1.
Name __________________________________________ Date ____________
Polizzi/Woska Math – 6
Study Guide
Math Test
FRACTIONS
Topics on Test:
1. Least Common Multiple 6. Compare/Order Fractions
2. Lowest Terms 7. Add/Subtract Fractions
3. Mixed Numbers 8. Multiply/Divide Fractions
4. Improper Fractions 9. Add/Subtract Mixed Numbers
5. Equivalent Fractions 10. Multiply/Divide Mixed Numbers
Least Common Multiple
A multiple of a number is the product (answer in multiplication) of that number and a whole number.
Multiples of 3: 3, 6, 9, 12, 15, 18, and 21
Least Common Multiple
The LCM of two or more numbers is the smallest multiple that is common to both numbers.
The LCM of 4 and 6 is 12
4: 4, 8, 12, 16, 20, 24
6: 6, 12, 18, 24
Lowest Terms
Lowest terms (simplest form) is when the only common factor of the numerator and denominator is 1.
To write a fraction in simplest form, divide the numerator and denominator by the GCF.
Example: Write 20 in simplest form.
28
The GCF or 20 and 28 is 4. (20: 1, 2, 4, 5, 10, 20)
(28: 1, 2, 4, 7, 14, 28)
Divide the numerator and denominator by 4.
20 ÷ 4 = 5
28 ÷ 4 = 7
Mixed Numbers
2.
3
A mixed number is a number with a whole number and a fraction combined. Ex: 6
4
Writing Mixed Numbers as Improper Fractions
Multiply the whole number by the denominator, add that number to the numerator, and write this sum
over the denominator.
3 27 3 27
6 Step 1: 6 x 4 = 24 Step 2: + 3 Step 3: So, 6 =
4 4 4 4
Improper Fractions
9
Improper fractions have a numerator greater than the denominator. Ex:
4
Writing Improper Fractions as Mixed Numbers
Divide the numerator by the denominator. The quotient is the whole number. Put the remainder over
the original denominator.
9 Step 1: 2 Step 2: 2 ¼
4 4 9
- 8_
1
Equivalent Fractions
Equivalent fractions are fractions that represent the same amount. For example, if we cut a pie
exactly down the middle, into two equally sized pieces, one piece is the same as one half of the pie.
And if another pie (the same size) is cut into 4 equal pieces, then two pieces of that pie represent the
same amount of pie that 1/2 did. So we can say that 1/2 is equivalent (or equal) to 2/4.
In order to see if fractions are equivalent, you should find a common denominator (making a list of
multiples).
Comparing/Ordering Fractions
3.
To compare and order fractions, use the least common denominator.
Comparing fractions:
3 7
Ex: and Step 1: Find the least common multiple (20).
4 10
3 15 7 14
Step 2: Write equivalent fractions. = and =
4 20 10 20
15 14 3 7
Step 3: Compare: Therefore,
20 20 4 10
Adding/Subtracting Fractions
To add or subtract fractions with common denominators, simply add or subtract the numerators and
keep the same denominator.
2 7
Ex:
5 8
1 2
+ -
5 8
3 5
5 8
* Sometimes fractions have an uncommon denominator. In order to add or subtract them, you must
find a common denominator.
1 3
Ex: = 4: 4, 8, 12, 16, 20
4 12
3: 3, 6, 9, 12, 15
2 8
+ = 12 is a common denominator
3 12
11
*Remember, what you multiply the denominator by to get to 12, you must
12
multiple the numerator by the same number. You subtract the same way.
Multiplying/Dividing Fractions
To multiply fractions:
1. Multiply the numerators together to make a new numerator.
2. Multiply the denominators together to make a new denominator.
3. Simplify if necessary.
2 1 2 1
Ex: x = =
3 4 12 6
To divide fractions: *Dividing fractions is the same as multiplying by its reciprocal.
reciprocal – numbers whose numerators and denominators have been switched.
4.
1. Keep the first fraction.
2. Find the reciprocal of the second fraction.
3. Multiply as usual.
4 8 4 15 60 5
Ex: = x = =
9 15 9 8 72 6
Adding/Subtracting Mixed Numbers
To add mixed numbers:
1. Add the whole numbers.
2. Add the fractions.
3. Put the two parts together.
If the sum of the fractions is an improper fraction, you may need to rewrite it as a mixed number and
add the whole number parts together.
1 3
Ex: 1 1
2 6
5 5
+ 3 3
6 6
8
4 Add the whole numbers. Then add the fractions.
6
2
4+1 Rewrite the improper fraction as a mixed number.
6
2 1
5 = 5 Add the whole number parts. Write the sum in lowest terms.
6 3
Multiplying/Dividing Mixed Numbers
To multiply mixed numbers:
1. Change to an improper fraction.
2. Simplify.
3. Multiply.
4. Simplify.
1 2 15 12 180 5 1
Ex: 2 x2 = x = =5 =5
7 5 7 5 35 35 7
To divide you do the same and follow the rules for division of fractions (find the reciprocal).
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