Percentage questions for class 6

Per means ‘for every’ or ‘out of‘ and cent means ‘hundred’ . Thus percent means ‘ for every hundred’ or ‘out of hundred’. The term percent comes from two Latin words per centum which means ‘out of 100’. Thus 5 percent means 5 out of 100=

$\frac{5}{100}$ = 5 hundredths. The symbol for percent is $%$ . Example 23% =23 hundredths= $\frac{23}{100}$

percentage questions for class 6

Converting a Percentage into a Fraction or Decimal:

To convert a given percentage into a fraction or decimal

(i) Remove the sign of percentage and at the same time divide by 100.

(ii) Reduce the resulting fraction into its lowest terms or decimal as required.

Example 1. Express each of the following as fraction.

(a) 40%

Sol. 40 % = $\frac{40}{100}=\frac{2}{5}$

(b) 37.5%

Sol. 37.5 % = $\frac{37.5}{100}=\frac{375}{1000}=\frac{3}{8}$

Example 2. Express each of the following as a decimal.

(a) $6\frac{1}{4} %$

Sol. $6\frac{1}{4} %=\frac{25}{4} %= \frac{25}{4}\times \frac{1}{100}=\frac{1}{16}=0.0625$

(b) 7.5 %

S0l. 7.5%= $\frac{7.5}{100}=\frac{75}{1000}=0.075$

Converting a Given Fraction or Decimal into Percentage

To convert a given fraction or decimal into percentage , multiply by 100.

Example 1. Convert $2\frac{3}{5}$ into percentage.

Sol. $2\frac{3}{5}=\frac{13}{5}=(\frac{13}{5} \times 100)%=260 %$

Example 2 . Convert 0.08 into a percentage.

Sol. 0.08=(0.08 x 100) % = $(\frac{8}{100}\times 100)%=8%$

Finding the Percentage of a Given Number

To find percentage of a number , convert the given percentage to a fraction and then multiply the fraction by the given number.

Example : Find 6 % of 400.

Sol. 6 % of 400= $\frac{6}{100}\times 400=24$

Convert one Quantity as a Percentage of the other

Divide the first quantity by the second one and multiply the result by 100%.

Example 1. Write 20 m as a percentage of 1 km.

Sol. 1 km =1000 m

20 m as a percentage of 1 km= $(\frac{20}{1000}\times 100) % = 2%$ of a km

Example 2. Express 20 kg as a percent of 400 kg .

Sol. 20 kg as a percent of 400 kg = $(\frac{20}{400}\times 100%)= 5 %$

MCQ on percentage questions for class 6

(i) Convert 40% as a fraction .

(a) $\frac{2}{5}$ (b) $\frac{1}{5}$ (c) $\frac{3}{6}$ (d) $\frac{3}{4}$

Sol. $40 %= \frac{40}{100}=\frac{2}{5}$

Hence option (a) is correct.

(ii) Convert $\frac{3}{4}$ into a percentage.

(a) 25 % (b) 60 % (c) 35 % (d) 75 %

Sol. $\frac{3}{4}=(\frac{3}{4}\times 100) % =75%$

Ans. Option (d) is correct.

(iii) Find 8 % of 160 km .

(a) 13 km (b) 14 km (c) 12.8 km (d) 10 km

Sol. 8 % of 160 km = $\frac{8}{100}$ of 160 km = $160 \times \frac{8}{100}= \frac{64}{5}$ km = 12.8 km

Hence option (c) is correct .

(iv) An English test was conducted out of 80 marks. Vani scored 90 %, Tanya scored 85% and Pranoy scored 82.5%. How many marks did each one score?

(a) 72, 68, 66 (b)75, 68, 60 (c) 72, 70, 64 (d) 70, 68, 58

Sol. Marks scored by Vani= 90% of 80 = $\frac{90}{100}\times 80=72$