Fractions – Decimals – Percents

Fractions 

Fractions are used to name numbers between whole numbers. 

Examples: ½  ( one half), 1/3 (one third), ¼ (one quarter or one fourth), ¾ (three quarters or three fourths). 

Fractions are used for measuring:  

• School is 3 and ½ miles from my house.

• I need 1 and ½ cups of sugar
• My brother is 4 and ½ feet tall.

They are also used to name parts of a whole: 

• I’m going to give each of my brothers ¼ of this pie.

• ½ of my class are boys.

 Fractions are written as a/b. The number below, b, is called the denominator. The denominator tells you how many equal parts the whole is divided into.

 The number on top, a, is called the numerator. The numerator tells you how much of the whole is being considered.

 ¾ tells you the whole is divided into 4 parts, and we are measuring or counting 3 of them.  

• A number can be written as a fraction in many ways – they are called equivalent fractions.

Example: ½ = 2/4 = 4/8 = 8/16. 

• You can make an equivalent fraction by multiplying or dividing the numerator and the denominator by the same number (2 in the above example).

Fractions can be compared, added or subtracted only if they have the same denominator, called the common denominator. 

To find the common denominator, find the multiples of each denominator. 

Example: Find the common denominators of 2/4 and 5/8: 

• Multiples of 4: 4,8,12,16,20,24,28,32…
• Multiples of 8: 8,16,24,32…
• Common denominators are: 8,16,24,and 32

The least common denominator is the smallest common denominator . 

• The least common denominator in the example above is: 8

Compare 2/3 and 3/5: 

• Find the least common denominator.
  • The common denominators for 2/3 are: 3,6,9,15,18…
  • The common denominators for 3/5 are: 5,10,15,20,25,…
  • The least common denominator for 2/3 and 3/5 is: 15

15 is 5 times 3, and 3 times 5) 

• The equivalent fraction for 2/3 with a denominator of 15 is: 10/15

(multiply the numerator and the denominator by 5) 

• The equivalent fraction for 3/5 with a denominator of 15 is: 9/15

(multiply the numerator and denominator by 3) 

Conclusion: 10/15 > 9/15 which means 2/3 > 3/5. 

We could also add these fractions: (2/3 + 3/5) = (10/15 + 9/15) = 19/15. 

And we could subtract them: (2/3 – 3/5) = (10/15 – 9/15) = 1/15. 

Notice: when we add or subtract the fractions, the common denominator stays the same, and we add or subtract the numerators. 

Decimals 

Decimals are also use to name numbers between whole numbers.  

0.5 = 5 tenths = 5/10 = ½ 

A fraction can be changed into a decimal by dividing the numerator by the denominator: 

• ¾ = 3 divided by 4

So ¾ = 0.75 

Try this with 3/5 or 3 ÷ 5.  Did you get 0.60 

Percents 

0.75 is read as 75 hundreths. So if 1 is divided into 100 parts, 0.75 means 75 of those one hundredth parts.  

 0.60 is read as 60 hundreths. Again, if one is divided into 100 parts, 0.60 means 60 of those hundredth parts.

 Percent means per hundred or out of a hundred. 75% means 75 out of 100.

60% means 60 out of 100. 

Summary 

¾ = 0.75  = 75/100 = 75% 

3/5 = 0.60 = 60/100 = 60% 

½ = 0.50 = 50/100 = 50% 

0.93  = 93/100 = 93%