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## Percent, Fraction, And Decimal Equivalences

Any real number can be expressed as a decimal, a percentage, or a fraction number. For instance, 3/10, 30%, and 0.3 are all different forms of the same value, or quantity. You must know how to convert one form to another as part of solving problems. You should know how to write any equivalence quickly and confidently.

## Percent to Decimal or Vice Versa

To convert a percentage to a decimal number, move the decimal point two place to the left and drop the percent sign. Alternatively, to convert the decimal number to percentage, move the decimal point two places to the right and add percent sign.

10.5% = 0.105%

0.005 = 0.5%

## Percent to Fraction or Vice Versa

To convert a percentage to a fraction, divide the percentage by 100 and drop the percent sign. Alternatively, to convert a fraction to a percentage, multiply by 100 and add a percent sign. Also, note that percentages which are greater than 100% are converted to numbers greater than 1.

910% = 910/100 = 91/10 = 9 1⁄10

3/4 = 300/4 % =  75%

## Note

Percentages which are greater than 100 or less than 1 (such as 457% and .067%) can be confusing, because it’s a bit harder to grasp the magnitude of these numbers. To stay away from mistakes when dealing with numbers, always remember the magnitude of the number you are dealing with. For example, think of 0.09% as just less than 0.1%, which is one-tenth of a percent, or a thousandth (a pretty small valued number). Think of 0.4/5 as just less than 0.5/5, which is obliviously 1/10 or 10%. Think of 668% as more than 6 times a complete 100%, or between 6 and 7.

## Fraction to Decimal or Vice Versa

To convert a fraction to a decimal number, divide the numerator by the denominator of the fraction number, using long division. The resulted number might be one of the following:

• A precise value
• An approximation with a repeating pattern
• An approximation with no repeating pattern.

### Example

• 5/8=0.625 → The equivalent decimal number is precise after three decimal places.
• 5/9≈0.555 The equivalent decimal number can only be approximated (the digit 5 repeats indefinitely).
• 5/7≈0.714 The equivalent decimal number can safely be approximated.

Certain fraction-decimal-percent equivalents show up to us more often than others. You need to memorize the following conversions to be able to rewrite these numbers from one form to another without consuming time.

 Percent Decimal Fraction 50% 0.5 1/2 25% 0.25 1/4 75% 0.75 3/4 10% 0.1 1/10 30% 0.3 3/10 70% 0.7 7/10 90% 0.9 9/10 33% 0.33 1/3 66% 0.66 2/3
 Percent Decimal Fraction 16.67% 0.1667 1/6 83.33% 0.8333 5/6 20% 0.2 1/5 40% 0.4 2/5 60% 0.6 3/5 80% 0.8 4/5 12.5% 0.125 1/8 37.5% 0.375 3/8 62.5% 0.625 5/8 87.5% 0.875 7/8

## Simplifying and Combining Fractions

Using one of the basic operations (addition, subtraction, multiplication and division), a question might ask you to combine two or more fractions. The rules that are used to combine fractions by addition and subtraction are different from the ones used for multiplication and division.

Also read: Problems Involving Rate Of Production Or Work

## Addition and Subtraction and the LCD

For fractions addition and subtraction, the fractions must have a common denominator. Follow the below steps to work your way up when combining fractions by addition or subtraction:

• If the fractions already have common denominator, then, add or subtract directly.
• If they don’t have common denominator, then, you have to find one by using the following techniques:
• You can always multiply the denominators of all the fractions to get the common one. However, in sometimes, the result of the common denominator would be a big number which is clumsy to work with.
• Instead, you better find the lowest common denominator (LCD) by working your way up in multiples of the greatest denominator of the subject fractions. For example, denominators 6, 5 and 3. The largest denominator is 6. Hence, try the multiples of 6 until you come across the LCD. Start like this: 12, 18, 24, 30. 30 is the LCD of fractions 6, 5 and 3.

## Example

Q: 5/3 – 5/6 + 5/2 =

1. 15/11
2. 5/2
3. 15/6
4. 10/3
5. 15/3

The correct answer is (4). To find the LCD, do the following:

1. Try multiples of 6 until you hit one that is also a multiple of both 2 and 3.
2. The LCD is 6.
3. Multiply each numerator by the number by which you would multiply the denominator to get the resulted LCD “6”.
4. Place the products over the LCD.
5. Combine the number in the numerators only.
6. Pay attention to the signs when you combine.

Finally, simplify to lowest terms:

5/3 – 5/6 + 5/2 = 10/6 – 5/6 + 15/6 = 20/6 = 10/3

## Multiplication and Division

• Multiplication: to multiply fractions, multiply the numerators and denominators respectively. No need for the denominators to be the same to multiply as the case in addition and subtraction.
• Division: to divide one fraction by another, multiply the fraction before the division sign by the reciprocal of the fraction after the division sign. Then, divide the numerator by the denominator to simplify the result.

### Multiplication Example

1/5 x 5/3 x 1/7 = 5/105 = 1 / 21

### Division Example

2/5 ÷ 30/40 = 2/5 x 4/3 = 8/15

## Note

To simplify multiplication and division, you can factor out common numbers between the numerators and denominators. Let’s take an example:

3/4 x 4/9 x 3/2.

Factor out 3 and 4 from the first two fractions. The operations simplifies to 1/1 x 1/3 x 3/2. Then, factor out 3 from the second two fractions simplifying the operation to 1/1 x 1/1 x 1/2 = 1/2.

## Conclusion

You can rewrite fractions as decimals or percentages, or vice versa by using simple techniques. Also, in the above article, we underlined how to combine numbers by addition, subtraction, multiplication or division.

If you still have any question, don’t hesitate to place a comment below.