| FRACTIONS PRIMER |
What Are Fractions?
When we look at a fraction, what do we see? There's one whole number over another whole number. If the top number is smaller than the bottom one, we call it a proper fraction. If the top number is bigger than the bottom one, we call it an improper fraction.
The top number in a fraction is called the numerator
The bottom number is called the denominator
The numerator is divided by the denominator.
The denominator divides into the numerator.
Though we usually think a fraction is a smaller part of a whole something, that's only true sometimes. Other times, a fraction is bigger than a whole something. But a fraction is always a division statement. The number ½ says that we divided 1 whole thing into 2 equal parts. In the same way, ¾ says we divided something -- say a pizza -- into 4 equal parts and we ate 3 of them. It could also mean we have 4 things of equal size or value, and 3 of them are of interest because of something about them -- a quality they share -- they're all red or they've all been eaten. So if we ordered 4 pizzas and ate 3 of them, we'd have eaten ¾ of all the pizzas. We would have 1 of 4 or ¼ of all the pizzas left over.
A Fraction Means DIVISION
When we take half of something, we divide by 2.
If we need a fifth of a number, we divide it by 5.
Here are some fraction images. Notice that the blue and red circles are all exactly the same size and that the parts or sections of the rectangle and the pie are also equal in size.
Naming Fractions
Fractions are named by their denominators. Most names for fractions end with "th" -- like one fifth, one nineteenth, one twenty-seventh -- but -- (why is there always a "but"??) -- there are exceptions.
We call the fraction 1 over 2 (½) one half, not one twoth ( that we take to the dentist). 1 over 3 is called a third, not a threeth. And then there's one fourth -- which could be called one quarter and often is -- especially when we're talking about money or football games.
Also, if the denominator has 1, 2, or 3 in the 1's place -- such as
,
the fraction has a special name that ends in "st", "nd" or "rd".
1 over 31 is called one thirty-first,
1 over 52 is called one fifty-second
and 1 over 43 is called one forty-third.
If the number in the 1's place is bigger than 3, we add "th" to the digit name.
So, 1 over 27 is pronounced one twenty-seventh.
Writing 1 as a Fraction
We know that a fraction means division -- and we know that any number divided by itself is equal to 1 -- so to write 1 as a fraction, we put the same number in the numerator and in the denominator. Multiplying a number by 1 doesn't change the value, just the form.
Now get a pencil, an eraser and a note book, copy the questions,
do the practice exercise(s), then check your work with the solutions.
If you get stuck, review the examples in the lesson, then try again.
Fractions Exercise 1
1) Use the diagram to fill in the table. The first one is done for you.
| equal parts | red part in digits |
blue part in words |
| a) 6 |  |
five-sixths |
| b) | ||
| c) | ||
| d) | ||
| e) |
2) Write a fraction = 1 with these denominators:
| a) 19 | b) 23 | c) 207 | d) 45 | e) 64 |
Now continue with the lesson
Equivalent Fractions
Equivalent Fractions are Equal in Value
Example: Replace the ? to create an equivalent fraction:
Since we multiplied 7 (the denominator) by 6 to get 42,
we do the same to the numerator (5).
The solution is: 
Because 
, we didn't change the value of the fraction.
We multiplied it by one to change its form.
Now get a pencil, an eraser and a note book, copy the questions,
do the practice exercise(s), then check your work with the solutions.
If you get stuck, review the examples in the lesson, then try again.
Fractions Exercise 2:
Fill in the blanks to create an equivalent fraction.
1)  |
2)  |
3)  |
4)  |
5)  |
Now continue with the lesson
Adding and Subtracting Fractions
Fractions with the Same Denominator:
Fractions that have the same denominator are very easy to add and subtract. We simply add or subtract the numerators as instructed and write the sum or difference over the denominator. Since all the denominators are the same, that number is called the common denominator -- for it is common to all the fractions we have to add or subtract.
the first common denominator is 5, the second is 11.
Fractions with Different Denominators:
In the picture of the pie (above), we put together 2 quarter-pieces of a pie to get ½ a pie. We saw that ¼ + ¼ = ½. In the picture it was obvious that the 2 quarter-size pieces made up half the pie. When we have 2 of the coins we call "quarters" -- because it takes 4 of them to make a dollar -- we all know we have half a dollar. What if we need to add ½ and ¼? The pieces are not the same size, but we can cut a half in half to get 2 quarters, so ½ plus ¼ is exactly the same as 2-quarters plus 1-quarter which is ¾.
If we look back at the pie image, it's clear that 3 of the 4 pieces together, make up ¾ of the pie.
When we multiply the numerator and denominator of a given fraction by the same number, we create an equivalent fraction. Since we multiply by one (1), we do not change the value of the original fraction, just the form.
Remember there's no prejudice in math!!! -- what you do to the top, you do to the bottom!
So, to change ½ into 
we multiply top and bottom by 2 like this:
We have twice as many pieces but they're half as big as before.
Example: Find the difference 
We have to cut the 2 third-size pieces in half to make sixths:
But we know that 3/6 is ½ -- so our answer is ½.
.
Fractions Summary
Now get a pencil, an eraser and a note book, copy the questions,
do the practice exercise(s), then check your work with the solutions.
If you get stuck, review the examples in the lesson, then try again.
.
Fractions Exercise 3:
Add and Subtract as indicated. Remember to find common denominators.
a)  |
b)  |
c)  |
d)  |
e)  |
f)  |
g)  |
h)  |
Solutions
| equal parts | red part in digits |
blue part in words |
| a) 6 parts |  |
five-sixths |
| b) 9 parts |  |
four-ninths |
| c) 5 parts |  |
three-fifths |
| d) 8 parts |  |
five-eighths |
| e) 4 parts |  |
three-fourths three-quarters |
2) Write a fraction = 1 with these denominators:
a)  |
b)  |
c)  |
d)  |
e)  |
Fill in the blanks to create an equivalent fraction.
1)  |
2)  |
3)  |
4)  |
5)  |
Add and Subtract as indicated. Remember to find common denominators.
a)  |
b)  |
c)  |
d)  |
e)  |
f)  |
g)  |
h)  |
(all content of the MathRoom Lessons © Tammy the Tutor; 2004 - ).
