Download Mixed Numbers into FG1 and Back:

Name: __________________​Unit
2 Study Guide
period: _______
Review of Decimal Multiplication and Division
13.45 x 32
142.5 x 0.13
81.4 x 2.3
12.45 ​÷ 15
232 ÷
​ 0.75
423.5 ÷ 1.21
From Decimals to Fractions and Back:
Strategies:
Decimals to Fractions1. Read​ the decimal “like a mathematician.”
3.24
​
= “three ​and twenty four hundredths”
24
2. Write the ​fraction​ that matches!
​
“three ​and twenty three hundredths” = 3 100
24
3. Simplify​ if necessary!
3 100
÷ 44 = 3 256
Fractions to Decimals
Sometimes works:
● Is it already in base ten?
1. Read the fraction like a
mathematician.
2. Write the decimal that
matches!
17
4 1000
= 4.017
Sometimes works:
● Can we make it base ten?
1. Create an equivalent
fraction with the
denominator that
matches the decimal
places (tenth, hundredth,
etc).
2. Write the decimal that
matches!
6 207
×
5
5=
35
6 100
=
ALWAYS works:
● Fractions ARE division
1. Divide the numerator by
the denominator!
3. Remember to add a
decimal and annex 0’s!
4. Go out three decimal
spaces.
2
7
6.35
= 2 ÷ 7 = 0.285
Practice:
41
100
6
50
=
=
11
2 18
=
9
100
=
25
5 500
=
10
36
=
3
7 10
=
3
15
=
12 17 =
Mixed Numbers into FG1 and Back:
You can tell when you’re looking at a mixed number because
_________________________________
_________________________________________________________________________________.
You can tell when you’re looking at a fraction greater than one because ________________________
_________________________________________________________________________________.
When you are converting between Mixed #s and FG1s, your goal is to create an equivalent fractional
amount with “a different name.”
→ Just like I can be called Mrs. Hosek, Mrs. Hanna, or Sarah but I’m the same person, 3 13 , 103 , or 3 26
are all the ​same amount but just have different names.
How we do it:
F​G​1 to Mixed:
Make them ​G.L.A.D.
M​ixed to FG1:
Make them ​M.A.D.
M​ultiply the denominator by the
whole number
​
A​dd that product to the numerator
D​enominator stays the same!
G​o divide! (numerator ÷ denominator)
L​eave whole number as t​ he whole
number
A​lways make the remainder the
numerator
D​enominator stays the same!
Practice:
11
2 18
=
95
36
12 17 =
=
120
15
=
Adding and Subtracting Fractions:
1.​ MUST HAVE​ common denominators! ​Show your work ​in the problem!
6 35 + 2 14
=
2. Simply if necessary!
6 35 × 44 + 2 14 × 55
12
5
6 20
+ 2 20
=
=
17
6 20
Subtracting Fractions with Regrouping:
​
1. MUST HAVE​ common denominators! ​Show your work ​in the problem!
6 15 + 2 34
=
6 15 × 44 + 2 34 × 55
=
4
15
6 20
+ 2 20
2. Now you have two options: ​borrowing or converting them into FG1s.
(Examples and practice on the next page!)
Borrowing:
1. “Cross it out, make it less”
2. **Think about what “base system” your
problem is in! --Add a denominator to your
numerator**
3. Subtract numerators, denominators stay the
same.
4. Simplify if necessary!
Regrouping:
Converting:
1. Make both fractions “​M.A.D​”
2. Subtract numerators, denominators stay
the same.
3. Make your answer “​G.L.A.D​”
4. Simplify if necessary!
Converting:
Multiplying Fractions:
Why it works:
Multiplication is taking the first factor and replicating it the amount of times of the 2nd factor.
→ 4 x 3 is 4 three times, or 4 + 4 + 4
→ 14 x 3 is 14 three times, or 14 + 14 + 14 (= 34 )
When the second factor is a fraction, it means the first factor is replicated ​less than one time.
