Hopefully, you know your fraction rules by now, and if you forget, remember that you can always use your calculator - as long as you follow Calculator Rule #1 and put parentheses around all fractions before typing them in.
Fraction Review:
A fraction represents something divided into pieces - so
5
---------
8
represents something divided into 8 pieces (the denominator, or bottom number is how many pieces it’s divided into) and we are interested in 5 of those 8 pieces (the numerator, or top number, is the number of those pieces we are going to be dealing with.) A mixed number consists of an integer and its fractional remainder, like 2
1
---------
3
. An improper fraction has a numerator larger than the denominator, so instead of writing the mixed number 4
3
---------
5
you would write
23
---------
5
, keeping everything in “pieces” instead of talking about the number of whole objects you have. To change a mixed number into an improper fraction, multiply the denominator by the integer, and add the numerator. Then place that answer on top of the original denominator. So 6
3
---------
7
?
45
---------
7
To change an improper fraction into a mixed number, divide the numerator by the denominator, and put the remainder on top of the original denominator. So
19
---------
9
? 2
1
---------
9
.
Adding/Subtracting Fractions
Use your calculator. Seriously. But be sure to use parentheses.
If you do decide to do the math longhand, know that you can only add or subtract fractions when the denominator is the same. So to add
2
---------
3
+
5
---------
6
you would first need to multiply by
2
---------
2
to make it
4
---------
6
, and then you could add
4
---------
6
+
5
---------
6
to get
9
---------
6
. Remember that any time your numerator and denominator are equal, the result is 1. This may come in handy with more complex fractions involving variables.
Multiplying/Dividing Fractions
To multiply fractions, simply multiply the numerators straight across and multiply the denominators straight across:
6
---------
7
×
8
---------
9
=
48
---------
63
Keep in mind that the SAT answer choices will be reduced, so if you don’t see your answer in the answer choices, check to see if your answer is in lowest terms.
-Hint: If your fraction is not in lowest terms, but involves higher numbers whose factors you don’t know well, don’t waste time trying to figure out lowest terms on your own. Simply use the answer choices given: plug your answer into the calculator to get the decimal equivalent, then do the same with each answer choice to see which one matches.
The reciprocal of a fraction is the fraction with the numerator and denominator flipped. The reciprocal of
2
---------
5
is
5
---------
2
. The negative reciprocal is the same thing, but also with the opposite sign, so the negative reciprocal of -
6
---------
11
is +
11
---------
6
. What about whole numbers? Simply write them as a fraction, that is, put them over 1, and then flip to find the reciprocal. The reciprocal of 2 is
1
---------
2
.
To divide fractions, flip and multiply. That is, set it up as (fraction fraction). Keep the first number the same, change the sign to times, and make the second number its reciprocal. So
4
---------
9
÷
8
---------
13
becomes
4
---------
9
×
13
---------
8
. Then follow the multiplication rules above.
-Hint: Cross-cancel if you can. When can you cross-cancel? You can ONLY cross-cancel once you have the problem set up as a multiplication problem. Do not try to cross-cancel in division form, and definitely do not cross-cancel when you are adding, or when you have to cross and equals sign. So which of these is the proper use of cross-canceling?
Comparing Fractions
To compare fractions, type the fraction into your calculator to get the decimal value. On the SATs, it is almost never a good idea to try to find the lowest common denominator the way you were taught in school. It just takes too long.
fraction). Keep the first number the same, change the sign to times, and make the second number its reciprocal. So 
