Estimation - Examples, Exercises and Solutions

We look for the closest fraction to be able to divide the numerator by the denominator:

$\frac{5}{25}$

We break down the denominator into a multiplication exercise:

$\frac{5}{5\times5}$

We simplify:

$\frac{1}{5}$

We convert the fraction into a percentage

$\frac{1}{5}\times100=\frac{100}{5}=$

$20\%$

We are looking for the closest fraction to be able to divide the numerator by the denominator:

$\frac{15}{5}=3$

Convert the fraction into percentage:

$3\times100=300$

$300\%$

Find the closest fraction so we can divide the numerator by the denominator:

$\frac{50}{200}$

We break down the denominator into a multiplication exercise:

$\frac{5}{50\times4}$

We simplify:

$\frac{1}{4}$

We convert the fraction to a percentage:

$\frac{1}{4}\times100=\frac{100}{4}=$

$25\%$

The easiest way to convert a fraction to a percentage is to convert the denominator to 100.

However, 100 is not in the multiplication table of 7, so in this exercise, we will use an estimation.

First, we will take 7 to a close number that can be easily converted to 100 - 20.

We know that 20*5 is 100 and that 7*3=21.

Although 21 is not equal to 20, it is approximately close.

Therefore, we will first multiply the entire fraction (the numerator and the denominator) by 3 to reach the denominator of 20.

Then we multiply the denominator and the numerator by 5 to reach the denominator 100.

We will arrive at a result of 15/100, that is 15%, which is the correct answer!

It can be said with certainty that the shaded area is larger than half of the shape.

That is, the shaded part is more than 50%.

Therefore, we can disregard answers B and D.

The unshaded part is greater than 1% of the figure; it is not possible for 100 such parts to form the complete shape, therefore, we can disregard answer C.

Therefore, the correct answer must be 80%.

$12\%=\frac{12}{100}=0.12$

Now we will convert all values into percentages and see which are greater and which are less than 12%.

$\frac{6}{40}\times\frac{2.5}{2.5}=\frac{15}{100}=15\%$

$\frac{11}{100}=11\%$

$0.1=\frac{10}{100}=10\%$

$0.13=\frac{13}{100}=13\%$

Now we can observe which are greater and less than 12%.

To solve this problem, we need to compare each given value with $\frac{4}{2}$.

• Calculate $\frac{4}{2} = 2$.

Now, convert all given values to decimals:

• The value $1.3$ is already in decimal form: $1.3$.
• Convert $\frac{1}{2}$ to decimals: $0.5$.
• Convert $150\%$ to decimals by dividing by 100: $\frac{150}{100} = 1.5$.
• Calculate $\frac{74}{12} \approx 6.1667$.
• $0.5$ is already in decimal form: $0.5$.

Now, compare each value with $2$:

• Values less than $2$: $1.3, \frac{1}{2}, 150\%, 0.5$ (i.e., $1.3, 0.5, 1.5, 0.5$).
• Values greater than $2$: $\frac{74}{12}$ (i.e., approximately $6.1667$).

Therefore, the solution to the problem is:

$1.3, \frac{1}{2}, 150\%, 0.5 < \frac{4}{2}$

$\frac{74}{12} > \frac{4}{2}$