2.01 Finding the whole
Choose the statement that is the same as 20\% of a quantity:
One twentieth of that quantity.
One fifth of that quantity.
One tenth of that quantity.
One quarter of that quantity.
Choose the statement that is the same as 500\% of a quantity:
One five hundredth of that quantity.
Five hundred times that quantity.
Five times that quantity.
Five hundred more than that quantity.
Complete the table of conversions between fractions and percentages. Fully simplify each fraction.
| Fraction | Percentage |
|---|---|
| \quad \enspace \dfrac{1}{2} | \quad \enspace 50\% |
| \quad \enspace \dfrac{1}{4} | |
| \quad \enspace \dfrac{1}{5} | |
| \quad \enspace 10\% | |
| \quad \enspace \dfrac{1}{20} |
| Fraction | Percentage |
|---|---|
| \quad \enspace \dfrac{1}{1} | |
| \quad \enspace \dfrac{1}{8} | |
| \quad \enspace 4\% | |
| \quad \, \dfrac{1}{50} | |
| \quad \enspace 1\% |
Find the whole number if:
\dfrac{1}{2} of the number is equal to 6.
\dfrac{1}{4} of the number is equal to 20.
\dfrac{1}{3} of the number is equal to 8.
\dfrac{1}{5} of the number is equal to 14.
\dfrac{1}{6} of the number is equal to 11.
\dfrac{1}{10} of the number is equal to 82.
\dfrac{1}{20} of the number is equal to 9.
\dfrac{1}{25} of the number is equal to 10.
Find the whole number if:
10\% of the number is equal to 9.
20\% of the number is equal to 7.
5\% of the number is equal to 12.
600\% of the number is equal to 54.
25\% of the number is equal to 12.
50\% of the number is equal to 11.
10\% of the number is equal to 6.5.
300\% of the number is equal to 36.
Find the whole quantity if:
\dfrac{1}{2} of the quantity is equal to \$13.
\dfrac{1}{5} of the quantity is equal to 6 \text{ kg}.
\dfrac{1}{4} of the quantity is equal to 90\text{ mL}.
\dfrac{1}{10} of the quantity is equal to 15\text{ m}.
25\% of the quantity is equal to \$2.50.
50\% of the quantity is equal to \$0.75.
10\% of the quantity is equal to 840\text{ g}.
200\% of the quantity is equal to 120\text{ mL}.
For each of the following:
Find the 1\% of the number.
Hence, find the whole number.
9\% of the number is 72.
9\% of a number is 63.
60\% of a number is 480.
47\% of a number is 188.
4\% of a number is 236.
15\% of a number is 7500.
12\% of a number is 576.
8\% of a number is 230.
For each of the following:
Find the 1\% of the quantity.
Hence, find the whole quantity.
5\% of a quantity is \$320.
11\% of a quantity is \$16.50.
30\% of a quantity is 2700\text{ mL}.
54\% of a quantity is 6210\text{ mL}.
14\% of a quantity is 7280\text{ g}.
22\% of a quantity is 88\,000\text{ g}.
34\% of a quantity is 918\text{ L}.
78\% of a quantity is 10\,959\text{ cm}.
For each of the following:
Find 10\% of the quantity.
Hence, find the whole quantity.
150\% of a quantity is 135.
240\% of a quantity is 1464.
80\% of a quantity is \$160.
320\% of a quantity is \$13\,280.
For each of the following:
Find the 25\% of the quantity.
Hence, find the whole quantity.
125\% of a quantity is 30.
50\% of a quantity is 85.
150\% of a quantity is 75\,000.
250\% of a quantity is 1500.
For each of the following, find the whole quantity:
14\% of a quantity is 637.
26\% of a quantity is 10\,400.
32\% of a quantity is \$10\,240.
120\% of a quantity is \$87.30.
80\% of a quantity is 840\text{ mL}.
57\% of a quantity is 4651.2 \text{ g}.
64\% of a quantity is \$10\,400.
92\% of a quantity is 4738\text{ m}.
Melted snow accounts for 4800 \text{ ML} of a town's water supply in a year. This represents 12\% of its total supply.
Find 1\% of the yearly water supply.
Calculate the town's whole yearly water supply.
A rock sample was taken from a dig site. 3.7 \text{ kg} of the sample was pure gold. The team determined that the sample contained 25\% of the total gold found at the site. Calculate how many kilograms of gold were at the dig site overall.
Kate spends 40\% of her weekly income on rent. If her rent is \$480 each week, find her weekly income.
A total of 45\,000 new farmers entered the workforce last year. This is 9\% of all the farmers currently employed in the workforce. Find the number of farmers that are in the workforce altogether.
Tara knows that there are 423 radio towers in her city, and that this represents 9\% of the total number of towers in the city. Find the total number of towers in Tara's city.
Quentin knows that his house is 1.84 \text{ km} along the road from its start, and that the distance from the start of the road to his house represents 23\% of the road's total length. Find the road's total length.
A factory produces car seats for children. Last year 2400 car seats were identified as faulty by quality control experts and removed from the production line before sale.
These faulty seats represented 3\% of the total number of car seats produced by the factory that year. Find the total number of car seats produced by the factory.
A high school had 780 students participate in their athletics carnival. This represents 65\% of the total number of enrolled students. Find the total number of students enrolled at the high school.