than \(100\%\) or less than \(1\%\)
  • Percentage of quantities 
    • Percentage of a quantity 
    • Express one quantity as a percentage of another quantity
    • Compare two quantities by percentage
  • Percentage change

 

Fractions, Ratio, Decimals and Percentage

Let’s understand this with the help of some examples:


 

Fractions

Ratio

Percentage

Decimals

\(\begin{align} \frac{2}{5} \end{align}\) \(2:5\) \(\begin{align} \frac{2}{5} \times 100 = 40\% \end{align}\) \(\begin{align*} 40\% &= \frac{40}{100}\\ \\       &= 0.4 \end{align*}\)
\(\begin{align} 25\% &= \frac{25}{100}\\\\  &= \frac{1}{4} \end{align}\) \(1:4\) \(25\%\) \(0.25\)
\(\begin{align} \frac{90}{100} = \frac{9}{10} \end{align}\) \(9:10\) \(\begin{align} 0.9 \times 100\% = 90\% \end{align}\) \(0.9\)

 

 

Percentages Greater Than \(100\%\) or Less Than \(1\%\)

Let’s understand this with the help of some examples:

 

Question 1:

Without using a calculator, express each of the following percentages as a fraction.

  1. \(105\%\)
  2. \(0.04\%\) 

 

Solution: 

  1.  

\(\begin{align*} 105\% &= \frac{105}{100}\\ &= \frac{21}{20}\\ &= \frac{11}{20} \end{align*}\)

 

  1.  

\(\begin{align*} 0.04\% &= \frac{0.04 × 100}{100 × 100}\\ &= \frac{4}{10000}\\ &= \frac{1}{2500} \end{align*}\)

 

 

Question 2:

Without using a calculator, express each of the following percentages as a decimal.

  1. \(274\%\)
  2. \(0.38\%\)

 

Solution: 

  1.  

\(\begin{align*} 274\% &=  \frac{274}{100}\\ \\                   &= 2.74 \\ \\ \end{align*}\)

 

  1.  

\(\begin{align*} 0.38\% &= \frac{0.38}{100}\\ \\                     &= 0.0038\\ \end{align*}\)

 

 

Percentage Of A Quantity

Let’s understand this with the help of some examples:

 

Question 3:

A box contains \(60\) balls, of which \(16\) are red.

  1. If \(40\%\) of the balls are green, find the number of green balls.
  2. The rest of the balls in the box are yellow.

If \(70\%\) of the yellow balls are removed, find the number of yellow balls left.

 

Solution: 

  1. Number of green balls\(\begin{align} = \frac{40}{100} \times 60\\ \end{align}\)

\(\qquad\qquad\qquad\qquad\qquad= 24 \;balls\)

OR

Number of green balls \(= 0.4 × 60\)

 \(\qquad\qquad\qquad\qquad\quad\;\;= 24 \;balls\)

 

  1. Number of yellow balls at first\(\begin{align*} &= 60 \;– 16 \;– 24 \end{align*}\)

\(\qquad\qquad\qquad\qquad\qquad\qquad\qquad= 20\)

Number of yellow balls remaining \(= \frac{30}{100} × 20\)

\(\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad= 6 \;balls\)

OR

Number of yellow balls remaining \(= 0.3 × 20\) 

\(\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad= 6 \;balls\)\(\)


 

Comparing two quantities by percentage

Let’s understand this with the help of some examples:

 

Question 4:

Shop \(A\) sold \(225\) out of \(1000\) vinyl records in January. Shop \(B\) sold \(400\) out of \(1500\) vinyl records in the same month. Which shop had a higher proportion of sales in January?

 

Solution: 

Percentage of sales by Shop\(\begin{align} A=\frac{225}{1000} \times 100 \end{align}\)

\(\begin{align} \qquad\qquad\qquad\qquad\qquad\qquad\qquad=22.5\% \end{align}\)

Percentage of sales by Shop\(\begin{align} B= \frac{400}{1500} \times 100 \end{align}\)

\(\begin{align} \qquad\qquad\qquad\qquad\qquad\qquad\qquad= 26 \frac{2}{3}\% \end{align}\)

Shop \(B\) had a higher proportion of sales in January.

Continue Learning
Basic Geometry Linear Equations
Number Patterns Percentage
Prime Numbers Ratio, Rate And Speed
Functions & Linear Graphs 1 Integers, Rational Numbers And Real Numbers
Basic Algebra And Algebraic Manipulation 1 Approximation And Estimation
Resources - Academic Topics
Primary
Primary 1
Primary 2
Primary 3
Primary 4
Primary 5
Primary 6
Secondary
Secondary 1
English
+ More
Maths
Basic Geometry
Linear Equations
Number Patterns
Percentage
Prime Numbers
Ratio, Rate And Speed
Functions & Linear Graphs 1
Integers, Rational Numbers And Real Numbers
Basic Algebra And Algebraic Manipulation 1
Approximation And Estimation
+ More
Science
+ More
Secondary 2
Secondary 3
Secondary 4
+ More
Sign up for a free demo
(P1 to S4 levels)
Our Education Consultants will get in touch to offer a complimentary product demo and Strength Analysis to your child.
Ready to power up your
child's academic success?
Let our Education Consultants show you how.
*By submitting your phone number, we have your permission to contact
you regarding Geniebook. See our Privacy Policy.