3.2 adding rational numbers pg 106-113. making connections how do we add integers? 5 + 6 = 11 14 +...
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3.2 Adding Rational Numbers
Pg 106-113
Making Connections
• How do we add integers? 5 + 6 = 11 14 + (-2) = 12
• This is very similar to how we add fractions. – In order to add fractions we first need a
COMMON DENOMINATOR
Definitions
• Common Denominator – Means that both fractions have the same value in the denominator, that is a multiple of both original denominators.
• Lowest Common Denominator – Means that both fractions have the lowest possible multiple of both original denominators.
How to Add Fractions3
5
1
2(Notice that these two DO NOT have matching denominators.)
Step 1: Find a common denominator. To get a common denominator, simply write out the multiples of 5 and 2.
Multiples of 5: 5, 10, 15, 20, 25, ......
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, …
Step 2:Circle all common multiples
Step 3:Pick lowest pair
How to Add Fractions1
23
5
How to Add Fractions
Step 4:Change both fractions to have the LCD
2
25
56
10
5
10
1
23
5
1
2
3
5
Step 5:Simply add the numerators and LEAVE THE DENOMINATORS ALONE
6 5
10
11
10
1110
How to Add Fractions
6
10
5
10
• With the fractions we must find
a common denominator!• Since 8 is a multiple of 2, we need to multiply
by both 4 on the numerator and denominator
5 7
8 2
7
2
How to Add Fractions With Mixed Numbers
5 7 4
8 2 4
5 28
8 8
33
8
148
Step 1:
How to Add Fractions With Mixed Numbers
Step 2:
Step 3:
Step 4: Turn into a mixed number.
Converting improper fractions to mixed fractions
• Step 1: Divide the denominator evenly into the numerator.
• Step 2:Write the whole number and then the remainder becomes the new numerator.
• TRY…
a) 22 8
b) 31 5
Converting Fractions to Decimals
• Step 1: Divide the Numerator by the Denominator.• THAT’S IT!!!
Converting Decimals to Fractions
The decimal 0.3 has numbers going to the tenths place so place the three over ten
0.3 becomes 3/10
.05 becomes 5/100
12.936 becomes 12936/1000
1. 2. 3.
4. 5. 6.
EXIT SLIPAnswer at least 3 of these using
any method you want.7
9
76
3
84
5
2 4
9 3
33
4 1
1
6
2 10
9 12 2
3
42
5
Page 111-113 #5 all, 6, 7 all, 9acf, 11aei, 13, 20ac
Homework