Download Chapter 3 Study Guide

Chapter 3 Study guide
Fraction- represents a part of a whole object, set, or unit. P. 96
Numerator- the number ABOVE a fraction bar. P. 96
Denominator- the number BELOW a fraction bar. P. 96
Note: The denominator indicates how many parts make up the whole, while the numerator indicates how
many parts are counted. P. 96
Example
3 is the numerator
12 is the denominator
Unit fraction- a fraction that has a numerator of 1 and a denominator that is a positive integer. P. 132
Equivalent fractions- fractions that represent the same part-to-whole relationship. P. 133
Example
½ = 6/12
Benchmark fractions- common fractions you can use to estimate the value of fractions. P. 143
Inequality- a statement that one number is less than or greater than another number. P. 146
Multiplicative Identity Property states: a x 1 = a, where “a” is a nonzero number. P. 156
Simplest Form- a way of writing a fraction so the the numerator and denominator have no common
factors other than 1. P. 157
Common denominator- a whole number that is a common multiple of the denominators of the fractions.
P. 168
Least Common Denominator (LCD) is the least common multiple of the denominators of two or more
fractions. P. 168
Note: When working with fractions (comparing, adding, or subtracting) it is important to have the
same denominator or least common denominator. Find the Least Common Denominator by finding the
Least Common Multiple.
Mixed Number- a whole number and a fraction together. P. 178
Improper fraction- a fraction whose numerator is greater than the denominator. P. 178
Reciprocal- a fraction created by reversing the numbers in the numerator and denominator of a fraction.
P. 205
Multiplicative inverse- this is known as the “reciprocal” of a number (fraction). P. 205
Example: a/b is the number b/a where a and b are nonzero numbers.
Multiplicative Inverse Property states a/b x b/a = 1, where “a” and “b” are nonzero numbers. P. 205
Sample Fraction Problems
Compare
/4and 
1. Write the multiples of each of the denominators.
4x1=4, 4x2=8, 4x3=12 etc
4, 8, 12, 16, 20
3x1=3, 3x2=6, 3x3=9, 3x4=12
3, 6, 9, 12, 15,
You are looking for the smallest number that both denominators can be multiplied to. It is 12 (the LCM
or LCD).
2. Multiply the multiple by both numerator and denominator which will make the denominator equal 12
on both fractions. Remember to be fair. Whatever you do to the denominator you must do to the
numerator.
1 x3= 3
2 x4= 8
this makes the new fractions
4 x3=12
3 x4=12

and

3. Since both denominators are the same, you can now compare the fractions
<
since 8 is larger than 3,
is the larger fraction.
<
*Pictures can be used to see the difference between the two fractions and/or cross multiply.
Adding and Subtracting Fractions w/like Denominators
4. Since both denominators are the same, now you can add or subtract the fractions. When
adding and subtracting, the numerator changes, but the denominator stays the same.
+
=
Count all the shaded area.
_____________________________________________________________________________________
-
=
Since it is subtraction, cross out the amount in the numerator.
5.) Changing an improper fraction into a mixed number.
1.)
2.)
3.)
4.)
Divide the numerator by the denominator
The denominator always stays the same.
The quotient becomes the whole number
The remainder becomes the numerator
The blocks are broken into 6
pieces. (denominator) There
are a total of 13 pieces shaded
in. (numerator)
______________________________________________________________________________
6.) Changing a mixed number into an improper fraction
1.)
2.)
3.)
4.)
Multiply the denominator and the whole number
Take the sum and add the numerator
The denominator always stays the same
Take the answer and it becomes your new numerator
6 x 2 = 12 + 1 = 13
There are two blocks completely shaded in. 2 is the whole number. There is 1 block left shaded.
This is the numerator. The blocks are broken into six pieces. This is the denominator.
Adding and Subtracting Fractions w/unlike Denominators
7.) What to do if the denominators are not the same.
1.) Find the least common denominator
2.) Break each block into the common denominator amount.
3.) Count how many blocks are completely shaded. This is our whole number.
4.) Count how many shaded blocks are left over. This is our numerator.
1.) LCM 2, 4, 6
4, 8, 12
2.)
3.)
*Remember a mixed number cannot have an improper fraction in it. If this happens, you must simplify.
8.) How to simplify a fraction.
1.) Find a number that you can divide the numerator and denominator by evenly.
2.) Divide both to get an equivalent fraction in a lower form.
3.) Continue until there is no number that will go evenly into both the numerator and denominator.
Note: Please review Chapter Summary in textbook pages 217-223.