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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.
12.45 ÷ 15 232 ÷ 0.75 423.5 ÷ 1.
From Decimals to Fractions and Back:
Strategies: Decimals to Fractions-
- Read the decimal “like a mathematician.” 3.24 = “three and twenty four hundredths”
- Write the fraction that matches! “three and twenty three hundredths” = 3 10024
- Simplify if necessary! 3 10024 ÷ 44 = 3 256
Fractions to Decimals Sometimes works: ● Is it already in base ten?
- Read the fraction like a mathematician.
- Write the decimal that matches!
4 100017 = 4.
Sometimes works: ● Can we make it base ten?
- Create an equivalent fraction with the denominator that matches the decimal places (tenth, hundredth, etc).
- Write the decimal that matches!
6 207 × 55 = 6 10035 = 6.
ALWAYS works: ● Fractions ARE division
- Divide the numerator by the denominator!
- Remember to add a decimal and annex 0’s!
- Go out three decimal spaces.
72 = 2^ ÷ 7= 0.
Practice:
10041 = 1009 =^7 103 =
506 =^5 50025 = 153 =
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 31 , 103 , or 3^26 are all the same amount but just have different names.
How we do it:
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!
F G 1 to Mixed:
Make them G.L.A.D.
G o divide! (numerator ÷denominator) L eave whole number as the whole number A lways make the remainder the numerator D enominator stays the same!
Practice:
2 1811 = 3695 = 12 17 =^12015 =
Adding and Subtracting Fractions:
- MUST HAVE common denominators! Show your work in the problem!
6 53 + 2 41 = 6 53 × 44 + 2 41 × 55 = 6 2012 + 2 205 = 6 2017
- Simply if necessary!
Subtracting Fractions with Regrouping:
- MUST HAVE common denominators! Show your work in the problem!
6 51 + 2 43 = 6 51 × 44 + 2 43 × 55 = 6 204 + 2 2015
- Now you have two options: borrowing or converting them into FG1s. (Examples and practice on the next page!) Borrowing:
- “Cross it out, make it less”
- Think about what “base system” your problem is in! --Add a denominator to your numerator
- Subtract numerators, denominators stay the same. 4. Simplify if necessary!
Converting:
- Make both fractions “ M.A.D ”
- Subtract numerators, denominators stay the same.
- Make your answer “ G.L.A.D ” 4. Simplify if necessary!
Regrouping: Converting:
2 1511 x 3 15 = 2 123 x 53 =^16 x 54 = 3 x 149 =
1511 ÷^ 3 =^2 15 ÷^35 =^16 ÷^45 = 3 ÷ 1^94 =
Results and Reflection:
Study Guide Reflection
Section Score Reflection Need more practice?
Decimal x and ÷
/
yes/no
From Decimals to
Fractions and
Back: /
yes/no
Mixed Numbers
into FG1 and
Back: /
yes/no
Adding and
Subtracting
Fractions /
yes/no
Subtracting
Fractions with
Regrouping /
yes/no
Multiplying
Fractions /
yes/no
Dividing Fractions:
/
yes/no
Name: __________________ Unit 2 Study Guide period: _______
Review of Decimal Multiplication and Division
13.45 x 32
142.5 x 0.
81.4 x 2.
12.45 ÷ 15
232 ÷ 0.
_
423.5 ÷ 1.
From Decimals to Fractions and Back:
Strategies: Decimals to Fractions-
- Read the decimal “like a mathematician.” 3.24 = “three and twenty four hundredths”
- Write the fraction that matches! “three and twenty three hundredths” = 3 10024
- Simplify if necessary! 3 10024 ÷ 44 = 3 256
Fractions to Decimals Sometimes works: ● Is it already in base ten?
- Read the fraction like a mathematician.
- Write the decimal that matches!
4 100017 = 4.
Sometimes works: ● Can we make it base ten?
- Create an equivalent fraction with the denominator that matches the decimal places (tenth, hundredth, etc).
- Write the decimal that matches!
6 207 × 55 = 6 10035 = 6.
ALWAYS works: ● Fractions ARE division
- Divide the numerator by the denominator!
- Remember to add a decimal and annex 0’s!
- Go out three decimal spaces.
72 = 2^ ÷ 7= 0.
Practice:
10041 =^ 0.41 1009 =^ 0.09^7 103 =^ 7.
506 =^ 0.12^5 50025 =^ 5.05 153 =^ 0.
_
_
3610 =^ 0.27^12 71 =^ 12.
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 41 three times, or 14 + 41 + 14 (= 43 )
When the second factor is a fraction, it means the first factor is replicated less than one time. → 4 x 31 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 31 = 14 x^ 31 =^34 =^113 → 14 x 23 is 14 two-thirds of a time. You would look at 23 of 41 by taking 14 , cutting it into thirds and focusing on 2 of them. 41 x 32 = 122 = 61
*You CANNOT multiply Mixed Numbers -- they MUST be changed into FG1s
How we do it:
- You DO NOT need common denominators! 25 x 3^23
- Convert to FG1s if necessary. 25 x^113
- Multiply numerators to find your new numerator. 25 x 113 =^22
- Multiply denominators to find your new denominator. 25 x 113 =^2215
- Simplify if necessary! 2215 = 1 157
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:
2 1511 x 3 15 =
1541 x^165 =^65675 =^87556
2 123 x 53 =
1227 x^53 =^6081 = 1^6021 =^1
7 20
16 x 54 =
3 x 149 =
31 x 139 = 399 = 4 39 =
1511 ÷^ 3 =
1511 ÷^31 =^1511 ×^13 = 4511
2 15 ÷ 35 =
115 ÷ 35 = 1511 × 53 = 4555
16 ÷ 45 =
16 × 54 = 245
3 ÷ 1 94 =
13 ÷^139 =^13 ×^139 = 1327
