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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 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?

Adding Fractions

Adding Mixed Numbers

Estimate the sum

Add

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?

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?

Subtracting Fractions

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

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?

Adding Mixed Numbers

Subtracting Mixed Numbers

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.

Multiplying Fraction and Mixed Numbers

Dividing Fractions and Mixed Numbers

Original number

Fraction

Reciprocal

1.

101

4.

1

2

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

Dividing Fractions and Mixed Numbers