Fractions can represent parts of a whole that is divided into equal sections. A fraction has a numerator above the line and a denominator below. Equivalent fractions have the same value even if they look different. Mixed numbers contain a whole number and fraction, while improper fractions are larger than 1. To add or subtract fractions, their denominators must be the same, so they may need to be converted to an equivalent form by multiplying the numerator and denominator by the same number.
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Fractions
1. Page | 1
Fractions
What is a fraction?
When an object is divided into a number of equal parts then each part is called a
fraction.
Numerator / Denominator
We call the top number the Numerator, it is the number of parts we have. We call the
bottom number the Denominator; it is the number of parts the whole is divided into.
Numerator
Denominator
Equivalent Fractions
Some fractions may look different, but are really the same, for example:
It is usually best to show an answer using the simplest fraction (1/2 in this case). That is
called Simplifying, or Reducing the Fraction.
Example:
4/8 2/4 1/2
Says how many parts are shaded in the friction.
Says how many parts the shape is divided.
2. Page | 2
Mixed Fractions and Improper Fractions
I can convert improper fractions to mixed fractions and vice versa.
Convert To change from one to another
Mixed numbers A whole number and a fraction.
Improper Fractions A fraction larger than 1 whole: The numerator
is larger than the denominator.
Converting mixed fractions to improper fractions.
Multiplythe whole number part by the fractions denominator. Add that
to the numerator. Write that resulton top of the denominator.
Example:
3. Page | 3
Converting improper fractions to mixed fractions.
Divide the number by the denominator. Write down the whole number
answer. Then write down any remainder above the denominator.
Example:
Adding Fractions
4. Page | 4
1/4 + 1/4
Step 1: The bottom numbers (the denominators) are already the same. Go straight to
step 2.
Step 2: Add the top numbers and put the answer over the same denominator:
1/4 + 1/4 = 1 + 1/4 = 2/4
Step 3: Simplify the fraction: 2/4 = 1/2
Example:
1/3 + 1/5
Again, the bottom numbers are different (the slices are different sizes)!
But let us try dividing them into smaller sizes that will each be the same:
5. Page | 5
The first fraction: by multiplying the top and
bottom by 5 we ended up with 5/15:
The second fraction: by multiplying the top and bottom
by 3 we ended up with 3/15 :
The bottom numbers are now the same, so we can go ahead and add the top numbers:
6. Page | 6
The result is already as simple as it can be, so that is the answer: 8/15
Making the Denominatorsthe Same
In the previous example how did we know to cut them into 1/15ths to make the
denominators the same? We simply multiplied the two denominators together (3 × 5 =
15).
Subtracting Fractions
There are 3 simple steps to subtract fractions
Step 1. Make sure the bottom numbers (the denominators) are the same
Step 2. Subtract the top numbers (the numerators). Put the answer over the same
denominator.
Step 3. Simplify the fraction (if needed).
