# Estimation - Examples, Exercises and Solutions

## Estimation

In fact, estimation allows us to guess (hence the redundancy) the supposed result, without performing the exact calculation.
That is, in certain cases, we don't need to know the solution precisely, a rough idea is sufficient to solve a particular mathematical problem.

Sometimes we are asked to compare mathematical expressions, draw deductions from one exercise to another, round numbers to simplify a calculation, and other similar tasks.

For example:

It can be estimated that half of 1603 is approximately 800.

### Suggested Topics to Practice in Advance

1. How to Calculate Percentage

## Examples with solutions for Estimation

### Exercise #1

Approximately what is $\frac{6}{25}$ as a percentage?

### Step-by-Step Solution

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

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

$20\%$

20%

### Exercise #2

Approximately what is $\frac{50}{204}$ written as a percentage?

### Step-by-Step Solution

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:

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

$25\%$

25%

### Exercise #3

Approximately what is $\frac{14}{5}$ as a percentage?

### Step-by-Step Solution

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:

$3\times100=300$

$300\%$

300%

### Exercise #4

Approximately what is $\frac{1}{7}$ written as a percentage?

### Step-by-Step Solution

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!

15%

### Exercise #5

What percentage does the shaded area of the figure represent?

### Step-by-Step Solution

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%.

80%

### Exercise #6

Organise the following into two groups of values less than 12% and values greater than 12%.

$\frac{11}{100},0.1,0.13,\frac{6}{40},20\%$

### Step-by-Step Solution

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

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%.

0.13,\frac{6}{40},20\%>12\%

\frac{11}{100},0.1<12\%

### Exercise #7

Approximately what is $\frac{11}{50}$ written as a percentage?

20%

### Exercise #8

Approximately what is $\frac{1}{9}$ as a percentage?

10%

### Exercise #9

Approximately what is $\frac{15}{61}$ written as a percentage?

25%

### Exercise #10

Approximately what is $\frac{80}{11}$ written as a percentage?

800%

### Exercise #11

Approximately what is $\frac{34}{70}$ written as a percentage?

50%

### Exercise #12

Approximately what is $\frac{12}{13}$ written as a percentage?

96%

### Exercise #13

Approximate what is $\frac{49}{102}$ written as a percentage?

50%

### Exercise #14

Approximately what is $\frac{41}{51}$ written as a percentage?

### Video Solution

Approximately what is $\frac{43}{200}$ written as a percentage?