→ 4 x 13 is 4 one-third of a time. You would find 13 of 4 by cutting 4 into three pieces and focusing on
one of them. 4 x 13 = ​________
→ 14 x 23 is 14 two-thirds of a time. You would look at 23 of 14 by taking 14 , cutting it into thirds and
focusing on 2 of them. 14 x 23 =​________
***You ​CANNOT​ multiply Mixed Numbers -- they MUST be changed into FG1s**
How we do it:
1. You DO NOT need common denominators!
2. Convert to FG1s if necessary.
3. Multiply numerators to find your new numerator.
4. Multiply denominators to find your new denominator.
5. Simplify if necessary!
2
2
5x 33
2 11
5x 3
2 11
22
5x 3 =
2 11
22
5 x 3 = 15
22
7
15 = 1 15
Dividing Fractions:
1. The quick way to divide fractions is to “______, _______, _______.”
2. Once it is a multiplication problem, you can multiply like normal.
***You ​CANNOT​ divide Mixed Numbers -- they MUST be changed into FG1s FIRST**
Practice of all operations:
11
7 15
- 3 15 =
3
2 12
+
3
5
=
11
2 15
x 3 15 =
3
2 12
x
3
5
=
1
6
x 45 =
2 15 ÷
3
5
=
1
6
÷
11
15
÷ 3=
12 16 - 3 45 =
4
5
=
1 23 + 1 49 =
3 x 1 49 =
3 ÷ 1 49 =
Results and Reflection:
Study Guide Reflection
Section
Score
Reflection
Need more
practice?
yes/no
Decimal x and ÷
/6
From Decimals to
Fractions and
Back:
Mixed Numbers
into FG1 and
Back:
Adding and
Subtracting
Fractions
Subtracting
Fractions with
Regrouping
Multiplying
Fractions
yes/no
/9
yes/no
/6
yes/no
/3
yes/no
/1
yes/no
/4
yes/no
Dividing Fractions:
/4
Name: __________________​Unit
2 Study Guide
period: _______
Review of Decimal Multiplication and Division
13.45 x 32
142.5 x 0.13
81.4 x 2.3
430.4
12.45 ​÷ 15
18.525
232 ÷
​ 0.75
187.22
423.5 ÷ 1.21
_
309.3
0.83
350
From Decimals to Fractions and Back:
Strategies:
Decimals to Fractions4. Read​ the decimal “like a mathematician.”
5. Write the ​fraction​ that matches!
6. Simplify​ if necessary!
3.24 = “three ​and twenty four hundredths”
24
“three ​and twenty three hundredths” = 3 100
24
3 100
÷ 44 = 3 256
Fractions to Decimals
Sometimes works:
● Is it already in base ten?
3. Read the fraction like a
mathematician.
4. Write the decimal that
matches!
17
4 1000
= 4.017
Sometimes works:
● Can we make it base ten?
5. Create an equivalent
fraction with the
denominator that
matches the decimal
places (tenth, hundredth,
etc).
6. Write the decimal that
matches!
6 207
×
5
5=
35
6 100
=
ALWAYS works:
● Fractions ARE division
2. Divide the numerator by
the denominator!
7. Remember to add a
decimal and annex 0’s!
8. Go out three decimal
spaces.
2
7
6.35
= 2 ÷ 7 = 0.285
Practice:
41
100
6
50
2
= ​0.41
= ​0.09
25
5 500
= ​5.05
= ​0.12
11
18
9
100
_
= ​2.61
10
36
_
= ​0.27
3
7 10
= ​7.3
3
15
= ​0.2
12 17 = ​12.142
Mixed Numbers into FG1 and Back:
You can tell when you’re looking at a mixed number because ​it is composed of a mix -- a whole
number ​AND a fraction​.
You can tell when you’re looking at a fraction greater than one because _​the numerator is greater than
the denominator. The fraction has more parts in it than in one whole (
12
7 has 12 parts but only needs 7 for a whole) .
When you are converting between Mixed #s and FG1s, your goal is to create an equivalent fractional
amount with “a different name.”
→ Just like I can be called Mrs. Hosek, Mrs. Hanna, or Sarah but I’m the same person, 3 13 , 103 , or 3 26
are all the ​same amount but just have different names.
