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TRANSCRIPT
Fraction Packet
Name ________________
Fractions Vocabulary / PhrasesWord _____________________________________________________
Definition: a small part or item forming a piece of a whole
Example:
Word _____________________________________________________
Definition: the bottom number of a fraction that tells the number of equal parts in a whole.
Example:
Word _____________________________________________________
Definition: the top number of a fraction that tells the number of equal parts compared to the number of equal parts in a whole.
Example:
Word _____________________________________________________
Definition: fractions that name the same number or are of equal value
Example:
Word _____________________________________________________
Definition: when the numerator and the denominator have no common factor other than 1.
Example:
Word ____________________________________________________
Definition: A complete amount lacking no part, member, or elementExample:
Word _____________________________________________________
Definition: When the numerator is larger than the denominatorExample:
Word _____________________________________________________
Definition: A whole number and a fraction.Example:
Word _____________________________________________________
Definition: When the denominators in two or more fractions are the same.Example:
Word ____________________________________________________
Definition: The least common multiple (LCM) of the denominators of two or more fractions.Example:
Word _____________________________________________________
Definition:
Example:
Word _____________________________________________________
Definition:
Example:
How to simplify a fraction:Simplifying (or reducing) fractions means to make the fraction as simple as possible.
Why say four-eighths (4/8) when you really mean half (1/2) ? 4/8 ==> 2/4 ==> 1/2
(Four-Eighths) (Two-Quarters) (One-Half)
1. Find a common factor of the numerator and denominator. A common factor is a number that will divide into both numbers evenly. Two is a common factor of 4 and 14.
2. Divide both the numerator and denominator by the common factor.
3. Repeat this process until there are no more common factors.
4. The fraction is simplified when no more common factors exist.
Reduce each of the fractions to simpliest form.1).
16
30
2). 18
22
3). 7
11
4). 4
28
5). 21
36
6). 9
45
Example:
8/15 9/11 7/11
1/7 7/12 1/5
Divisibility TricksTwo (2)
Numbers are divisible by 2 if the ones digit is evenly divisible by 2.
This means that even numbers are divisible by 2.
Example: 22, 40, 56
Three (3)Numbers are divisible by 3 if the sum of all the
individual digits is evenly divisible by 3.
Example: the sum of the digits for the number 3627 is 18 (3 + 6 + 2 + 7 = 18),
18 is evenly divisible by 3 (18 ÷ 3 = 6)so the number 3627 is evenly divisible by 3.
Four (4)Whole numbers are divisible by 4 if the number formed by the last two individual digits is evenly
divisible by 4.
Example: the number formed by the last two digits of the number 3628 is 28,
which is evenly divisible by 4 (28 ÷ 4 = 6) so the number 3628 is evenly divisible by 4.
Five (5)Numbers are evenly divisible by 5 if the last digit of
the number is 0 or 5
Example: 25, 85, 40
Six (6)Numbers are evenly divisible by 6 if they are evenly
divisible by both 2 AND 3.
Even numbers are always evenly divisible by 2.
Numbers are evenly divisible by 3 if the sum of all the individual digits is evenly divisible by 3.
Example: the sum of the digits for the number 3627 is 18
(3 + 6 + 2 + 7 = 18) , which is evenly divisible by 3
(18 ÷ 3 = 6)but 3627 is an odd number so it is not divisible by 2
so the number 3627 is not evenly divisible by 6.
Seven (7)To determine if a number is divisible by 7, take the last digit off the number, double it and subtract the doubled number from the remaining number. If the result is evenly divisible by 7 (e.g. 14, 7, 0, -7, etc.),
then the number is divisible by seven. This may need to be repeated several times.
Example: Is 3101 evenly divisible by 7?
- take off the last digit of the number (1) - double the removed digit and subtract it - repeat the process by taking off the 8 - doubling it to get 16 which is subtracted - the result is 14 which is a multiple of 7
Eight (8)Numbers are divisible by 8 if the number formed by
the last three individual digits is evenly divisible by 8.
Example: the last three digits of the number 3624 is 624,
624 is evenly divisible by 8 (624 ÷ 8 = 78)
so 3624 is evenly divisible by 8.
Nine (9)Numbers are divisible by 9 if the sum of all the
individual digits is evenly divisible by 9.
Example:the sum of the digits of the number 3627 is 18
(3 + 6 + 2 + 7 = 18)which is evenly divisible by 9
(18 ÷ 9 = 2)so 3627 is evenly divisible by 9.
Ten (10)A number is divisible by 10 only if the last digit is a 0.
Example: 50, 90, 30
Even Numbers
End with ‘0’ or ‘5’
310- 2308- 16 14
End with ‘0’
Mixed Numbers to Improper Fractions
1. Work in a clockwise direction, beginning with the denominator.
2. Multiply the denominator by the whole number
3. Add that answer to the numerator of the fraction.
4. Put over the denominator.
Change Mixed number to Improper Fraction:
9 = 2 = 8 =
10 = 7 = 3 =
Example:
6 10
2 9
1 7
1 5
410
34
Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator
2. Write the mixed number in the form:
Whole number
Change Improper Fraction to Mixed Number: 20 9
7 2
47 5
68 8
17 3
56 9
Least Common Denominator (LCD)Method 1:1. List the multiples of each of the given numbers.
remainderdenominator
Example:
= = =
= = =
2. The LCD is the first multiple common on both lists.
Method 2:1. List the multiples of the larger number.
