Learn Estimation Techniques for Calculating the Percent of a Number

Number	Percent	Fraction
$10$	$10 %$	$\frac{1}{1 0}$
$20$	$20 %$	$\frac{1}{5}$
$25$	$25 %$	$\frac{1}{4}$
$50$	$50 %$	$\frac{1}{2}$
$75$	$75 %$	$\frac{3}{4}$

Number

Percent

Fraction

10

10 %

\frac{1}{1 0}

20

20 %

\frac{1}{5}

25

25 %

\frac{1}{4}

50

50 %

\frac{1}{2}

75

75 %

\frac{3}{4}

Describe any real-world problem in which the percent of a number gives a result that is greater than the original number? Then, solve the problem.

Let's consider the following real-life problem.

We need to calculate 150 % of 18 to find the number of pages Emily read that one day. Let's start by rewriting 150 as a decimal number. That can be done by dividing the percent by 100 % by moving the decimal point two places to the left.

Next, multiply 1.5 by 18. 1.5* 18=27 We calculated that 150 % of 18 is 27. This means that Emily read 27 pages instead of the planned 18. In this case, the percent of the number 27 is greater than the number itself, 18. ccc & & Percent of [-0.1cm] Number& & a Number ↓ & & ↓ 18 & < & 27 In general, one number is usually set to represent 100 % in real-world situations. This number is then compared to another number. Calculating any percent that is greater than 100 %, like 136 % or 201 %, will result in a number greater than the original number. Here are a few more examples.

Original Number	Percent of the Number	Calculation	Comparison
The life expectancy in the US was about 77.3 years in 2020.	Sarah Knauss born in 1880 lived for 154 % of that number.	154 %* 77.3≈ 119	77.3< 119
The cost of a gallon of milk was $2.78 in 2000.	In 2021, the cost of a gallon of milk was 128 % of that price.	128 % * $2.78≈ $3.55	$2.78< $3.55
LaShay earns $18 per hour.	After getting a raise, she now earns 115 % of what she earned before.	115 % * $18= $20.7	$18< $20.7

Order the percents of numbers from least to greatest without finding their exact values.

Let's start by looking at the list of the percents of numbers. 32 % &of 45 70 % &of 28 20 % &of 45 70 % &of 39 We can see that one pair shares the same number 45, while the other pair shares the same percent 70 %. Let's consider each pair one at a time.

Pair With the Same Number

Now, let's take a closer look at the pair that shares the same number. 32 % &of 45 20 % &of 45 Here, we need to calculate 32 % and 20 % of the same number 45. Since 32 is greater than 20, 32 % of 45 is a greater number than 20 % of 45. 20 % of 45 < 32 % of 45

Pair With the Same Percent

We can consider the second pair that shares the same percent in a similar fashion. 70 % &of 28 70 % &of 39 The same percent is calculated of different numbers 28 and 39. Since 28 is less than 39, 70 % of 28 is less than 70 % of 39. 70 % of 28 < 70 % of 39

Final Comparison

We ordered the percents from least to greatest in two pairs. Pair I: 20 % of 45 < 32 % of 45 Pair II: 70 % of 28 < 70 % of 39 Now, let's consider the greater expression from the first pair and the smaller expression from the second pair. 32 % of 45 70 % of 28 Note that we can round both 32 and 28 to 30. Let's do this! ccc 32 % of 45 & ≈ & 30 % of 45 70 % of 28 & ≈ & 70 % of 30 Also, recall that the percent and the number can be interchanged and the result will still be the same. We can use this property to interchange 70 and 30 in the second pair. 70 % & of 30 &⇕ 30 % &of 70 This way we get a pair with the same percent once again. 30 % of 45 30 % of 70 The number 45 is less than 70, so 30 % of 45 is less than 30 % of 70. ccc 30 % of 45 & < & 30 % of 70 ↓ & & ↓ 32 % of 45 & < & 70 % of 28 We found that the greater expression from the first pair is smaller than the smaller expression from the second pair. 20 % of 45 < 32 % of 45 < < 70 % of 28 < 70 % of 39 Finally, we can order the percents of numbers from least to greatest. 20 % of 45 32 % of 45 70 % of 28 70 % of 39

Estimation and Percent of a Number

Catch-Up and Review

Connection Between Percents and Numbers

How to Find a Percent of a Number?

Finding the Percent of a Number

Extra

Counting Fish in a Pond

Hint

Solution

Comparing Fish Sizes

Hint

Solution

Estimating the Percent of a Number

Traveling Across the Pacific Ocean

Hint

Solution

Finding Percents of Numbers

A Secret for Faster Calculations

Pair With the Same Number

Pair With the Same Percent

Final Comparison

Estimation and Percent of a Number

Recommended exercises

	9 Theory slides
	11 Exercises - Grade E - A
	Each lesson is meant to take 1-2 classroom sessions