Introduction

In this lesson, we solve problems on finding a percentage of a total amount without a calculator involving sales tax, commission and discount.

Consider the following solved examples.

Example 1

Thesalestaxona$1050computersystemis$63.Whatisthesalestaxrate?

Solution

Step 1:

Price of the computer = $1050

Sales tax = $63

Step 2:

Rate of Sales tax = ⟮$63$1050⟯×100

= 6%

Example 2

At a store, a $60 dress is sold at a discount of $12? What is the percentage of discount and sale price of the dress?

Solution

Step 1:

Discount = $12

Marked price of dress = $60

Step 2:

Percentage of discount = ⟮$12$60⟯×100=20%

Sales price of the dress = $60 $12

= $48

Example 3

Mike is a salesman who earns a base salary of $360 per week plus $567 as commission on sales. What was Mikes percentage of commission and weekly salary if his total sales for the week were $6300?

Solution

Step 1:

Total sales for the week = $6300

Commission on sales = $567

Step 2:

Percentage of commission = ⟮$567$6300⟯×100=9%

Base salary = $360

= $360 + $567 = $927

Introduction

In this lesson, we solve problems involving percent equations. Percent problems can be reduced to equations and the unknown quantity is found by solving that equation

Consider the following example problems

Example 1

125% of 50.8 is what number?

Solution

Step 1:

In this problem, the words of, is, and what translate to a multiplication sign ×, an equal to sign = and an unknown variable x.

Step 2:

The problem is re-written as 125% of 50.8 = x

This reduces to percent equation 125% × 50.8 = x

or 1.25 × 50.8 = x

Step 3:

Solving for x, x = 1.25×50.8 = 63.5

So, 125% of 50.8 is 63.5

Example 2

10.78 is what percent of 19.6?

Solution

Method 1

Step 1:

In this problem, the words of, is, and what translate to a multiplication sign × and an equal to sign = and an unknown variable x.

Step 2:

The problem is re-written as x % of 19.6 = 10.78

This reduces to percent equation x % × 19.6 = 10.78

or 0.0x × 19.6 = 10.78

Step 3:

Solving for x, x=(10.78×100)19.6=55

So, 55% of 19.6 is 39

Method 2

10.78 = x% × 19.6

10.78/19.6 = x=(x%×19.6)19.6=x

x = 0.55; converting the decimal to percent we get

x = 0.55 = 55%

Example 3

What is 90% of 218?

Solution

Step 1:

In this problem, the words of, is, and what translate to a multiplication sign × and an equal to sign = and an unknown variable x.

Step 2:

The problem is re-written as 90% of 218 = x

This is reduced to percent equation 90% × 218 = x

or 0.90 × 218 = x

Step 3:

Solving for x, x = 0.90×218 = 196.2

So, 90% of 218 is 196.2

Introduction

In this lesson, we solve problems involving percent equations. Percent problems can be reduced to equations and the unknown quantity is found by solving that equation

Consider the following example problems

Example 1

36 is what percent of 80?

Solution

Step 1:

In this problem, the words of, is, and what translate to a multiplication sign × and an equal to sign = and an unknown variable x.

Step 2:

The problem is re-written as x% of 80 = 36

This is reduced to percent equation x% × 80 = 36

or 0.0x × 80 = 36

Step 3:

Solving for x, x = 36×100/80 = 45

So, 45% of 80 is 36

Example 2

65% of what is 39?

Solution

Step 1:

In this problem, the words of, is, and what translate to a multiplication sign × and an equal to sign = and an unknown variable x.

Step 2:

The problem is re-written as 65% of x = 39

This reduces to percent equation 65% × x = 39

or 0.65 × x = 39

Step 3:

Solving for x, x = 39×100/65 = 60

So, 65% of 60 is 39

Example 3

42 is what percent of 140?

Solution

Step 1:

In this problem, the words of, is, and what translate to a multiplication sign × and an equal to sign = and an unknown variable x.

