### Key Concepts

- Determine the amount of percent with in a group of 100 objects.
- Determine how much something will cost if it is discounted by a given percent.
- Estimate the percent of number using equivalent Fraction
- Estimate the value using rounding of the percent.

**Introduction: **

**Estimating the Round off number to easy to work with:-**

If we are trying to find n percent of x, we can estimate this percent using the following steps:

Round both n and x up or down to numbers that are easy to work with.

Multiply the rounded numbers together.

Divide the result by 100.

**Examples:-**

Let’s suppose that when you and your friend had dinner, so when you round your 17%, you decide to round up to 20% since 20 is an easy number to work with. You also have to round your $51.64. Since this is very close to $50, and 50 is easy to work with, you round to $50.

**The next step is to multiply 20 by 50.**

You can estimate a percent of a number by substituting a fraction that is close to a given percent.

**Let’s understand to estimating percent. **

**Use a fraction to estimate 26% of 62.**

26% of 62

1/4 × 62 (Here, 26% is about 25% And 25% is equivalent to 1/4)

1/4 × 60 Change 62 to a compatible number

26% of 62

15

Note: Compatible number are the close to the calculation it help you to solve the mental maths problems.

**Examples 2:-**

Alma’s T’s is offering two T shirts at 16, While good T’s is running their 9.99 get one of 50% off sale. Which stores offers the best sale?

**Solution:-**

First find the discount price for two T-shirts at Good’s T’s

50% of $9.99 = 1/2 of 9.99

=1/2 of 10

= $5

The second shirt cost approximately $5. Since 10 + 5 =** $ 15**

The Two T-shirts for $ 15 at Good’s T’s is better deal

**Using rounding off number to Estimate Percent. **

In this process of estimation first we round off the number near to the multiple of 10, 100, 1000 etc. By the rounding of numbers become easy to calculate.

**Example 1:- **You purchase a Set of ten T-shirts in a shop for $578.80 and the shopkeeper gives a discount of 19%. How much is estimated to be paid?

**Solution:**

Given, the bill of T-shirt = Rs.578.80

Rounding of the bill we get = Rs.580

We have to find a 19% discount first.

So, by rounding off 19 near tens we get 20%

20% of 580

= 20/100 × 580

= 116

Now estimated amount to be paid to the shopkeeper.

= 580 – 116

= $464

**Estimating percent by moving the decimal**

Find 1% of any number is easy task, By finding the one percent makes easy to calculate desirable percent. We can understand it by the following examples.

**Example 1:** Find 21% of 94

1% of 94

94 = 0.94 (Moving the decimal point two digit to the left)

Now, Find the 21% = 0.94 × 21

= 19.74

**More Example: Estimate to find percent**

**Estimate the following percentage.**

**Find 47% of 153**

**Solution:-** 47% is near to 50% And 153 is near to 150

Now, 50% of 150

1/2 × 150 (Cross Multiplication)

= 75(Approximate)

**Find 36% of 781**

**Solution:-** 36% is near to 40% And 781 is near to 800

Now, 40% of 800

= 40/100 × 800

= 2/5 × 800(Cross Multiplication)

= 2 × 160

= 320(Approximate)

**Find 41% of 231**

**Solution:-** 41% is near to 40% And 231 is near to 230

Now, 40% of 230

2/5 × 230(Cross Multiplication)

= 2 × 46

= 92(Approximate)

**Concept Map:**

### What have we learned:

- Determine the amount of percent with in a group of 100 objects.
- Determine how much something will cost if it is discounted by a given percent.
- Estimate the percent of number using equivalent Fraction
- Estimate the value using rounding of the percent.

#### Related topics

#### Composite Figures – Area and Volume

A composite figure is made up of simple geometric shapes. It is a 2-dimensional figure of basic two-dimensional shapes such as squares, triangles, rectangles, circles, etc. There are various shapes whose areas are different from one another. Everything has an area they occupy, from the laptop to your book. To understand the dynamics of composite […]

Read More >>#### Special Right Triangles: Types, Formulas, with Solved Examples.

Learn all about special right triangles- their types, formulas, and examples explained in detail for a better understanding. What are the shortcut ratios for the side lengths of special right triangles 30 60 90 and 45 45 90? How are these ratios related to the Pythagorean theorem? Right Angle Triangles A triangle with a ninety-degree […]

Read More >>#### Ways to Simplify Algebraic Expressions

Simplify algebraic expressions in Mathematics is a collection of various numeric expressions that multiple philosophers and historians have brought down. Talking of algebra, this branch of mathematics deals with the oldest concepts of mathematical sciences, geometry, and number theory. It is one of the earliest branches in the history of mathematics. The study of mathematical […]

Read More >>#### How to Solve Right Triangles?

In this article, we’ll learn about how to Solve Right Triangles. But first, learn about the Triangles. Triangles are made up of three line segments. These three segments meet to form three angles. The lengths of the sides and sizes of the angles are related to one another. If you know the size (length) of […]

Read More >>
Comments: