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### Adding Fractions Estimate the sum Add Find the least common denominator 35 x = 5 1 ~ ...(find the LCM of 8 and 5).. x = 5 40 ~ 8: 8, 16, 24, 32, 40 – PowerPoint PPT presentation

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1
Estimate the sum
Find the least common denominator
35
x
5
1
...(find the LCM of 8 and 5)..
x
5
40
8 8, 16, 24, 32, 40 5 5, 10, 15, 20, 25,
30, 35, 40
The LCM is 40.
x
8
32
Change both denominators to 40
1
x
8
40
...then change both numerators
Add the new numerators, then keep the denominator
the same.
2
67
1
27 40

Convert to a mixed number.
40
Is the sum close to the estimate?
2
3
Estimate the sum
Find the least common denominator
1
18
x
2
9 10
2
...(find the LCM of 10 and 4)..
x
2
20
10 10, 20, 30, 40 4 4, 8, 12, 16, 20 ...
The LCM is 20.
4
x
5
5
1 4
Change both denominators to 20
4
x
5
20
...then change both numerators
Add the new numerators, then keep the denominator
the same.
1
3 20
23

20

6
Convert to a mixed number.
5
Add the whole numbers to the sum.
3 20
6
Is the sum close to the estimate?
4
Subtracting Fractions
Estimate the difference
Subtract
Find the least common denominator
39
x
3
13 14
1
...(find the LCM of 14 and 6)
x
3
42
14 14, 28, 42, 56, 70, 84... 6 6, 12, 18,
24, 30, 36, 42...

The LCM is 42.
x
7
35
5 6
Change both denominators to 42
1
x
7
42
...then change both numerators
Subtract the new numerators, then keep the
denominator the same.
0
4
2 21
2

Simplify by finding the GCF 4 1, 2, 4
42 1, 2, ...
42

2
Is the sum close to the estimate?
5
Subtracting Fractions
6
Subtracting Mixed Numbers
Rewrite each mixed number by borrowing.
3
Take one from 4 (now you have 3...)
\
3
4 9
4
9 9
13 9
...then add it back to the fraction

9 9
Remember 1
1
7 11
2
18 11

2 3
1
5 3

7
5 9
8
14 9

9
3 8
10
11 8

7
Subtracting Mixed Numbers
6
Estimate the difference
\
Find the least common denominator
7
16
x
8
2 3
24 24
40 24
8

...(find the LCM of 3 and 8)..
x
8
24
3 3, 6, 9, 12, 15, 18, 21, 24 8 8, 16, 24

The LCM is 24.
6
x
3
21
7 8
Change both denominators to 24
7
x
3
24
...then change both numerators
To avoid negative fraction, lets borrow from the
whole number
19 24
Take one from 7 (now you have 6...)
1
...then add it back to the fraction
Subtract the new numerators, then keep the
denominator the same.
Is the estimate close to the difference?
8
Subtracting Mixed Numbers
9
Multiplying Fraction and Mixed Numbers
4

9

36
Estimate the product.
?
4 9
4

9
Convert each to a simple fraction
40 9
9 1

Cross-simplify.
\
1
40 1
40

40 9
9 1
\

Multiply numerators, then denominators
1
Simplify the product.
10
Multiplying Fraction and Mixed Numbers
11
Dividing Fractions and Mixed Numbers
Original number
Fraction
Reciprocal
1.
101
4.
1
2
12
Dividing Fractions and Mixed Numbers
5

9
?
1 2
Estimate the quotient.
?
Convert each to a simple fraction
3 8
5

9
Keep the first fraction the same
Change the division to multiplication
Flip the 2nd fraction
5 1
75 8

Cross-simplify.
1
\
8 17
Multiply numerators, then denominators

5 1

8 75
\
17
13
Dividing Fractions and Mixed Numbers