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M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally - straight computation only).

M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

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Page 1: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

M4.A.3 Compute accurately and fluently and make reasonable estimates.

M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally -

straight computation only).

Page 2: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

M4.A.3.2 Eligible Content

• M4.A.3.2.1 Solve addition or subtraction problems involving decimals through hundredths (decimal numbers must have the same number of places).

• M4.A.3.2.2 Solve addition or subtraction problems with fractions with like denominators (denominators to 10, no simplifying necessary).

Page 3: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

M4.A.3.2.1 Solve addition or subtraction problems involving decimals through hundredths

(decimal numbers must have the same number of places).

Page 4: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

PSSA Sample Item

Page 5: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Adding and Subtracting DecimalsWhen adding & subtracting numbers with decimals, stack the numbers on top of each other lining the decimals up. Remember, if a number doesn’t have a decimal, it comes at the end of the number.EX: 5.2 + 97.44 97.44

+ 5.2

I can fill in empty spots with zeros. When I subtract, I have to fill in empty spots with 0’s. It’s not necessary with addition.

Page 6: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Adding and Subtracting Decimals

EX: 5.2 + 97.44 97.44

+ 5.20

102.64

I can fill in empty spots with zeros. When I subtract, I have to fill in empty spots with 0’s. It’s not necessary with addition.

Page 7: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Addition of Decimals

2.35

+ 4.92

Page 8: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Addition Algorithm for Decimals

2.35

+ 4.92

7

Place Value: Start with smallest pieces (hundredths)

Basic Fact: 5 hundredths + 2 hundredths = 7 hundredths

Basic Fact: 5 + 2 = 7

Rename: not needed

Page 9: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Addition Algorithm for Decimals 1

2.35

+ 4.92

.27

Place Value: tenths

Basic Fact: 3 tenths + 9 tenths = 12 tenths

Basic Fact: 3 + 9 = 12

Rename: 12 tenths as 1 one + 2 tenths

Page 10: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Addition Algorithm for Decimals 1

2.35

+ 4.92

7.27

Place Value: ones

Basic Fact: 1 one + 2 ones + 4 ones = 7 ones

Basic Fact: 1 + 2 + 4 = 7

Rename: not needed

Page 11: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

• 722.86 + 0.02 722.86

+ 0.02

722.88

ON ADDITION, you don’t have to fill in 0’s but you can.

With SUBTRACTION, you need to fill in 0’s if the number is on top. EX: 8 – 2.54

8.00

- 2.54

5.46

Page 12: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

• 75 – 0.24 75 (add a decimal - 0.24 & a couple 0’s)

75.00 - 0.24 74.76

Now try these:a) 10 - 0.25 b) 100 – 0.48 c) 342.7 – 3.86 d) 43 – 7.23

Page 13: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

• 72.3 – 4

• 89 – 42.36

• 44.2 – 39.67

• 66.23 – 44.97

• Line up the decimals as shown below

• These will all need 0’s added.

• 72.3 89.00 44.20 66.23

- 4.0 -42.36 -39.67 -44.97

Page 14: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Lesson 35: Add, Subtract, Multiply & Divide Decimal Numbers

Rule for adding and subtracting decimals: Line up the decimal point!!

Example 1: Add 3.6 + .36 + 36 3.6 + .36

Add “0” if needed to keep decimalplace.

3.60 + 0.36

Answer: 3.96

Page 15: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Example 2: Subtract 12.3 - 4.567

Step 1: write the numbers vertical, aligning the decimal point

12.3- 4.567

Add “0” to even out the places 12.300- 4.567

Step 2: Subtract (be sure to borrow correctly when needed)

Answer: 12.300 - 4.567 7.733

Page 16: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Adding and Subtracting Decimals

• LINE UP DECIMAL POINTS BEFORE YOU ADD OR SUBTRACT.

123.76

0.0009

+34.098

Trying to add like this can be confusing, the place values are all mixed up

123.76

0.0009

+34.098

Now you can’t confuse the VALUE of each digit.

