6.10: Divide Whole Numbers by Fractions

Steps1.) Rename the whole number as a fraction with a denominator of 1.

2.) Change division sign to multiplication sign.

3.) Write the reciprocal of the second fraction. (Flip the second fraction)

4.) Multiply across the numerators and denominators.

5.) Rename improper into mixed or whole number (if needed)

6.) Put in simplest form (if needed)

Example

Think

Think

Think Think

Chapter 6216

Divide Whole Numbers by Fractions6-10

To divide a whole number by a fraction:

Rename the whole number as afraction with a denominator of 1.

Multiply by the reciprocal of the divisor.

Simplify using the GCF where possible.Then multiply the numerators and multiplythe denominators.

Rename the product as a whole ormixed number when needed.

A carpenter cut a 4-ft board into -ft boards.How many pieces of board did the carpenter make?

Study these examples.

The carpenter made 6 pieces of -ft board.

4 ft

ft23

ft23

ft23

ft23

ft23

ft23

23

23

34

323

818 3

4! !

43

81

10 23

"

13

301

10 13! !

31

30

"

101

101

23

414 2

3! !

61

6 whole number

2

1

32

41 "

How many s are in 4?23

and arereciprocals.

23

32

34

??" 1 1

3??" 1

23

2 31 1

""

8 41 3

""

10 31 1

""

4 31 2

""

orYou can multiply by the reciprocal of the divisor since dividing by anumber is the same as multiplying by the reciprocal of that number.

!234 6

mixed number whole number

To find the number of -ft boards,divide: 4

You can use a diagram:

n.!23

8205-4_216 10/6/07 8:57 PM Page 216

Step 1: Write with denominator of 1

Step 2: Flip division sign to multiplication

Think

Think

Think Think

Chapter 6216

Divide Whole Numbers by Fractions6-10

To divide a whole number by a fraction:

Rename the whole number as afraction with a denominator of 1.

Multiply by the reciprocal of the divisor.

Simplify using the GCF where possible.Then multiply the numerators and multiplythe denominators.

Rename the product as a whole ormixed number when needed.

A carpenter cut a 4-ft board into -ft boards.How many pieces of board did the carpenter make?

Study these examples.

The carpenter made 6 pieces of -ft board.

4 ft

ft23

ft23

ft23

ft23

ft23

ft23

23

23

34

323

818 3

4! !

43

81

10 23

"

13

301

10 13! !

31

30

"

101

101

23

414 2

3! !

61

6 whole number

2

1

32

41 "

How many s are in 4?23

and arereciprocals.

23

32

34

??" 1 1

3??" 1

23

2 31 1

""

8 41 3

""

10 31 1

""

4 31 2

""

orYou can multiply by the reciprocal of the divisor since dividing by anumber is the same as multiplying by the reciprocal of that number.

!234 6

mixed number whole number

To find the number of -ft boards,divide: 4

You can use a diagram:

n.!23

8205-4_216 10/6/07 8:57 PM Page 216

Think

Think

Think Think

Chapter 6216

Divide Whole Numbers by Fractions6-10

To divide a whole number by a fraction:

Rename the whole number as afraction with a denominator of 1.

Multiply by the reciprocal of the divisor.

Simplify using the GCF where possible.Then multiply the numerators and multiplythe denominators.

Rename the product as a whole ormixed number when needed.

A carpenter cut a 4-ft board into -ft boards.How many pieces of board did the carpenter make?

Study these examples.

The carpenter made 6 pieces of -ft board.

4 ft

ft23

ft23

ft23

ft23

ft23

ft23

23

23

34

323

818 3

4! !

43

81

10 23

"

13

301

10 13! !

31

30

"

101

101

23

414 2

3! !

61

6 whole number

2

1

32

41 "

How many s are in 4?23

and arereciprocals.

23

32

34

??" 1 1

3??" 1

23

2 31 1

""

8 41 3

""

10 31 1

""

4 31 2

""

orYou can multiply by the reciprocal of the divisor since dividing by anumber is the same as multiplying by the reciprocal of that number.

!234 6

mixed number whole number

To find the number of -ft boards,divide: 4

You can use a diagram:

n.!23

8205-4_216 10/6/07 8:57 PM Page 216

Think

Think

Think Think

Chapter 6216

Divide Whole Numbers by Fractions6-10

To divide a whole number by a fraction:

Rename the whole number as afraction with a denominator of 1.

Multiply by the reciprocal of the divisor.

Simplify using the GCF where possible.Then multiply the numerators and multiplythe denominators.

Rename the product as a whole ormixed number when needed.

A carpenter cut a 4-ft board into -ft boards.How many pieces of board did the carpenter make?

Study these examples.

The carpenter made 6 pieces of -ft board.

4 ft

ft23

ft23

ft23

ft23

ft23

ft23

23

23

34

323

818 3

4! !

43

81

10 23

"

13

301

10 13! !

31

30

"

101

101

23

414 2

3! !

61

6 whole number

2

1

32

41 "

How many s are in 4?23

and arereciprocals.

23

32

34

??" 1 1

3??" 1

23

2 31 1

""

8 41 3

""

10 31 1

""

4 31 2

""

orYou can multiply by the reciprocal of the divisor since dividing by anumber is the same as multiplying by the reciprocal of that number.

!234 6

mixed number whole number

To find the number of -ft boards,divide: 4

You can use a diagram:

n.!23

8205-4_216 10/6/07 8:57 PM Page 216

Step 3: Write the reciprocal

=Step 4: Multiply across 12

2Step 5: Turn into mixed

or whole number.

6