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In today’s class, we will be talking more about fractions. Enjoy the class!
Fractions
Conversion of fractions to decimals
To convert fractions to decimals, look at the fraction as a division problem. Take the top number, or the numerator, of the fraction and divide it by the bottom number, or the denominator. You can do this in your head, by using a calculator, or by doing long division. For example, ¼ is just 1 divided by 4, or 0.25.
Just divide the top of the fraction by the bottom, and read off the answer!
Example 1:
What is 5/8 as a decimal
get your calculator and type in 5 / 8 = 0.625
Example 2:
here is what long division of 5/8 looks like:
0.625
8)5.000
0
5.0
4.8
20
16
40
40
0
In that case, we inserted extra zeros and did 5.000/8 to get 0.625
Another method
Yet another method you may like is to follow these steps:
- Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0.
- Step 2: Multiply both top and bottom by that number.
- Step 3. Then write down just the top number, putting the decimal point in the correct spot (one space from the right-hand side for every zero in the bottom number)
Example 3:
Convert 3/4 to a Decimal
Step 1: We can multiply 4 by 25 to become 100
Step 2: Multiply top and bottom by 25:
| 3/4 ×25 | = | 75/100 |
Step 3: Write down 75 with the decimal point 2 spaces from the right (because 100 has 2 zeros);
Answer = 0.75
Example 4:
Convert 3/6 to a Decimal
Step 1: We have to multiply 16 by 625 to become 10,000
Step 2: Multiply top and bottom by 625:
| 3/6 ×625 | = | 1,875/10,000 |
Step 3: Write down 1875 with the decimal point 4 spaces from the right (because 10,000 has 4 zeros);
Answer = 0.1875
Example 5:
Convert 1/3 to a Decimal
Step 1: There is no way to multiply 3 to become 10 or 100 or any “1 followed by 0s”, but we can calculate an approximate decimal by choosing to multiply by, say, 333
Step 2: Multiply top and bottom by 333:
| 1/3 ×333 | = | 333/999 |
Step 3: Now, 999 is nearly 1,000, so let us write down 333 with the decimal point 3 spaces from the right (because 1,000 has 3 zeros):
Answer = 0.333 (accurate to only 3 decimal places !!)
To convert a decimal to a fraction
To convert a Decimal to a Fraction, follow these steps:
Step 1: Write down the decimal divided by 1, like this: decimal/1
Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
Step 3: Simplify (or reduce) the fraction
Example 1:
Convert 0.75 to a fraction
Step 1: Write down 0.75 divided by 1:
0.75/1
Step 2: Multiply both top and bottom by 100 (because there are 2 digits after the decimal point so that is 10×10=100):
| 0.75/1 × 100 | = | 75/100 |
(Do you see how it turns the top number into a whole number?)
Step 3: Simplify the fraction (this took me two steps):
| 75/100 | ÷5= | 15/20 | ÷ 5 = | 3/4 |
Answer = 3/4
Note: 75/100 is called a decimal fraction and 3/4 is called a common fraction!
Example 2:
Convert 0.625 to a fraction
Step 1: write down:
0.625/1
Step 2: multiply both top and bottom by 1,000 (3 digits after the decimal point, so 10×10×10=1,000)
625/1000
Step 3: Simplify the fraction (it took me two steps here):
| 625/1000 | ÷ 25= | 25/40 | ÷ 5= | 5/8 |
Answer = 5/8
When there is a whole number part, put the whole number aside and bring it back at the end.
Example 3:
Convert 2.35 to a fraction
Put the 2 aside and just work on 0.35
Step 1: write down:
0.35/1
Step 2: multiply both top and bottom by 100 (2 digits after the decimal point so that is 10×10=100):
35/100
Step 3: Simplify the fraction:
| 35/100 ÷ 5 | = | 7/20 |
Bring back the 2 (to make a mixed fraction):
Answer = 2 7/20
Example 4:
Convert 0.333 to a fraction
Step 1: Write down:
0.333/1
Step 2: Multiply both top and bottom by 1,000 (3 digits after the decimal point so that is 10×10×10=1,000)
333/1000
Step 3: Simplify Fraction:
Can’t get any simpler!
Answer = 333/1000
In our next class, we will be talking more about Fractions. We hope you enjoyed the class.
Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.
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