Now, just add or subtract as you normally would. You may add zeros to the end of a decimal to line up place values – just like comparing decimals.

Page 17: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers

Ex) Max went to Wal-Mart with $812.50. He then bought a television for $599.87. How much money did he have left over?

Page 18: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers

Ex) Max went to Wal-Mart with $812.50. He then bought a television for $599.87. How much money did he have left over?

Solution: Line up the numbers vertically according to place value.

Page 19: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers

8 1 2 . 5 0

- 5 9 9 . 8 7

Page 20: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers

8 1 2 . 5 0

- 5 9 9 . 8 7

Page 21: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers 4

8 1 2 . 5 0

- 5 9 9 . 8 7

Page 22: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers 4

8 1 2 . 5 10

- 5 9 9 . 8 7

Page 23: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers 4

8 1 2 . 5 10

- 5 9 9 . 8 7

3

Page 24: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers 1 4

8 1 2 . 5 10

- 5 9 9 . 8 7

3

Page 25: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers 1 14

8 1 2 . 5 10

- 5 9 9 . 8 7

3

Page 26: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers 1 14

8 1 2 . 5 10

- 5 9 9 . 8 7

6 3

Page 27: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers 1 14

8 1 2 . 5 10

- 5 9 9 . 8 7

. 6 3

Page 28: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers 0 11 14

8 1 2 . 5 10

- 5 9 9 . 8 7

. 6 3

Page 29: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers 0 11 14

8 1 2 . 5 10

- 5 9 9 . 8 7

2 . 6 3

Page 30: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers 71011 14

8 1 2 . 5 10

- 5 9 9 . 8 7

2 . 6 3

Page 31: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers 71011 14

8 1 2 . 5 10

- 5 9 9 . 8 7

1 2 . 6 3

Page 32: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers 71011 14

8 1 2 . 5 10

- 5 9 9 . 8 7

2 1 2 . 6 3

Page 33: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Decimal Numbers 71011 14

8 1 2 . 5 10

- 5 9 9 . 8 7

2 1 2 . 6 3

Max had $212.63 left.

Page 34: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Practice Adding Decimals

a) 4.2

+ 5.6b) 3.2+ 1.5

c) .7+ .4

d) .2 + .3

e) .49+ .35

f) .32+ .69

g) 4.54+ 5.94

h) 3.03+ 4.15

Page 35: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Practice Adding Decimals

a) 4.2

+ 5.6 9.8

b) 3.2+ 1.5 4.7

c) .7+ .4 1.1

d) .2 + .3 .5

e) .49+ .35 .84

f) .32+ .69 1.01

g) 4.54+ 5.94 10.48

h) 3.03+ 4.15 7.18

Page 36: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Practice Subtracting Decimals

a) .9 - .3

b) .5 - .2

c) .8 - .7

d) 6.7 - 5.2

e) 4.9 - 3.3

f) 7.89 - 3.96

g) 14.34 - 6.36

h)3.71 - .4 

Page 37: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Practice Subtracting Decimals

a) .9 - .3 .6

b) .5 - .2 .3

c) .8 - .7 .1

d) 6.7 - 5.2 1.5

e) 4.9 - 3.3 1.6

f) 7.89 - 3.96 3.93

g) 14.34 - 6.36 7.98

h)3.71 - .4  3.31

Page 38: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

M4.A.3.2.2 Solve addition or subtraction problems with

fractions with like denominators (denominators to 10, no simplifying necessary).

Page 39: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

PSSA Sample Item

Page 40: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

PSSA Sample Item

Page 41: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

PSSA Sample Item

Page 42: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Parts of a Fraction

3

4

= the number of parts

= the total number of parts that equal a whole

Page 43: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Parts of a Fraction

3

4

= numerator

= denominator

Page 44: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Adding and Subtracting Fractions with like Denominators

You know that the bottom number of a fraction tells how may parts each whole is divided into.

In this picture each circle is divided into 4 parts so the bottom number for this

fractions is 4. 4

We use or shade 5 parts so the top number of this fraction is 5. The picture shows the fraction 5 .

