|
Fractions –
Decimals – Percents (Part 1)
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.
|
 
|
|
|
|
|
|
1 mile
|
1 mile
|
1 mile
|
1
|
mile
|
- 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.
 
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:
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%
|
