Fractions are basic math, but brushing up on the rules surrounding using fractions in math equations can help a person reduce some of the stress that fractions sometimes cause. It is important to once again note that those using calculators should always remember to use parentheses around fractions before typing them into the calculator.
Fraction Review and Overview:
Basically, a fraction is a number that represents something that has been divided into pieces. For example 1 / 2 means something has two pieces and the number (the fraction) represents one of them (or half.) The denominator is the bottom number and the numerator is the top number. When a fraction also has an integer, it is known as a mixed number - 2 1 / 2.
Improper fractions have numerators that are larger than the denominators. So, instead of 4 and 3 / 5 it would be written as 23 / 5. Switching mixed numbers to improper fractions allows you to add, subtract or even multiply fractions. To turn a mixed integer into an improper fraction, simply divide the numerator by the denominator. The remainder should be put on the top of the original denominator used.
Adding/Subtracting Fractions
It is only possible to add and subtract fractions when their denominator is the same. For example, to add 2 / 3 + 5 / 6 you would need to multiply by 2 / 2 to make it 4 / 5. At that point you could add 4 / 6 + 5 / 6 = 9 / 6.
Multiplying/Dividing Fractions
In order to multiply fractions, it is simply a matter of multiplying the numerators straight across as well as multiplying the denominators.
6 / 7 x 8 / 9 = 48 / 63
The SAT answer choices will be reduced fractions. Because of this, if the answer does not match the choices, it may be necessary to reduce the fraction.
A reciprocal of a fraction is simply the fraction with the denominator and numerator switched or flipped. For example, the reciprocal of 2 / 7 is 7 / 2.
A negative reciprocal is like a reciprocal fraction, but with the opposite sign. So, for example, the negative reciprocal of - 8 / 13 is + 13 / 8.
For whole numbers, turn them into a fraction first. So, 3 would become 3 / 1 and the reciprocal would be 1 / 3.
In order to divide fractions, it is necessary to flip and multiply. So, for example, 4 / 9 divided by 8 / 13 would be 4 / 9 x 13 / 8. It is then a simple matter of following multiplication rules for fractions.
TIP: In some cases it may be possible to cross-cancel. This only works for multiplication problems.
Comparing Fractions
To compare fractions, simply type the fraction into a calculator to get the decimal value of the fraction. 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. Instead, use the calculator to reduce the chance or errors and mistakes when taking the math section of the SAT.
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