- Finding Percents and Percent Equations
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- Finding a percentage of a whole number
- Finding a percentage of a whole number without a calculator: Basic
- Finding a percentage of a whole number without a calculator: Advanced
- Applying the percent equation: Problem type 1
- Applying the percent equation: Problem type 2
- Finding a percentage of a total amount: Real-world situations
- Finding a percentage of a total amount without a calculator: Sales tax, commission, discount
- Estimating a tip without a calculator
- Writing a ratio as a percentage without a calculator
- Finding the rate of a tax or commission
- Finding the total amount given the percentage of a partial amount
- Finding a percentage of a total amount in a circle graph

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# Finding a percentage of a whole number without a calculator: Advanced

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%. Other percentages can be written as combinations of these standard percentages. Like 2% is twice of 1%; 5% is half of 10%, 20% is twice of 10% and so on.

**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.

To find other percentages of whole numbers, we use the combinations of the standard percentages to find them.

What is 2% of 19.5?

### Solution

**Step 1:**

To find 1% of any whole number, we shift the decimal two places to the left in the whole number. To find 2% of any whole number, we double the 1% of that number.

**Step 2:**

1% of 19.5 is found by shifting the decimal point two places to left

1% of 19.5 = 0.195

So, 2% of 19.5 = 2 × 1% of 19.5 = 2 × 0.195 = 0.390 = 0.39

What is 30% of 7.25?

### Solution

**Step 1:**

To find 10% of any whole number, we shift the decimal one place to the left in the whole number. To find 30% of any whole number, we triple the 10% of that number.

**Step 2:**

10% of 7.25 is found by shifting the decimal point one place to left

10% of 7.25 = 0.725

So, 30% of 7.25 = 3 × 10% of 7.25 = 3 × 0.725 = 2.175

What is 15% of 40?

### Solution

**Step 1:**

15% can be written as a sum of 10% and 5%

To find 10% of any whole number, we shift the decimal one place to the left in the whole number. To find 5% of any whole number, we divide the 10% of that number by 2.

**Step 2:**

10% of 40 is found by shifting the decimal point one place to left

10% of 40.0 = 4.00; 5% of 40 = $\frac{(10\%\:of \:40.0)}{2} = \frac{4}{2} = 2$

15% of 40 = 10% of 40 + 5% of 40 = 4 + 2 = 6

So, 15% of 40 = 6