Fractions

Word problems that contain fractions are exactly like word problems with whole numbers, but sometimes they can look confusing.

A few tips to remember for working specifically with fractions:

Just as you can't multiply with mixed numbers, you can't divide with mixed numbers either. When dividing with mixed numbers, mixed numbers must be turned into improper fractions, and then the division process can continue as usual (for more see lesson Convert Mixed Numbers to Improper Fractions and Multiply Fractions with Mixed Numbers/Whole Numbers)

Example: 

$\require{cancel}$Once you know how to multiply fractions, it's VERY easy to divide fractions.  You just find the reciprocal of the second fraction (flip it, so the the denominator becomes the numerator and the numerator becomes the denominator), and then multiply the fractions.  It's really that easy!

Why does this algorithm work?

$\require{cancel}$Multiplying fractions is easy and cross cancelling can be fun.  The only tricky part about multiplying fractions is that you can't multiply fractions with mixed numbers.  Mixed numbers must be turned into improper fractions.  After you convert to improper fractions, the multiplication process can continue as usual (for more see lesson Convert Mixed Numbers to Improper Fractions)

Example: 

$\require{cancel}$Multiplying fractions is probably the easiest fraction operation to do: you simply multiply the numerator times the numerator and the denominator times the denominator.  For more details, see lesson Multiply Fractions (basic).

But, what do you do when the numbers just get too big?  For example: 

$\dfrac{6}{20}\times\dfrac{8}{12}=\dfrac{6 \times 8}{20 \times 12}=\dfrac{48}{240}$

Multiplying fractions is probably the easiest fraction operation to do: you simply multiply the numerator times the numerator and the denominator times the denominator.

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Just as you sometimes have to borrow when you subtract whole numbers, you sometimes have to borrow when you subtract mixed number fractions. Essentially, when you're working in the realm of positive numbers, you can subtract from any number a number that is smaller. BUT, even when an entire number is smaller, every digit is not smaller, so we have to borrow from the digit to the left.  

Subtracting fractions is just like adding fractions (except, of course, you are taking away instead of adding!).

Remember, when you subtract fractions, you need to make the fractions have the same denominator (which means that the pieces you are subtracting are the same size -- for more info on finding common denominators, review the Add Fractions Lesson).

Fractions show the number of pieces a whole is cut into (the denominator) and the number of those pieces that you have (numerator).  So, if you have $\dfrac{1}{4}$ of a pizza, you know that the pizza is cut into 4 equal pieces and you have one of them. 

Because fractions are numbers, you can add, subtract, multiply, and divide them. 

The most difficult part of adding fractions is finding the common denominator.  Even when you add mixed numbers, the hardest part is finding the common denominators.  When you add fractions with mixed numbers, focus first on adding the fractions.  Then add the whole numbers (it's just like regular addition, start with the digits to the right, and move to the left). Then, you just have to simplify and combine the fraction and whole number.

Example: