Percentage, Fractions And Decimals
In this article, we will learn about P5 Percentages.
The learning objectives are:
- Conversion of fraction/decimal to percentage and vice versa
- Solve simple words problems using percentage
Definition Of Percentage
Any number written as a part out of 100 can be written as a percentage. It can be converted to a fraction or a decimal. The symbol for percentage is %.
Example:
17 out of 100 expressed as a fraction is \(\frac {17}{100}\).
17 out of 100 expressed as a decimal is 0.17.
17 out of 100 expressed as a fraction is 17%.
Hence, \(\begin{align}\\[2ex] 17\% &= \frac{17}{100} \\[2ex] &= 0.17 \end{align} \).
1. Conversion Of Fraction/Decimal To Percentage And Vice-Versa
Question 1:
Express \(\frac {1}{20}\) as a percentage.
Solution:
\(\begin{align*} \frac {1}{20}&= \frac {1}{20} \times 100\% \\ &= \frac {1}{20} \times \frac {100\%}{1} \\ &= 5\% \end{align*}\)
Answer:
\(5\% \)
Question 2:
Express \(\frac {3}{5}\) as a percentage.
Solution:
\(\begin{align*} \frac {3}{5}&= \frac {3}{5} \times 100\% \\ &= \frac {3}{5} \times \frac {100\%}{1} \\ &= 60\% \end{align*}\)
Answer:
\(60\%\)
Question 3:
Express \(1\frac {1}{5}\) as a percentage.
Solution:
\(\begin{align*} 1\frac {1}{5} &= \frac {6}{5}\\ &= \frac {6}{5} \times 100\% \\ &= \frac {6}{5} \times \frac {100\%}{1} \\ &= 120\% \end{align*}\)
Answer:
\(120\%\)
Question 4:
Express \(5\frac {3}{4}\) as a percentage.
Solution:
\(\begin{align*} 5\frac {3}{4} &= \frac {23}{4}\\ &= \frac {23}{4} \times 100\% \\ &= \frac {23}{4} \times \frac {100\%}{1} \\ &= 575\% \end{align*}\)
Answer:
\(575\%\)
Question 5:
Express 1.34 as a percentage
Solution:
\(\begin{align*} 1.34 &= 1.34 \times 100\% \\ &= 134\% \end{align*}\)
Answer:
\(134\%\)
Question 6:
Express 3.4 as a percentage.
Solution:
\(\begin{align*} 3.4 &= 3.4 \times 100\% \\ &= 340\% \end{align*}\)
Answer:
\(340\%\)
Something To Think About
Your help is needed. Tim and Jim are in a heated argument about who scored a better grade for their spelling date. Tim scored 34 and Jim scored 710.
Who do you think scored higher?
In order to compare any two fractions, the denominator of both the fractions must be made the same. Once the denominators are the same, we compare the numerators of the two fractions.
Tim |
Jim |
\(\frac {3}{4}\) |
\(\frac {7}{10}\) |
\(\frac {(3\;×\;5)}{(4\;×\;5)}\) |
\(\frac {(7\;×\;2)}{(10\;×\;2)}\) |
\(\frac {15}{20}\) |
\(\frac {14}{20}\) |
Since, 15 is greater than 14, Tim scored higher than Jim.
We can also convert the fractions to percentages to compare.
\(\begin{align*} \frac {3} {4}&= \frac {3} {4} \times 100\% \\ &= \frac {3} {4} \times \frac {100\%} {1} \\ &= 75\% \end{align*}\)
\(\begin{align*} \frac {7} {10}&= \frac {7} {10} \times 100\% \\ &= \frac {7} {10} \times \frac {100\%} {1} \\ &= 70\% \end{align*}\)
After converting from fractions to percentages, Tim’s score is 75% while Jim’s score is 70%.
Tim scored higher than Jim.
Question 7:
Express the following percentage as a fraction in its simplest form.
\(48\% =\) ________
Solution:
\(\begin{align*} 48\%&= \frac {48} {100} \\ &= \frac {12} {25} \end{align*}\)
Answer:
\(\frac {12} {25}\)
Question 8:
Express the following percentage as a fraction in its simplest form.
