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Chapter 5—Comparing + Ordering Fractions and Decimals (5-1) (5-2)
WORD BANK:
multiple
least common multiple
LCM
terminating decimal
repeating decimal
A ______________ of a number is the product of that number and another number.
You can use a Venn diagram to sort the multiples of two numbers.
multiples of 4
multiples of 6
Multiples of 4: 4, 8, 12, 16, 20, 24…
Multiples of 6: 6, 12, 18, 24…
So 12 and 24 are two common multiples of 4 and 6, while 12 is their___________
____________ _________________ (LCM).
You can find the LCM of two numbers by using their prime factorizations, then
multiplying their prime factors to find the multiple.
Example: 12 = 22 * 3 and 40 = 23 * 5
Use the greatest power of each factor: 23 * 3 * 5 = 120
So: The least common multiple of 12 and 40 is 120.
The following problems are copied from Prentice Hall Pre-Algebra:
Practice: (pp 235+236) Find equivalent fractions then order from least to greatest:
30) 2/5, 3/8, 1/3, 2/4
2/ =
5
3/ =
8
1/ =
3
2/ =
4
________________________________________________________________
Answers: 1/3, 3/8, 2/5, 2/4 or 8/24, 9/24, 16/40, 20/40
Chapter 5—Comparing + Ordering Fractions and Decimals (5-1) (5-2)
Fractions can be written as decimals, thus each is represented in base ten. This makes
it possible to compare them.
To convert a fraction to a decimal, just divide the numerator by the denominator. When
you have no remainder, the quotient is called a ___________________
___________________. When you have a number or block of numbers that repeat the
quotient is called a _______________ __________________.
Both of these are rational numbers. For a number to be irrational, it must not repeat or
terminate when converted to a decimal.
Practice: (pp. 240+241) Write each as a decimal:
#1) 7/25
#2) 3/5
#4) 6 ¼
#33) 5 3/8
#37) – 31/100
Write as a decimal then order from least to greatest on the number line:
#12 and 15) - ¼, - 1/8, -0.75, -0.625, 2.1, 22/10, 2.01, 22/11
-¼=
- 1/8 =
22/
10 =
22/
11 =
__________________________________________________________________
Answers: 1) .28; 2) .6; 4) 6.25; 33) 5.375; 37) .31; -1/4 = - 0.25, - 1/8 = - 0.125, 22/10 = 2.2, 22/11= 2 so – 0.125, - 0.25,
0.625, 0.75, 2, 2.01, 2.1, 2.2
Chapter 5—Comparing + Ordering Fractions and Decimals (5-1) (5-2)
Practice: (pp. 240+241) Write each as a mixed number or a fraction in simplest form:
#16) 2.25
#18) 0.08
#19) 7.15
#27) – 0.333
#45) 0.06
.666
Complete each equation or inequality using <, >, or =:
#28) ½ ______ 1.2
#29) 7/8 ______ 0.875
#30) 3/5 _____ 0.25
#31) 1/8 _______ 0.375
*Write your own:
Answers: 16) 2 ¼; 18) 2/25; 19) 7 3/20; 27) – 1/3; 45) – 3/50, 2/3; 28) <; 29) =; 30) >; 31) <
Chapter 5—Operations with Fractions (5-3) (5-4)
WORD BANK:
common denominator
improper fractions
simplify
reciprocals
Before adding or subtracting fractions with unlike denominators, first write equivalent
fractions for each with a ___________ ____________. You can use the least common
multiple to find equivalent fractions, or you can find an equivalent decimal for any
fraction by dividing the numerator by the denominator. Then add or subtract the
numerators.
To multiply or divide mixed numbers, first write them as __________ ___________.
___________ before you multiply. Then ___________ again.
When dividing fractions, you can:
1. Find equivalent fractions and divide the numerators only.
OR
2. Multiply the first number by the ____________ of the second number.
Practice: (p. 246) Compute then simplify:
#10) 12/20 – ¼ =
#16) 3 5/8 + 2 7/12 =
#20) 1 7/8 – 2 ¾ =
#11) - 3/10 – 5/100 =
#18) 5 ¾ - 2 1/8 =
#25) – 4 7/8 + 15 1/10 =
Answers: 10) 7/20; 11) – 7/20; 16) 6 5/24; 18) 3 5/8; 20) – 7/8; 25) 10 9/10
Chapter 5—Operations with Fractions (5-3) (5-4)
Practice: (p 251) Compute then simplify:
#5) (- 7/8)(- 4/5) =
#37) (- 7/12)(- 5/6) =
#14) ½ ÷ 1/3 =
#19) ¾ ÷ ½ =
#39) – ½ ÷ 2/3 =
#34) 4/t • 3t/8 =
#42) 4/9x ÷ 2/3x =
#45) 2/9 ÷ w/3 =
#49) 10 • ¼ =
#50) 10 ÷ ¼ =
Answers: 5) + 7/10; 37) + 7/10; 14) 1 ½; 19) 1 ½; 39) ¾; 34) 1 ½; 42) 2/3; 45) 2/3 w; 49) 2 ½; 50) 40
Chapter 5—Using Customary Units of Measurement (5-5)
WORD BANK:
customary system
conversion factors
dimensional analysis
converting
metric system
In the U.S. most people use the ____________________ _____________ of
measurement. You can use ______________ ______________ to change from one
unit to another in a process called ______________ _______________. ____________
units can help you make comparisons.
