Download Adding and Subtracting with Fractions

Adding and Subtracting with Fractions
Fraction meaning: 13 is how many parts
25 of this whole amount
Equivalent Fractions review:
1 = __
2
4
3=6
9
8= 2
12
9 = 3
27
Lowest Terms review:
2 =
4
7 =
14
3 =
18
1
Lowest Common Denominator review:
In order to add or subtract or divide fractions that are not
alike, we must convert the unlike fractions to the same
subdivisions of the whole. In other words, we must find
the lowest common denominator.
3+ 1=
5 2
+
As you can see above, 3 out of 5 cannot be added to 1 out
of 2, because they are not the same size parts.
LCD method:
Place the two denominators in a vertical layout. Then…
x1 x2
x3
x4 x5
5=
5 10
15
20
25
2=
2
6
8
10
4
2
The LCD for denominators 2 and 5 is 10
3x2 = 6
5x2
10
1x5= 5
2 x 5 10
6 + 5 = 11
10
10
10
Move 4 shaded cells from the bottom figure to the top
figure and get 1Whole. There will be 1 part remaining in
the lower figure. We now have 11 = 1 1
10
10
3
Practice:
A) Add / Subtract pictorially and symbolically:
5 - 1 =
6
3
3 - 2 =
4
3
2 + 1 =
3
6
B) Find the LCD:
2-1=
8 7
8=
7=
4+5=
6 9
6=
9=
7 - 5=
10 12
10 =
12 =
9 +1=
10 3
10 =
3=
*3- 4=
5 11
5=
11 =
(Prime Numbers)
4
Practice continued…
Understand: When at least one denominator is a prime
number, multiply the two denominators to find the LCD.
(except if one denominator is a multiple of the other. Ex 1/25 + 1/5).
C) Sketch fraction bars to prove that 3 - 1 = 2 is not
correct
8 4
4
Sketch fraction bars to prove that 1 + 1 = 2 is not correct
4 4 8
D) Create two different pairs of fractions whose sum is
1
2
E) Solve mentally: 1/7 + 4/7 =
1/2 + 5/8 =
1/2 - 1/8 =
5 + 2/5 =
6 - 2 3/4 =
4 - 1/5 =
F) Do not use a diagram; do not solve symbolically.
Explain why the following is incorrect:
5 + 5 = 10 = 5
6 8 14 7
5
Understand: Mixed fractions should be converted to
Improper Fractions:
13= 4 + 3 =7
2 1 = 5 + 5 + 1 = 11
4
4
4 4
5
5 5 5 5
Shortcut: 1 3 = 4 x1 + 3 = 7
4
Try: 9 3/4
2 1 = 5 x 2 + 1 = 11
5
6 1/2
3 3/5
2 2/3
Textbook:
page 89 - 3 4 5bcdegi 7 8 9 10a
page 90 - Estimating: do 2abc using your handout.
Remember that about means to estimate ~
page 91 - do 1 2 3 4 5
page 92 - do 7 8 9 10 11
page 94 - do 5 6 From UA do 1efhi
page 95 - do 5ef
6
Add and Subtract with Positive and Negative Fractions
Addition Rules:
Same signs:
add the numbers and use the same sign in the answer.
+1/3 + (+1/3) = +2/3
-1/3 + (-1/3) = -2/3
Different signs:
subtract the numbers and use the sign of the “larger”
number in the answer.
-3/4 + (+1/4) = -2/4
+7/8 + (-2/8) = +5/8
Subtraction Rule: use the shortcut: Add the Opposite
-6/7 - (-2/7) = -6/7 + (+2/7) = -4/7
Practice: From the handout do 2 7abef 8abef
7
Order of Operations using Signed Fractions
a) 5 x (-1/4) ÷ - 4 =
8
8
b) 4 x 1 ÷ -8 =
-3 -3
9
c) -10 ÷ 6 x (-7/3) =
-9 5
d) -5 1 ÷ 2 2 ÷ (-4 1/2) =
3
3
e) 2 x (-1/4) ÷ (3/-2) =
3
f) 5 ÷ 3 1 - 3 3 x (-2/9) =
6
3
4
Challenge:
[1 1/2 + (1/-4) ] x [4/3 - 7/5] =
8