2. Divide each by the smaller number.
3. The LCD is the multiple that the smaller number divides without leaving a remainder.
Method 3:1. Multiply the denominators.
2. Use that as the common denominator. This might NOT be the least common denominator (LCD) and when adding or subtracting you may have to reduce the answer.
Example:
Example:
Example:
Find the Common Denominator and find the equivalent fractions: 8 24
7 12
11 12
2 6
5 10
6 9
7 15
4 5
3 5
6 10
9 16
2 4
=
=
=
= =
=
=
=
=
= =
=
Comparing FractionsIf two fractions have the same denominator then they are easy to
compare
But if the denominators are not the same you need to make them the same
(make them equivalent fractions by finding a common denominator)
Compare the following fractions. Write >, <, or = in each .
2 2 1 1
Write the numbers in increasing order.
Adding Fractions with Like Denominators1. Because both fractions have the same denominator, you may add the numerator and keep the denominator the same.
Example:
Example:
1 12
9 10
24 6 4 1
916
9 10
2 6
121 11
916
14
18
34
34
28
16
48
116
DO NOT ADD THE DENOMINATORS!!!!2. Always change improper fractions to a mixed number.
3. Reduce, when possible.
Add Fractions with Like Denominators:
1 4 6 6
4 7 12 12
5 1 12 12
6 416 16
9 3 20 20
8 10 18 18
Example:
+ ++
+ + +
=
===
==
Adding Fractions with Unlike Denominators1. Because the fractions have unlike denominators, you must find a common denominator.
2. Make the fractions into equivalent fractions using the common denominator.
3. Once you have a common denominator, add the numerators. The denominator remains the same.
4. Always change improper fractions to a mixed number.
5. Reduce, when possible.Example:
Example:
Add Fractions with Unlike Denominators:
2 4 8 + 10
10 15 6 + 30
7 9 8 + 27
10 12 4 + 9
4 5 1 + 2
1 5 9 + 11
Subtracting Fractions with Like Denominators1. Because both fractions have the same denominator, you may subtract the numerator and keep the denominator the same. DO NOT ADD THE DENOMINATORS!!!!
2. Always change improper fractions to a mixed number.
3. Reduce, when possible.
Subtract Fractions with Like Denominators:
11 1 12 12
5 4 6 6
7 4 8 8
15 13 20 20
9 6 10 10
6 2 7 7
Subtracting Fractions with Unlike Denominators
Example:
-
--
--
-
=
===
==
1. Because the fractions have unlike denominators, you must find a common denominator.
2. Make the fractions into equivalent fractions using the common denominator.
3. Once you have a common denominator, subtract the numerators. The denominator remains the same.
4. Always change improper fractions to a mixed number.
5. Reduce, when possible.Example:
Example:
Subtract Fractions with Unlike Denominators:
1 3 1 - 8
1 2 2 - 7
4 5 1 - 6
1 8
1 - 32
3 8 3 - 10
3 5 4 - 15
Adding Mixed NumbersMethod 1:1. Change mixed numbers into improper fractions.
2. Find Common Denominator
3. Add numerators. Keep common denominator the same.
4. Change improper fraction into mixed number.Example:
Example:
Method 2:1. Add whole numbers.
2. Rewrite problem with new whole number
3. Find common denominator
4. Add fractions (add numerators, denominator stays the same)
5. Change improper fraction into mixed number.
6. Add mixed number to whole number including the fraction.Example:
Example:
Adding Mixed Numbers:
2 +2
3 +2
5 + 3
3 + 3
2+ 2
4 +6
7823
78
78
56
23
34
45
12
47
4556
Subtracting Mixed NumbersMethod 1:1. Change mixed numbers into improper fractions.
2. Find Common Denominator
3. Subtract numerators. Keep common denominator the same.
4. Change improper fraction into mixed number.Example:
Example:
Method 2:1. Subtract whole numbers.2. Rewrite problem with new whole number3. Find common denominator4. Subtract fractions (subtract numerators, denominator stays the same)
5. Change improper fraction into mixed number.
Example:
Example:
Subtracting Mixed Numbers:
4 - 2
2 - 1
4 - 4
2 -
3 -
6 - 4
3457
3845
3415
3716
1312
2516
Multiplying Fractions1. Multiply the numerators and multiply the denominators.
2. Always change improper fractions to a mixed number.
3. Reduce, when possible.
Multiply the Fractions:
5 3 6 4
7 9 8 10
6 8 9 9
10 3 12 4
2 8
4 2 5 3
Dividing Fractions
Example:
x
xxx
xx
4
=
==
==
=
1. Find the reciprocal of the second fraction. To find the reciprocal flip the numerator and the denominator. The reciprocal of 4/5 is 5/4.
2. Multiply the numerators.
3. Multiply the denominators.
4. Reduce to simplest form or change improper fraction to a mixed number.
Divide:
1 3 3 5
4 1 5 2
1 1 2 6
1 2 4 7 7 9
Example:
56
57
34
35
17
23
÷
÷÷
÷÷
÷
=
===
==