Use the chart below to choose an appropriate conversion factor:
Length: 1 foot = 12 inches
Capacity: 1 cup = 8 fluid ounces
3 feet = 1 yard
2 cups = 1 pint
5280 feet = 1 mile
4 cups = 1 quart
1760 yards = 1 mile
4 quarts = 1 gallon
Weight: 1 pound (lb) = 16 ounces (oz)
2,000 pounds = 1 ton
In order to choose the appropriate conversion factor, use the ratio that has the original
unit in its denominator so that it will cancel out.
You can use conversion factors to change from one unit of measure to another in a
process called dimensional analysis.
1. Write the original unit as a fraction over 1.
2. Choose the appropriate conversion factor.
3. Multiply.
Practice: (pp 255-257) Use dimensional analysis to complete each equation:
#5) 3 qt = ______gal
#23) 6 ¼ gal = ____ qt
#25) 3 ½ qt = ______pt
#28) 7 pt = ______c
#62) 13 pt = ______ qt
#65) 18 qt = ______ gal
#68) 20 c = ____ qt
Answers: 5) ¾ gal; 23) 25 qt; 25) 7 pt; 28) 14 cups; 62) 6 ½ qt; 65) 4 ½ gal; 68) 5 qt
Chapter 5—Using Customary Units of Measurement (5-5)
Practice: (pp 255-257) Use dimensional analysis to complete each equation:
#9) 18 in = _______ft
#10) 18 ft = _________in
#18) ½ yd = ___ft
#19) ½ mi = ________ ft
#26) 1 1/3 yd = _______in
#60) 2,640 ft = _________mi
#57) 28 in = ______ ft
#70) 2 ¼ yd = 6 ¾ ________
#24) ¾ lb = ____ oz
#56) A student converted 8 cups to pints. His answer was 16 pints. Use
dimensional analysis to determine whether the student’s answer was correct.
Explain.
Answers: 9) 1 ½ ft; 10) 216 in; 18) 1 ½ ft; 19) 2,640 ft; 26) 48 in; 60) ½ mi; 57) 2 1/3 ft; 70) ft; 24) 12 oz; 56) It should be 4
pints. There are two cups in each pint.
Chapter 5—Solving Equations with Fractions (5-7) (5-8)
You solve equations with fractions of decimals in the same way that you solve
equations with integers by undoing operations and doing the same thing to both
sides of the equation.
Practice: (pp 266+267)
#1) b + 4/5 = 9/10
#9) t – 2/3 = 4/9
#11) ½ = n – 5/8
#15) 5 ¼ = w + 2 ½
#29) g + 8 4/9 = 3 1/6
#42) 1 ¼ - c = 3/8
Answers: 1) b= 1/10; 9) t = 1 1/9; 11) n = 1 1/8; 15) w = 2 ¾; 29) g= – 5 5/18; 42) c = 7/8
Chapter 5—Solving Equations with Fractions (5-7) (5-8)
You solve equations with fractions of decimals in the same way that you solve
equations with integers by undoing operations and doing the same thing to both
sides of the equation.
Practice: (pp 270+272) Solve each equation:
#23) 2 ½ x = 2/5
#25) – 1 6/7 g = - 13/15
#26) 1/15 = - 1 1/10 t
#14) 4t = 24/35
#15) 5/7 y = 1/3
#17) – 8/9 g = 3/5
#18) 9/10 = ¼ w
#19) 1 ½ d = 5/22
Answers: 23) 4/25; 25) + 7/15; 26) – 2/33; 14) 6/35; 15) 7/15; 17) – 27/40; 18) 3 3/5; 19) 5/33
Chapter 5—Powers of Products and Quotients (5-9)
To raise a product to a power, raise each factor to the power.
Example: (5 * 3)4 = 54 * 34
To raise a quotient to a power, raise both the numerator and the denominator to
the power.
Example:
(/)
2
3
4
= 24 / 34
To simplify an expression, eliminate as many parentheses as possible.
Remember: the location of a negative sign affects the value of an expression.
Practice: (pp 276) Simplify each expression:
#3) (rs3)4
#4) (7t2)3
#13) (- 10x3)4
#15) (- 5b)3
#16) – (3x)2
#17) (- 5c3)2
#22) (2/5)2
#26) (4/9)2
#51) (2c/7d)2
#52) (- 3a/b2)3
Answers: 3) r4 s12; 4) 343t6; 13) 10,000 x12; 15) -125b3; 16) – 9x2; 17) 25 c6; 22) 4/25; 26) 16/81; 51) 4c2/ 49d2;
52) – 27a3 / b6