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Math Grade 4

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MathGrade 4

Mrs. Ennis

Adding and Subtracting Fractions Part 2

Lesson Twenty-Three

451 + X + 127 = 891

87,004 – 25,987 =

7 x R = 56

32 ÷ 4 =

What is the product of 3 and 5?

(>, <, =) 5ft. _________2 yards

7. What is the area (length x width) of this figure?

8. What is 200 more than 8,956?

9. It takes Nancy 15 minutes to walk a mile. How many miles would she walk in 1½ hours?

1m

1m

10m

6m

10. Larry reads an average of 20 pages an hour. How many hours will it take him to read a book with 160 pages?

Adding and Subtracting Mixed Numerals

A proper fraction has a numerator that is less than its denominator.

An improper fraction has a numerator that is more than or equal to its denominator.

A mixed number shows the sum of a whole number and a proper fraction.

ImproperFractions

Proper Fractions

5

7

12

9

8

9

10

3

Mixed Numbers

3

17

8

3

20

5

15

15

15

is an improper fraction.

4

4

4

3

3

4

For example,

We can write improper fractions as mixed numbers.

can be shown as

=

1

3

4

3

1

Improper Fraction

Mixed Number

9

4

2

1

4

Improper Fractions

2

3

8

3

2

15

4

3

3

4

- Multiply the denominator of the fraction by the whole number.
- Add the product to the numerator.
- The resulting sum is the numerator of the improper fraction.
- The denominator remains the same.

2

14

4

3

3

Denominator stays the same.

4 X 3

+ 2 = 14

4

19

3

5

5

Denominator stays the same.

3 X 5

+ 4 = 19

1

5

2

2

2

Denominator stays the same.

2 X 2

+ 1 = 5

4

34

6

5

5

Denominator stays the same.

6 X 5

+ 4 = 34

+

+

+

+

=

1

1

1

1

8

5

8

8

8

5

=

+

+

+

+

8

8

8

8

8

8

37

37

=

8

8

4

4

5

8

Convert to a mixed number.

+

+

+

+

=

1

1

1

1

3

3

3

3

2

2

=

+

+

+

+

3

3

3

3

3

3

14

14

=

3

3

4

4

2

3

Convert to a mixed number.

+

+

+

=

1

1

1

5

5

3

5

3

=

+

+

+

5

5

5

5

5

18

18

=

5

5

3

3

5

Convert to a mixed number.

- If you have an improper fraction, you can divide the denominator into the numerator.
- The quotient becomes the whole number part of the mixed number.
- The remainder is the numerator of the fraction.
- The divisor is the denominator of the fraction.

13

2

whole number

5

5

13

10

3

numerator

denominator

3

2

5

=

23

5

whole number

4

4

23

20

3

numerator

denominator

3

5

4

=

19

9

whole number

2

2

19

18

1

numerator

denominator

1

9

2

=

36

6

whole number

6

6

36

36

0

numerator

denominator

6

=

1

3

Change each improper fraction into a mixed numeral.

1

=

4

3

1

2

1

6

4

2

4

1

=

=

2

3

1

14

8

6

8

1

=

=

3

=

Change each improper fraction into a mixed numeral.

21

7

17

3

2

3

5

=

1

5

3

32

10

2

10

3

=

=

17

5

2

5

=

3

Change each mixed numeral into an improper fraction.

21

8

5

8

=

2

4

5

=

3

19

5

56

9

2

9

=

6

Change each mixed numeral into an improper fraction.

33

7

5

7

=

4

2

5

=

8

42

5

AddingMixed Numbers

Stack your problem

with fractions and whole numbers lining up.

2

7

2. Make sure your fractions have the same denominator.

6

3. Add your fractions.

4. Add your whole numbers.

5. Make sure any fractions are in simplest form.

3

7

4

+

10

5

7

AddingMixed Numbers

Stack your problem

with fractions and whole numbers lining up.

6

9

2. Make sure your fractions have the same denominator.

3

3. Add your fractions.

4. Add your whole numbers.

5. Make sure any fractions are in simplest form.

1

9

5

+

8

7

9

AddingMixed Numbers

Stack your problem

with fractions and whole numbers lining up.

6

10

2. Make sure your fractions have the same denominator.

4

3. Add your fractions.

4. Add your whole numbers.

5. Make sure any fractions are in simplest form.

2

10

5

+

9

8

10

4

5

=

AddingMixed Numbers

Stack your problem

with fractions and whole numbers lining up.

