adding fractions
TRANSCRIPT
How do I add fractions to fractions?
Fractions lesson 6
Integrated 1A
What is ?
• One way to do this is to draw pictures and cut them up and combine them.
1 1
4 2
1 1 3
4 2 4
There is a better way
• This is the part that confuses students most often.
• You must sometimes change fractions to show the same type of parts.
• Using equal fractions makes this easier.
1 1 3
4 2 4
1 2
4 4
Let’s begin with equal fractions.
• Let’s start with one half and make a list of equal fractions.
1
2
Make a new fraction that is equal to one half. Multiply the top number (1)by 2. Multiply the bottom number bythe same 2.
2
2
2
4
Let’s multiply one half by
• Now our list should look like this.
3
3
1
23
3
3
6
1 2 3
2 4 6
Add Another Fraction
1 2 3 ?
2 4 6 ?
• Let’s add another fraction to our list in our notebook.
• Start with the first number – one half. Multiply top and bottom by 4 this time.
• Write the new fraction.1
24
4
4
8
Add Another Fraction
1 2 3 4 ?
2 4 6 8 ?
• What comes next? Write the new fraction.
1
25
5
5
10
Add More
1 2 3 4 5 6 7 8 9
2 4 6 8 ? ? ? ? ?
• Continue this list in your notebook.
• What comes next? Write the new fractions.
1 2 3 4 5 6 7 8 9
2 4 6 8 10 12 14 16 18
Let’s multiply one third by
• Now our list should look like this.
2
2
1
32
2
2
6
1 2
3 6
A new list
1 2 3 4 5 6 7 8 9
3 6 ? ? ? ? ? ? ?
Start with one-third
Multiply the top and bottom by three. Do the same for the next one by multiplying one-third by four.
1 2 3 4 5 6 7 8 9
3 6 9 12 15 18 21 24 27
Going from the known to the unknown
• In a previous lesson last week, you divided top and bottom by the same number.
• You didn’t change the value of the fraction, just the appearance.
51
5
91
9
31
3
81
8
414
Is one-fourth equal to two-eighths?
1
42
2
2
8
Add these two fractions making them both a certain number of
eighths
3
4
3 ?
4 8
1 ?
8 8 1
8
We can’t easily add fourths to eighthsso we find a number to multiply times four to get eight on the bottom.
x2
x2
We are making a addition problem that becomes easier to work with.
3
4
3 6
4 8
1 1
8 8 1
8
One eighth doesn’t need to be changed,So just rewrite it.
x2
x2
Now add down the right side.3 6
4 8
1 1
8 8
6 1 ?
8 8 8
Six-eighths plus one-eighth is how many eighths?
87
Get a worksheet (F6)
What is the least common multiple of four and 8?
(What is the smallest number in both lists?)
Use eight as your common denominator.
1
43
8
Multiples of 4: 4, 8, 12, 16, 20, 24…
Multiples of 8: 8, 16, 24, 32…
min
numerator
deno ator
Terms:
Make your denominators the same.
What can you multiply by four to get eight?
The bottom number is already in eighths, don’t change it
1 ?
4 8
3 3
8 8
min
numerator
deno ator
x2
x2
Add.
Now add the column with the common denominators
Is five-eighths in simplest form?
1 2
4 8
3 3
8 8
min
numerator
deno ator
x2
x2
2 3 5
8 8 8
5
8
Worksheet #5
What is the least common multiple of 2 and 6?
(What is the smallest number in both lists?)
Use SIX as your common denominator.
1
25
6
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16…
Multiples of 6: 6, 12, 18, 24, 30…
min
numerator
deno ator
Make your denominators the same.
What can you multiply by two to get six?
The bottom number is already in sixths, don’t change it
1 ?
2 6
5 5
6 6
min
numerator
deno ator
x?
x?
Add down the right column.
Put your answer into simplest form, if necessary.
1 3
2 6
5 5
6 6
min
numerator
deno ator
x3
x3
8
6
3 4
113
4
3
Worksheet #9
What is the least common multiple of 5 and 10?
Use FIVE as your common denominator.
1
53
10
Multiples of 5: 5, 10, 15, 20, 25, 30,…
Multiples of 10: 10, 20, 30, 40, 50…
min
numerator
deno ator
Make your denominators the same.
What can you multiply by five to get ten?
The bottom number is already in tenths, don’t change it
1 ?
5 10
3 3
10 10
min
numerator
deno ator
x?
x?
Is your answer in simplest form?
Add the numbers down the right column.
1 2
5 10
3 3
10 10
min
numerator
deno ator
5?
10