How we do it:
F​G​1 to Mixed:
Make them ​G.L.A.D.
M​ixed to FG1:
Make them ​M.A.D.
M​ultiply the denominator by the
whole number
A​dd that product to the numerator
D​enominator stays the same!
G​o divide! (numerator ÷ denominator)
L​eave whole number as t​ he whole
number
A​lways make the remainder the
numerator
D​enominator stays the same!
Practice:
11
2 18
=
47
18
95
36
23
= 2 36
12 17 =
84
7
120
15
= ​8
Adding and Subtracting Fractions:
1. MUST HAVE​ common denominators! ​Show your work ​in the problem!
6 35 + 2 14
=
2. Simply if necessary!
6 35 × 44 + 2 14 × 55
12
5
6 20
+ 2 20
=
=
17
6 20
Subtracting Fractions with Regrouping:
1. MUST HAVE​ common denominators! ​Show your work ​in the problem!
6 15 + 2 34
=
6 15 × 44 + 2 34 × 55
=
4
15
6 20
+ 2 20
2. ​Now you have two options: ​borrowing or converting them into FG1s.
(Examples and practice on the next page!)
Borrowing:
1. “Cross it out, make it less”
2. **Think about what “base system” your
problem is in! --Add a denominator to your
numerator**
3. Subtract numerators, denominators stay
the same.
4. Simplify if necessary!
Regrouping:
Converting:
1. Make both fractions “​M.A.D​”
2. Subtract numerators, denominators stay
the same.
3. Make your answer “​G.L.A.D​”
4. Simplify if necessary!
Converting:
Multiplying Fractions:
Why it works:
Multiplication is taking the first factor and replicating it the amount of times of the 2nd factor.
→ 4 x 3 is 4 three times, or 4 + 4 + 4
→ 14 x 3 is 14 three times, or 14 + 14 + 14 (= 34 )
When the second factor is a fraction, it means the first factor is replicated ​less than one time.
→ 4 x 13 is 4 one-third of a time. You would find 13 of 4 by cutting 4 into three pieces and focusing on
one of them. 4 x 13 = 14 x 13 = 43 = 1 13
→ 14 x 23 is 14 two-thirds of a time. You would look at 23 of 14 by taking 14 , cutting it into thirds and
focusing on 2 of them. 14 x 23 = 122 = 16
***You ​CANNOT​ multiply Mixed Numbers -- they MUST be changed into FG1s**
How we do it:
1. You DO NOT need common denominators!
2. Convert to FG1s if necessary.
3. Multiply numerators to find your new numerator.
4. Multiply denominators to find your new denominator.
5. Simplify if necessary!
2
2
5x 33
2 11
5x 3
2 11
22
5x 3 =
2 11
22
5 x 3 = 15
22
7
15 = 1 15
Dividing Fractions:
1. The quick way to divide fractions is to “​keep, switch, flip​.”
2. Once it is a multiplication problem, you can multiply like normal.
***You ​CANNOT​ divide Mixed Numbers -- they MUST be changed into FG1s FIRST**
Practice of all operations:
11
7 15
- 3 15 =
3
2 12
+
3
5
12 16 - 3 45 =
=
8
4 15
11
2 15
x 3 15 =
41
15
x
11
15
÷ 3=
11
15
16
5
÷
=
3
1
=
656
75
11
15
×
1
3
11
= 45
11
​8 30
51
17
2 60
=​2 20
3
2 12
x
56
= ​8 75
1 23 + 1 49 =
27
12
3
5
3
5
x
3
5
11
5
3
5
÷
81
60
=
2 15 ÷
1
6
=
3 x 1 49 =
21
= 1 60
= ​1
4
30
7
20
1
6
=
=
x 45 =
11
15
×
10
= 1 45
5
3
55
= 45
= ​1 29
÷
4
5
1
2 10
9 =​3 9
=
2
15
3
1
x
13
9
=
39
9
= 4 39 =
​4 13
3 ÷ 1 49 =
=
1
6
×
5
4
5
= 24
3
1
÷
13
9
=
3
1
×
9
13
27
= 13
1
= ​2 13