Step 2:

The problem is re-written as x% of 140 = 42

This is reduced to percent equation x% × 140 = 42

or 0.0x × 140 = 42

Step 3:

Solving for x, x = 42×100/140 = 30

So, 30% of 140 is 42.

Introduction

We can find the percentages of whole numbers without a calculator in some cases where standard percentages are involved. Some standard percentages are like 1%, 10%, 25%, 50%, 100%.

Rules to find the percentage of a whole number without a calculator

• To find 1% of any whole number, we shift the decimal two places to the left in the whole number.
• To find 10% of any whole number, we shift the decimal one place to the left in the whole number.
• To find 25% of any whole number, we divide the whole number by 4.
• To find 50% of any whole number, we divide the whole number by 2.
• To find 100% of any whole number, we keep the whole number as it is.

Example 1

What is 10% of 180?

Solution

Step 1:

To find 10% of any whole number, we shift the decimal one place to the left in the whole number.

Step 2:

So, 10% of 180 is found by shifting the decimal point one place to left 180 = 180.0

So, 10% of 180 = 18.00 = 18

Example 2

What is 25% of 70?

Solution

Step 1:

To find 25% of any whole number, we divide the whole number by 4.

Step 2:

25% of 70 is found by divide the whole number by 4.

So, 25% of 70 = 704=17.50

Example 3

What is 100% of 127?

Solution

Step 1:

To find 100% of any whole number, we keep the whole number as it is.

Step 2:

So, 100% of 127 is found by keeping the whole number 127 as it is

So, 100% of 127 = 127

Introduction

In this lesson, we learn how to find the percentage of a whole number.

Finding percentage of a whole number is basically a multiplication problem.

It is a product of the percentage and the whole number. The percentage is written as a decimal and multiplied with the whole number to give the percentage of the whole number.

Rules to find the percentage of a whole number

• The percentage of a whole number is written as a product of the percentage and the whole number. For example: 60% of 98 is written as 60% × 98
• The percentage then is written as a decimal. To do this, the decimal point is shifted two places to the left and the percent sign is droppedFor example: 60% × 98 = 60.0% × 98 = 0.60 × 98
• The multiplication of the decimal and the whole number is carried out and product finally gives the percentage of the whole numberFor example: 0.60 × 98 = 58.80

Formula

x% of y where x is any number and y is a whole number

x% of y = x% × y = 0.0x × y

Example 1

What is 15% of 90?

Solution

Step 1:

15% of 90 = 15% × 90 = 15.0% × 90

Step 2:

To convert the percentage to a decimal, the decimal is shifted two places to left.

15.0% × 90 = 0.15 × 90

Step 3:

0.15 × 90 = 13.50

So, 15% of 90 = 13.50

Example 2

What is 25% of 72?

Solution

Step 1:

25% of 72 = 25% × 72 = 25.0% × 72

Step 2:

To convert the percentage to a decimal, the decimal is shifted two places to left.

25.0% × 72 = 0.25 × 72

Step 3:

0.25 × 72 = 18.00

So, 25% of 72 = 18.00 = 18

Example 3

What is 150% of 21?

Solution

Step 1:

150% of 21 = 150% × 21 = 150.0% × 21

Step 2:

To convert the percentage to a decimal, the decimal is shifted two places to left.

150.0% × 21 = 1.50 × 21

Step 3:

1.50 × 21 = 31.50

So, 150% of 21 = 31.50

This tutorial provides comprehensive coverage of finding percents and percent equations based on Common Core CCSS and State Standards and its prerequisites. Students can navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs. This simple tutorial uses appropriate examples to help you understand finding percents and percent equations in a general and quick way.

Audience

This tutorial has been prepared for beginners to help them understand the basics of finding percents and percent equations. After completing this tutorial, you will find yourself at a moderate level of expertise in finding percents and percent equations, from where you can advance further.

Prerequisites

Before proceeding with this tutorial, you need a basic knowledge of elementary math concepts such as number sense, addition, subtraction, multiplication, division, whole numbers, fractions, decimals, comparing and ordering whole numbers, ratios and proportion, percents and so on.