4

In a fraction the bottom number has a special name. The bottom number in a fraction is called the denominator. The denominator or the bottom number in a fraction tells how many parts each whole is divided into.

Page 45: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

What are the denominators in these fractions?

Two

Six

Eight

Five

Three

Remember the bottom number in a fraction is called the denominator.

1

2

4

6

7

8

7

5

2

3

Page 46: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

1 4 5

3 3 3

Fractions can be added and subtracted without using pictures.

Here’s a problem.

5 3

4 4

When you add and subtract fractions you do not work on the top and the bottom the same way.

You have learned to add fractions using pictures.

+ =+

=

+

=

Page 47: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

When you add and subtract fractions you COPY the denominator, then you work on the top. Remember, you copy the denominator and then you work on the top.

5 34 4

Look at this problem. What is the denominator? Yes, it’s 4.

What do you do with the denominator? Right, you copy it in the answer so the denominator in the answer is 4.

Now we can add the numbers on the top. What do we get when we add 5 + 3?Correct, 5 + 3 = 8.

We put the 8 on top in the answer so 5 + 3 = 8 . 4 4 4

+

=

4

Page 48: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

7 2

5 5

Here’s a different problem. First look at the sign. We are subtracting in this problem.

Next look at the denominators. What do we do with the denominator?

Yes, we copy it in the answer.

On the top the sign tells us to subtract. 7 – 2, what’s the answer?

Right, 7 – 2 = 5. We put the 5 on top.

5

5

7 2 5

5 5 5

=

5

- =

-

Page 49: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Let’s try another problem.

4 3

2 2

First you copy the denominator then you work the top.

What is the denominator?

Yes, it’s 2.

Now work on the top. What is 4 – 3?

Right, it’s 1.

So 4 3 1

2 2 2

- =

2

- =

Page 50: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Here’s a new problem.

2 3

4 4

What do we do with the denominator?

Yes, we copy the 4.

4

What do we get on top?

Good Job! 2 + 3 = 5.

2 3 5

4 4 4

+

=

+

=

Page 51: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtracting Like Denominators

1/444

1/4

1/414

34

1/4

- =

Only subtract the numerators

Page 52: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtract these fractions

1/5

1/51/5

1/5

45

15

- =35

Page 53: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtract these fractions

1/4

1/4

1/434

14

- =24

Page 54: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtract these fractions

36

26

56

- =

16

16

16

16

16

Page 55: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtract these fractions

26

26

46

- =

16

16

16

16

Page 56: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtract these fractions

312

512

- = 212

Page 57: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtract these fractions

310

910

- = 610

Page 58: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtract these fractions

39

49

- = 19

4 4

Page 59: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtract these fractions

18

78

- = 68

5 5

Page 60: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Subtract these fractions

29

89

- = 69

4 13

Page 61: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Your Turn

Copy these problems on your paper and write the answer.

1. 8 2

5 5

2. 5 2

3 3

3. 8 4

6 6

4. 10 3

4 4

5. 3 2

4 4

=

=

=

=

=

+

+

-

-

-

Check your work

6

5

7

3

4

6

7

4

5

4

Page 62: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

You have learned to work problems this way.

3 1 4 or 7 5 2

4 4 4 8 8 8

You can also work fraction addition and subtraction problems when they are written this way.

5 8

8 3

2 2

8 3

7 6

8 3

Just like before check to see if you can work the problem the way it is written, copy the denominator, then add or subtract.

+

-

+ - ==

Page 63: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Your Turn

1. 2. 3. 4. 5.

6 8 4 5 2

8 4 6 3 6

+ 1 - 3 + 2 - 6 - 1

8 4 6 3 6

Page 64: M4.A.3 Compute accurately and fluently and make reasonable estimates. M4.A.3.2 Compute using fractions or decimals (written vertically or horizontally

Your Turn

1. 2. 3. 4. 5.

6 8 4 5 2

8 4 6 3 6

+ 1 - 3 + 2 - 6 - 1

8 4 6 3 6

5

4

7

8

6

6

1

3

1

6