Percentage

In a class of students, 62% have brown hair. This means that, if there were 100 students, 62 of them would have brown hair. We could also say that the remaining 38 of them would not have brown hair as they are not in the 62%.

Back to the original example, if you scored 32 out of 48 on a test, the score is 32 and the total is 48. In this case, the percentage is $\frac{32}{48}\times 100\%=67\%$. So you scored 67% on your test, which is pretty good. However, if you need 70% to pass, you may need to revise a little more...

Work out 36% of 120

Solution:

Firstly, we can say that$36\%=30\%+6\%$.

Finding 30%:

We know that $30\%=10\%\times 3$and$10\%of120=120÷10=12$.

Thus,$30\%of120=12\times 3=36$.

Finding 6%

Now, $6\%=5\%+1\%$

$5\%of120=12÷2=6$.

$1\%of120=120÷100=1.2$

Thus,$6\%of120=6+1.2=7.2$.

Finding 36%

Thus,$36\%of120=36+7.2=43.2$.

Convert 34% to a fraction and decimal.

Solution:

To convert a percentage to a fraction, we simply put it over one hundred. Recall that percent means per hundred, so 34% is 34 out of 100, or $\frac{34}{100}$. Now, this fraction can be simplified by dividing both the numerator and denominator by two. Thus, $\frac{34}{100}=\frac{17}{50}$.

Now, to convert to a decimal, we take the percentage and divide it by 100. So, in this case, we take 34 and divide it by 100. We can do this by shifting the decimal place two spaces to the left. So, it becomes 0.34. Thus,$34\%=0.34$.

Convert$\frac{3}{10}$ to a percentage.

Solution:

To convert a fraction to a percentage, we multiply the fraction by 100.

In this case, we get $\frac{3}{10}\times 100=\frac{300}{10}=30\%$. Thus, $\frac{3}{10}=30\%$.

Convert 0.07 to a percentage

Solution

To convert a decimal to a percentage, we multiply the decimal by 100.

In this case, we get $0.07\times 100=7\%$. Thus, $0.07=7\%$

On Monday, Sam took a test and scored 56 out of 82. On Wednesday, he retook the same test and scored 78. What was his percentage change?

Solution:

The difference is$78-56=22$. Thus, the percentage change is $\frac{22}{82}\times 100\%=26.8\%$. Therefore, Sam scored 26.8% higher on Wednesday than he did on Monday.

Dave brought a house for £296,000. He sold the house for £400,000. Calculate the percentage increase in price.

Solution:

The difference is$400000-296000=\pounds 104000$. Thus, the percentage change is$\frac{104000}{296000}\times 100\%=35.1\%$. Therefore, Dave has made a profit of 35.1% of what he originally paid.

A company sold 31,250 televisions in 2020. In 2021, they sold 29,876 televisions. Calculate the percentage decrease in the number of televisions sold.

Solution:

The difference is$31250-29876=1374$. Therefore, the percentage change is$\frac{1374}{31250}\times 100\%=4.4\%$. Thus, the company sold 4.4% less televisions in 2021 than 2020.

In a shop, all items are reduced by 30%. Sam wants to buy a t-shirt that is marked as £30 before the discount. He also wants to buy a pair of jeans that are labelled as £45 before the reduction. Sam has £52. Does he have enough money to buy both items?

Solution:

The t-shirt is £30 and we need to decrease this by 30% to work out the new price. To do so, we work out 30% of £30. We can say that 10% of £30 is £3 since $30÷10=3$. Now, to work out 30%, we need to multiply 10% by 3. So, 30% of 30 is £9.

We, therefore, need to reduce £30 by £9 to get the new price. Thus, the new price of the t-shirt is $\pounds 30-\pounds 9=\pounds 21$.

The pair of jeans is £45 so we need to reduce this by 30% to work out the new price of the jeans. We know that 10% of £45 is £4.50 since $45÷10=4.5$. Thus, 30% of £45 must be £13.50 since$4.5\times 3=13.5$. Therefore, we need to decrease £45 by £13.50 to get the new price. Since $45-13.50=31.50$we know that the new price of the jeans is £31.50.

Therefore, the cost of the t-shirt and the jeans together is $31.50+21=52.50$. So, Sam needs £52.50. Since he only has £52, he does not have enough money to buy both items.