What is a fraction?
A fraction is a part of a whole.
Example:
^{3}/_{4}
What is a numerator?
The top number of a fraction is called the numerator.
The numerator shows how many equal parts of a whole are in the fraction.
What is a denominator?
The bottom number of a fraction is called the denominator.
The denominator indicates how many parts make up a whole.
*** The denominator cannot equal zero.
What is a simple fraction?
In simple (common) fractions, both the numerator and the denominator are integers expressed as a ratio.
Examples:
^{3}/_{4}, ^{1}/_{3}
*** These are the types of fractions you'll see most often on the SAT.
What is a simplified fraction?
In simplified fractions, the greatest common factor of both the numerator and the denominator is 1.
Examples:
^{1}/_{2}, ^{3}/_{4}
What fractions are called proper fractions?
In proper fractions, the numerator is less than the denominator.
Examples:
^{1}/_{4}, ^{3}/_{4}
What fractions are called improper fractions?
In improper fractions, the numerator is equal to or greater than the denominator.
Examples:
^{23}/_{11}, ^{9}/_{7}
What fractions are called equivalent fractions?
Equivalent fractions have the same value, but are expressed differently.
Examples:
^{1}/_{2}, ^{2}/_{4}, ^{3}/_{6}
What are similar fractions?
Similar fractions have the same denominator.
Examples:
^{1}/_{4}, ^{3}/_{4}
When the numerator of a fraction is zero, the fraction is....?
When the denominator of a fraction is zero, the fraction is...?
When the numerator of a fraction is zero, it's called a zero fraction. It equals 0.
When the denominator of a fraction is zero, the fraction is undefined.
*** Remember, nothing can be divided by 0.
What are reciprocal fractions?
In reciprocal fractions, the numerators and the denominators are switched.
Examples:
5 is a reciprocal of ^{1}/_{5}.
^{3}/_{8} is a reciprocal of ^{8}/_{3}.
What are complex fractions?
In complex fractions, the numerator and the denominator are fractions themselves.
Example:
What are mixed fractions?
Mixed fractions combine an integer and a proper fraction.
Example:
6 ^{2}/_{3}
*** Mixed fractions are also called mixed numerals or mixed numbers.
How do you simplify a fraction by using the GCF (greatest common factor)?
Divide both the numerator and the denominator by their GCF.
Example:
Simplify ^{24}/_{36}
The GCF of 24 and 36 is 12. Simplify the fraction by dividing by 12. The lowest term of this fraction is ^{2}/_{3}.
How do you use prime factorization to simplify a fraction?
Write out the prime factorization of both the numerator and the denominator and cancel out any common prime factors.
Example:
Simplify ^{76}/_{84}
How do you reduce a fraction to its lowest terms?
To reduce a fraction to the lowest terms, factor out both the numerator and the denominator. Then, cancel out all common factors.
Example:
^{16}/_{24} = ^{4 x 2 x 2}/_{4 x 2 x 3} = ^{2}/_{3}
How do you add or subtract fractions that have the same denominator?
When fractions are similar (i.e. have like denominators), work with the numerators (add or subtract) and leave the denominators alone.
Example:
^{5}/_{22} + ^{7}/_{22} = ^{13}/_{22}
What is the Least Common Denominator (LCD) of two or more fractions?
The Least Common Denominator (LCD) of two or more fractions is the smallest whole number that is divisible by each of the denominators.
How do you find the LCD of two or more fractions?
To find the LCD, use the same methods used to find the Least Common Multiple (LCM) of two numbers:
Successive multiplication
Prime factorization
See "Factors and Multiples" deck for detailed explanation.
How do you add or subtract fractions with different denominators?
To add or subtract fractions with different denominators:
Find the LCD
Write equivalent fractions with the LCD
Add or subtract the numerators
Example:
^{1}/_{5} + ^{2}/_{7} = ^{7}/_{35} + ^{10}/_{35} = ^{17}/_{35}
How do you multiply fractions?

To multiply fractions, simply multiply the numerators, then multiply the denominators.

It doesn't matter whether fractions have same or different denominators.

Use cancelling whenever possible as a shortcut. Cancelling can take place only between numerators and denominators.
Example:
How do you divide fractions?
Rewrite the second fraction as its reciprocal and multiply by the first fraction.
Example:
^{5}/_{6} ÷ ^{2}/_{3} = ^{5}/_{6} x ^{3}/_{2} = ^{15}/_{12} = ^{5}/_{4}
How do you turn an improper fraction into a mixed number?
To convert an improper fraction into a mixed number, divide the numerator of the improper fraction by its denominator. If there is a remainder, it will become the numerator of the mixed number.
Example:
^{18}/_{14} = 1 ^{4}/_{14} = 1 ^{2}/_{7}
How do you turn a mixed number into an improper fraction?
To convert a mixed number into an improper fraction, multiply the denominator by the whole number and add the numerator. This number becomes the numerator of your improper fraction.
Example:
1 ^{2}/_{3} = ^{5}/_{3}
3 * 1 + 2 = 5 It's the numerator of the improper fraction.
How do you add or subtract mixed numbers containing similar fraction parts?
Add or subtract the fraction parts first, then work with the whole numbers. Simplify if possible.
Examples:
5^{3}/_{7} + 8^{2}/_{7 }= 13^{5}/_{7}
5^{3}/_{7} + 8^{6}/_{7} = 13^{9}/_{7} = 14^{2}/_{7}
*** If the answer contains an improper fraction, you must turn it into a mixed number.
How do you subtract mixed numbers with similar fraction parts when the numerator of the second number is greater than the numerator of the first number?
8^{3}/_{7}  5^{6}/_{7 }= ?
"Regroup," or remove 1 (or ^{7}/_{7}) from the whole part of the first mixed number by adding it to the fraction part:
8^{3}/_{7}  5 ^{6}/_{7}= 7^{10}/_{7}  5^{6}/_{7}
Perform the subtraction, dealing first with the fractions, then the whole numbers:
7^{10}/_{7}  5^{6}/_{7} = 2^{4}/_{7}
How do you add or subtract mixed numbers with different denominators?
5^{3}/_{5} + 8^{1}/_{4} = ?
5^{3}/_{5} + 8^{1}/_{4} = ?
Write equivalent fractions using the LCD of 4 and 5.
5^{3}/_{5} = 5^{12}/_{20} ; 8^{1}/_{4} = 8^{5}/_{20}
Add the fraction parts, then the whole numbers:
5^{3}/_{5} + 8^{1}/_{4 }= 5^{12}/_{20} + 8^{5}/_{20} = 13^{17}/_{20}
How do you subtract mixed numbers with different denominators?
8^{3}/_{7}  5^{2}/_{3} = ?
Using the LCD of 3 and 7, write new equivalent fractions :
8^{3}/_{7}  5^{2}/_{3} = 8^{9}/_{21}  5^{14}/_{21}
Make a new fraction equal to 1 and "regroup," or remove, that fraction from the whole part of the first mixed number by adding it to the fraction part:
8^{9}/_{21} = 7^{30}/_{21}
The fraction in the first mixed number is now greater than the fraction in the second number. Subtract the fractions first, then the whole numbers:
7^{30}/_{21 } 5^{14}/_{21} = 2^{16}/_{21}
How do you multiply or divide mixed numbers?
Change mixed numbers into improper fractions and follow the rules explained in "Multiplying and Dividing Fractions" cards.
What is decimal notation?
Decimal notation is the most common way to write the base 10 numeral system, which uses digits from 0 to 9 together with the decimal point (.)