\(80\% =\) ________
Solution:
\(\begin{align*} 80 \% &= \frac {80} {100} \\ &= \frac {4} {5} \end{align*}\)
Answer:
\(\frac {4} {5}\)
Question 9:
Express \(70\%\) as a decimal.
Solution:
\(\begin{align*} 70 \% &= \frac {70} {100} \\ &= 0.7 \end{align*}\)
Answer:
\(0.7\)
Question 10:
Express \(550\%\) as a decimal.
Solution:
\(\begin{align*} 550 \% &= \frac {550} {100} \\ &= 5.5 \end{align*}\)
Answer:
\(5.5\)
Question 11:
Express \(0.2\%\) as a fraction in its simplest form.
Solution:
\(\begin{align*} 0.2 \% &= \frac {0.2} {100} \\ &= 0.002 \\ &= \frac {2} {1000} \\ &= \frac {1} {500} \\ \end{align*}\)
Answer:
\(\frac {1} {500}\)
Question 12:
Express \(0.5\%\) as a fraction in its simplest form.
Solution:
\(\begin{align*} 0.5 \% &= \frac {0.5} {100} \\ &= 0.005 \\ &= \frac {5} {1000} \\ &= \frac {1} {200} \\ \end{align*}\)
Answer:
\(\frac {1} {200}\)
Question 13:
Express \(4\frac {1} {2}\%\) as a decimal.
Solution:
\(\begin{align*} 4 \frac {1} {2} \% &= 4\frac {5} {10}\% \\ &= 4.5\% \\ &= \frac {4.5} {100} \\ &= 0.045 \\ \end{align*}\)
Answer:
\(0.045\)
Question 14:
Express \(125\%\) as a decimal.
Solution:
\(\begin{align*} 1 \frac {2} {5} \% &= 1\frac {4} {10}\% \\ &= 1.4\% \\ &= \frac {1.4} {100} \\ &= 0.014 \\ \end{align*}\)
Answer:
\(0.014\)
2. Solve Simple Word Problems Using Percentage
Question 1:
In a school, the ratio of the number of boys to the number of girls is 1 : 4. What percentage of the pupils are boys?
Solution:
Number of Boys : Number of Girls
1 : 4
Number of boys \(=\) 1 unit
Number of girls \(=\) 4 units
Total number of pupils \(=\) 5 units
Percentage of the pupils that are boys
\(\begin{align} = \frac {\text{Number of boys}}{\text{Total number of pupils}} \times 100\% \end{align}\)
\(\begin{align} = \frac {1}{5} \times 100\% \end{align}\)
\(= 20\%\)
Answer:
\(20\%\)
Question 2:
There are 240 pupils in Primary 5. 180 of them go to school by bus. What percentage of pupils go to school by bus?
Solution:
Total number of pupils \(= 240\)
Number of pupils who go to school by bus \(= 180\)
Percentage of pupils who go to school by bus
\(\begin{align} &=\frac {\text{Number of pupils who go to school by bus}}{\text{Total number of pupils}} \times 100\%\\[2ex] &=\frac {180} {240} \times 100\% \\[2ex] &=75\% \end{align}\)
Answer:
\(75\%\)
Question 3:
In a chicken farm, there are 320 hens and 180 roosters. 20% of hens and 15% of roosters have white feathers. What percentage of the chickens have white feathers?
Solution:
Number of hens \(= 320\)
Number of roosters \(= 180\)
Total number of chickens \(\begin{align}\\[2ex] &= 320 + 180\\[2ex] &= 500 \end{align}\)
Number of hens with white feathers
\(= 20\%\) of hens
\(\begin{align} &=\frac {20} {100} \times 320 \\[2ex] &=64 \end{align}\)
Number of roosters with white feathers
\(= 15\%\) of roosters
\(\begin{align} &=\frac {15} {100} \times 180 \\[2ex] &=27 \end{align} \)
Total number of chickens with white feathers
\(= 64 + 27\)
\(= 91\)
Percentage of chickens with white feathers
\(\begin{align} &=\frac {\text{Number of chickens with white feathers}}{\text{Total number of chickens}} \times 100\% \\[2ex] &= \frac{91}{500} \times 100\% \\[2ex] &= 18.2\% \end{align}\)
Answer:
\(18.2\%\)