
If the numerator of a fraction is zero?
If the denominator is zero?
If the numerator of a fraction is zero, ␣that fraction equals zero.
If the denominator of a fraction is zero, that fraction is considered ‘undefined’. E.g. the fraction 03 = 0, but the fraction 30 = undefined.

How do you divide fractions?
Flip and Multiply! – To divide two fractions, flip the second fraction, and multiply the two together.

Simple vs. Complex fractions:
 1. Terms can only be cancelled within simple fractions. Terms within complex fractions can never be cancelled!
 2. It can be useful to remember that complex fractions contain a shortcut: the numerator of a complex fraction can always be split!

What is a reciprocal?
Reciprocals – Any two numbers whose product equals 1 are known as reciprocals.

What do i do with fractions within fractions?
To simplify any fraction that contains a fraction within its numerator and/or denominator, always multiply the numerator by the “flip” of the denominator!

Properties of Fractions
1.Increasing the numerator increases the value of the fraction
2. while the increasing the denominator decreases the value of the fraction:
 3. Increasing the numerator and the denominator by the same amount brings the value of a
 fraction closer to l
 4. while decreasing the numerator and the denominator by the same amount
 moves the value of a fraction away from 1.

Properties of Zero
– If the numerator of a fraction is zero, that fraction equals zero. If the denominator of a fraction is zero, that fraction is considered undefined.

Proper Fractions
: 0 < xy < 1 – Any fraction whose numerator is smaller than its denominator is known as a proper fraction.

If I multiply a proper fraction by a whole number?
always yields a product smaller than the original number.

What if I square a fraction?
Squaring any whole number always yields a product equal to or larger than the original number.
Squaring any proper fraction, however, always yields a product smaller than the original number.

When I divide a number by a fraction?
Dividing any number by a whole number always yields a quotient equal to or smaller than the original number.
Dividing any number by a proper fraction, however, always yields a quotient larger than the original number.

If I take the square root of a fraction?
Taking the square root of any whole number always yields a root equal to or smaller than the original number.
Taking the square root of a proper fraction, however, always yields a root larger than the original number.

How do I compare two fractions?
CrossMultiplying • The easiest way to compare any two fractions is to crossmultiply their numerators and denominators. Multiply from the bottom up, and write each product over the corresponding numerator, as shown below:  • The fraction under the larger product will always be larger
 Approximating
 • If the numerators and denominators of a given fraction are too large to multiply easily, identify approximateequivalentsthatareeasytoworkwith,suchas 41, 13, 12, 23,and 43.
Converting to decimals

Converting to decimals
Value of 1/3
= 1.333

Converting to decimals
Value of 1/6
= .166666

Converting to decimals
Value of 1/7
=~ .14

Converting to decimals
Value of 1/8
=.125

Converting to decimals
Value of 1/9
=.11111

Converting to decimals
Value of 1/11
= 0.09999999

Converting to decimals
Value of 1/99
= 0.011111