4

10

2. Make sure your fractions have the same denominator.

5

3. Add your fractions.

4. Add your whole numbers.

5. Make sure any fractions are in simplest form.

6

10

2

+

7

1

=8

10

10

+

=

AddingMixed Numbers

2

9

3

9

11

9

=1

6

8

9

4

=11

2

9

+

10 + 1

2

9

10

11

9

2

9

=11

AddingMixed Numbers

2

4

3

4

6

4

=1

7

3

4

4

=12

1

2

+

11 + 1

1

2

11

6

4

1

2

=12

AddingMixed Numbers

2

5

=1

5

5

2

3

5

5

= 8

+

7 + 1

7

5

5

= 8

Subtracting Mixed Numerals with Like Denominators

SubtractingMixed Numbers

Stack your problem

with fractions and whole numbers lining up.

5. Make sure any fractions are in simplest form.

3. Determine whether you need to make improper fractions.

5

7

2. Make sure your fractions have the same denominator.

4. Subtract your whole numbers and then your fractions.

6

_

3

7

4

2

2

7

SubtractingingMixed Numbers

5. Make sure any fractions are in simplest form.

3. Determine whether you need to make improper fractions.

Stack your problem

with fractions and whole numbers lining up.

6

9

4. Subtract your whole numbers and then your fractions.

2. Make sure your fractions have the same denominator.

8

3

9

1

3

=

_

3

9

2

6

6

3

9

1

3

SubtractingMixed Numbers

4

7

5. Make sure any fractions are in simplest form.

4. Subtract your fractions and then your whole numbers if necessary.

Stack your problem

with fractions and whole numbers lining up.

6

46

7

3. Determine whether you need convert mixed numerals to improper fractions.

2. Make sure your fractions have the same denominator.

=

_

6

7

3

27

7

=

19

7

5

7

2

=

SubtractingMixed Numbers

3

9

5. Make sure any fractions are in simplest form.

4. Subtract your fractions and then your whole numbers if necessary.

Stack your problem

with fractions and whole numbers lining up.

8

75

9

3. Determine whether you need convert mixed numerals to improper fractions.

2. Make sure your fractions have the same denominator.

=

_

5

9

1

14

9

=

61

9

7

9

6

=

SubtractingMixed Numbers

3

8

5. Make sure any fractions are in simplest form.

4. Subtract your fractions and then your whole numbers if necessary.

Stack your problem

with fractions and whole numbers lining up.

3

27

8

3. Determine whether you need convert mixed numerals to improper fractions.

2. Make sure your fractions have the same denominator.

=

_

5

8

5

8

=

3

4

22

8

6

8

2

2

=

SubtractingMixed Numbers

1

4

5. Make sure any fractions are in simplest form.

4. Subtract your fractions and then your whole numbers if necessary.

Stack your problem

with fractions and whole numbers lining up.

5

21

4

3. Determine whether you need convert mixed numerals to improper fractions.

2. Make sure your fractions have the same denominator.

=

_

3

4

3

15

4

=

6

4

2

4

1

2

1

=

http://www.aaamath.com/fra66ex2.htm

http://www.ixl.com/math/grade-4/add-and-subtract-fractions-with-like-denominators-word-problems

http://www.ixl.com/math/grade-3/add-and-subtract-fractions-with-like-denominators

Sharon has fewer than 20 coins. When she puts them in piles of 5, she has 1 left over. When she puts them in piles of 3, she also has 1 left over. How many coins does Sharon have?

Sharon has 16 coins.

5+5+5+1 = 16

3+3+3+3+3+1 + 16

Sylvia has 39 coins.

6+6+6+6+6+6+3 = 39

5+5+5+5+5+5+5+4 = 39

Sylvia has fewer than 40 coins but more than 10. If she puts them in piles of 6, she has 3 left over. If she puts them in piles of 5, she has 4 left over. How many coins does Sylvia have?

Resources:

- http://www.aaamath.com/fra66ex2.htm

- http://www.mrhammond.org/math/mathlessons/

- http://www.ixl.com/math/grade-4/add-and-subtract-fractions-with-like-denominators-word-problems

- http://www.teachingideas.co.uk/maths/contents08fracdecperratprop.htm

- http://www.ixl.com/math/grade-3/add-and-subtract-fractions-with-like-denominators