Download Adding and Subtracting mixed numbers

Math – Study Guide Chapter 4 (4.1 ~ 4.2)
Topics to be included:
1)Writing Fractions as Decimals
Two different ways:
a) Division ~ always works!
3
4
5
9
2
.75
.55555 = .5
4 | 3.00
9 | 5.00
- 28
- 45
20
50
-20
0
b) If the denominator is a factor of 10, 100, 1000 multiply numerator and
denominator by that number ~ simplify
6
12
= (x 2)
= .12
100
50
2) Writing Fractions as Decimals
Say the name of fraction ~ divide by the place value ~ simplify
0.02 = two hundredths =
2
1
=
100
50
3) Comparing Rational Numbers
 Compare fractions ~ Make denominators same ~ Compare numerators OR
 Cross multiply fractions
Example: Compare -
1
3
□ 4
8
Cross Multiply
□
-1
4
-3
8
so –
1
3
>4
8
 Compare decimals ~ Compare every digit
Example: Compare 0.25 □ .27
Tenths -> both 2
Hundredths -> 5 < 7
So, 0.25 < 0.27
4) Ordering Rational Numbers
Change all fractions into decimals, compare and order.
Example: Order from least to greatest: 0.056,
1
5
, -0.2, 20
9
Convert the fractions into decimals.
0.056
0.05 (
1
)
20
In order from least to greatest:
5
1
-0.555 (- ), -0.2, 0.05 (
), 0.056
9
20
-0.2
5
-0.5 (- )
9
Math – Study Guide Chapter 4 (4.3 ~ 4.5)
Topics to be included:
1) Adding Like & Unlike Fractions
Same Denominators
Different Denominators
2/5
+ 3/5
5/5 = 1
2/7 mult by 5
+ 3/5 mult by 7
10/35
+ 21/35
31/35
2) Subtracting Like & Unlike Fractions
Same Denominators
-
Different Denominators
4/5
3/5
1/5
-
5/6 mult by 1
2/3 mult by 2
5/6
- 4/6
1/6
3) Adding/Subtracting Mixed Numbers
Same Denominators
Different Denominators
3 2/7
+ 2 3/7
5 5/7
9 7/10 mult by 1
- 4 3/5 mult by 2
9 7/10
- 4 6/10
5 1/10
Different Denominators & Borrowing
4 1/3 mult by 5
- 3 3/5 mult by 3
4 5/15
- 3 9/15
* Cannot perform 5 -9, so borrow
1) Subtract whole number by 1: 4-1 = 3
2) Add denominator to numerator and make that your new numerator: 5 + 15 = 20
3) Subtract whole numbers
3 20/15
- 3 9/15
11/15
Subtracting from a whole number
1) Subtract whole number by 1: 12 – 1 = 11
2) Make a fraction have the same numerator and denominator as the second fraction:
4/4
3) Subtract whole numbers
12
- 3 1/4
11 4/4
- 3¼
8 3/4
Math – Study Guide Chapter 4 (4.6, 4.8)
Multiplying Fractions
1.
2.
3.
4.
Make into improper
Cross Simplify
Multiply across
Simplify (if needed.)
Examples:
5 4
5 2
1
·
= · =
8 10
8 5
4
2 ∙
7
8
=
2 7
∙ =
1 8
14
6
3
=1 =1
8
8
4
-
2
15
5
15
∙
∙ =5
22
8
88
2
2
8 12
32
∙ 12 = ∙
=
= 32
3
3
1
1
Dividing Fractions
1.
2.
3.
4.
Change mixed numbers into improper fractions
Keep the first fraction.
Change the division sign to a multiplication sign
Flip the second one (the divisor) upside down *** Remember this is called the
reciprocal ***
5. Follow the multiplication rules.
Examples:
4
8
4 9
3
÷
= ·
=
6
9
6 8
4
10
1
3
21 7
21 4 6
÷1 =
÷ =
∙ = =6
2
4
4
2
2 7 1