Transcript Add & subtract fractions & decimals

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.3.2 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).
M4.A.3.2.1 Solve addition or
subtraction problems involving
decimals through hundredths
(decimal numbers must have the
same number of places).
PSSA Sample Item
Adding and Subtracting Decimals
When 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.
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.
Addition of Decimals
2.35
+ 4.92
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
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
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
• 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
•
75 – 0.24 
-
75
0.24
(add a decimal
& a couple 0’s)
75.00
- 0.24
74.76
Now try these:
a) 10 - 0.25
c) 342.7 – 3.86
b) 100 – 0.48
d) 43 – 7.23
•
•
•
•
•
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
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
Add “0” if needed
to keep decimal
place.
3.6
+ .36
3.60
+ 0.36
Answer: 3.96
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
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.
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?
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.
Subtracting Decimal Numbers
812.50
- 599.87
Subtracting Decimal Numbers
812.50
- 599.87
Subtracting Decimal Numbers
4
812.50
- 599.87
Subtracting Decimal Numbers
4
8 1 2 . 5 10
- 599.87
Subtracting Decimal Numbers
4
8 1 2 . 5 10
- 599.87
3
Subtracting Decimal Numbers
1 4
8 1 2 . 5 10
- 599.87
3
Subtracting Decimal Numbers
1 14
8 1 2 . 5 10
- 599.87
3
Subtracting Decimal Numbers
1 14
8 1 2 . 5 10
- 599.87
63
Subtracting Decimal Numbers
1 14
8 1 2 . 5 10
- 599.87
.63
Subtracting Decimal Numbers
0 11 14
8 1 2 . 5 10
- 599.87
.63
Subtracting Decimal Numbers
0 11 14
8 1 2 . 5 10
- 599.87
2.63
Subtracting Decimal Numbers
71011 14
8 1 2 . 5 10
- 599.87
2.63
Subtracting Decimal Numbers
71011 14
8 1 2 . 5 10
- 599.87
12.63
Subtracting Decimal Numbers
71011 14
8 1 2 . 5 10
- 599.87
212.63
Subtracting Decimal Numbers
71011 14
8 1 2 . 5 10
- 599.87
212.63
Max had $212.63 left.
Practice Adding Decimals
a) 4.2
+ 5.6
e) .49
+ .35
b) 3.2
+ 1.5
f) .32
+ .69
c) .7
+ .4
g) 4.54
+ 5.94
d) .2
+ .3
h) 3.03
+ 4.15
Practice Adding Decimals
a) 4.2
+ 5.6
9.8
e) .49
+ .35
.84
b) 3.2
+ 1.5
4.7
f) .32
+ .69
1.01
c) .7
+ .4
1.1
g) 4.54
+ 5.94
10.48
d) .2
+ .3
.5
h) 3.03
+ 4.15
7.18
Practice Subtracting Decimals
a) .9
- .3
e) 4.9
- 3.3
b) .5
- .2
f) 7.89
- 3.96
c) .8
- .7
g) 14.34
- 6.36
d) 6.7
- 5.2
h)3.71
- .4
Practice Subtracting Decimals
a) .9
- .3
.6
e) 4.9
- 3.3
1.6
b) .5
- .2
.3
f) 7.89
- 3.96
3.93
c) .8
- .7
.1
g) 14.34
- 6.36
7.98
d) 6.7
- 5.2
1.5
h)3.71
- .4
3.31
M4.A.3.2.2 Solve addition or
subtraction problems with
fractions with like denominators
(denominators to 10, no
simplifying necessary).
PSSA Sample Item
PSSA Sample Item
PSSA Sample Item
Parts of a Fraction
3
4
= the number of parts
= the total number of
parts that equal a whole
Parts of a Fraction
3
4
= numerator
= denominator
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.
What are the denominators in these fractions?
1
Two
2
4
Six
6
7
Eight
8
7
Five
5
2
Three
3
Remember the bottom number in a fraction is called the denominator.
You have learned to add fractions using pictures.
+
1
=
+
3
4
3
=
5
3
Fractions can be added and subtracted without using pictures.
Here’s a problem.
+
5
4
3 =
4
When you add and subtract fractions you do not work on the top and the
bottom the same way.
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
4
3
=
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.
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
7
5
-
2
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.
5
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
5
-
2
5
=
5
5
Let’s try another problem.
4
2
-
3
2
=
First you copy the denominator then you work the top.
What is the denominator?
Yes, it’s 2.
2
Now work on the top. What is 4 – 3?
Right, it’s 1.
So
4
2
-
3
1
2 = 2
Here’s a new problem.
+
2
4
3
=
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
4
3
4
=
5
4
Subtracting Like Denominators
Only subtract the numerators
4 - 1
3
=
4
4
4
1/4 1/4
1/4 1/4
Subtract these fractions
4 - 1
3
=
5
5
5
1/5
1/5
1/5
1/5
Subtract these fractions
1/4
3 - 1
2
=
4
4
4
1/4
1/4
Subtract these fractions
1
6
1
6
1
6
1
6
1
6
5 - 2 = 3
6
6
6
Subtract these fractions
1
6
1
6
1
6
1
6
4 - 2 = 2
6
6
6
Subtract these fractions
5 - 3 = 2
12 12 12
Subtract these fractions
9 - 3 = 6
10 10 10
Subtract these fractions
4 - 3 =41
4
9
9
9
Subtract these fractions
7 - 1 =56
5
8
8
8
Subtract these fractions
8
6
2
- 3 =1
4
9
9
9
Your Turn
Copy these problems on your paper and write the answer.
6
1.
8
2
- 5 =
5
5
4.
5.
8
6
10
4
3
4
+
3.
5
3
+
2.
2
3
4
6
=
7
3
=
4
6
3
=
4
7
2
4
5
=
4
4
Check your work
You have learned to work problems this way.
+
3
4
1
4
4
=
4
or
7
8
-
5
8
2
=
8
You can also work fraction addition and subtraction problems when
they are written this way.
5
8
2
8
7
8
-
8
3
2
3
6
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.
Your Turn
1.
2.
3.
4.
5.
6
8
8
4
4
6
5
3
2
6
+ 1
8
- 3
+ 2
6
- 6
- 1
3
6
4
Your Turn
1.
2.
3.
4.
5.
6
8
8
4
4
6
5
3
2
6
+ 1
8
- 3
- 6
- 1
4
+ 2
6
3
6
7
5
6
1
1
8
4
6
3
6