### 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.

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