### Key Concepts

• Determine the percentage of a given objective presence within a group of 100 objects.

• Convert the percentage into a decimal.

• Determine how much something will cost if it is discounted by a given percentage.

• Use a model to represent problems involving percent

**Introduction**:

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

- Here we round up or down to both numbers to some close numbers, which makes the calculation easier.

- Multiply the rounded numbers together.

- Divide the result by 100.

This is actually perfect for when you are dining because you can round up or down based on the level of service you receive.

Let’s suppose that when you and your friend have dinner. You both decided the service was good, so when you round your 18%, you decide to round up to 20% since 20 is an easy number to work with. You also have to round your $52.74. 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.

20 × 50 = 1000

Lastly, we divide the result by 100

= 1000/100

= 10

We see that when we estimate 18% of $52.74, we get $10.00, which is pretty close to the exact answer.

**Let’s understand to Find the Percent of Number.**

Here, we have two major methods to find the percent of the whole number.

Double line graph method

Using decimal method

**Method 1: **

**Use a double line diagram and benchmark fraction equivalent to Estimate Percent**

Example 1: Find 26% of 875.

**Solution: **

26% ≈ 25 %

And 875 ≈ 900

Now =

25100×25100×

900

=

14×14×

900

= 225

**Method 2: **

Use the decimal form to find the percent of the whole number

**Example 1: Find 20% of 200.**

**Solution: **

= 0.2 × 200

= 40

**Example 2: Find 15% of 60.**

**Solution: **

= 0.15 × 60

= 9** **

**Example3: Find 40% of 450.**

**Solution: **

Quantity = 450, Percentage = 40%

Step 1 =

20100

Step 2 =

2010020100

×× 650

= 2

××

65

= 130

**More Word Problems: Understand Percent**

**Example 1: **Sophia saves 40% of her monthly income. If her monthly income is $35,500, how much money does she save every month?

**Solution:**** ** Monthly income of Sophia = $ 35,500

So, monthly saving of Sophia = 40% of $35500

=

4010040100

×× 35500

=

40× 35540× 355

=

1420014200

**Example 2: **A baseball pitcher won 80% of the games he pitched. If he pitched 35 ballgames, how many games did he win?

**Solution:**

First, we multiply 80 by 35

= 80 × 35

= 2800

Now, divide 2800 by 100 =

28001002800100

= 28

So, he played 28 games out of 35.

### What have we learned:

• Determine the percentage of a given objective presence within a group of 100 objects.

• Convert the percentage into a decimal.

• Convert the percentage into a fraction.

• Determine how much something will cost if it is discounted by a given percentage.

• Use a model to represent problems involving percent.

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