Pre-Algebra Unit 1 Rational Numbers - Mr....
Transcript of Pre-Algebra Unit 1 Rational Numbers - Mr....
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Pre-Algebra Unit 1
Rational Numbers
Name: ___________________________ Period: _______
Common Core State Standards CC.8.NS.1 - Understand informally that every number has a decimal expansion; the
rational numbers are those with decimal expansions that terminate in 0’s or eventually repeat. Know that other numbers are called irrational.
CC.8.EE.7 - Solve linear equations in one variable
CC.8.EE.7b - Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Scope and Sequence Day 1 Lesson 1-1 Day 7 Lesson 1-5
Day 2 Lesson 1-2 Day 8 Lesson 1-5
Day 3 Lesson 1-3 Day 9 Lesson 1-6
Day 4 Lesson 1-4 Day 10 Lesson 1-6
Day 5 Lesson 1-4 Day 11 Review
Day 6 Quiz / Tech Lab Day 12 Test
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IXL Modules
SMART Score of 80 is required Due the day of the exam
Lesson 1 8.D.1 Identify rational and irrational numbers
8.D.2 Simplify Fractions
8.D.6 Convert between decimals and fractions or mixed numbers
Lesson 2-3 8.E.1 Reciprocals and multiplicative inverses
8.E.5 Multiply and divide rational numbers
8.E.6 Multiply and divide rational numbers: word problems
8.E.9 Evaluate variable expressions involving rational numbers
Lesson 4 8.E.2 Add and subtract rational numbers
8.E.3 Add and subtract rational numbers: word problems
Lesson 5 8.U.4 Solve one-step linear equations
Lesson 6 8.U.5 Solve two-step linear equations
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Lesson 1-1
Rational Numbers
Warm-Up
Vocabulary
A rational number is any number that can be written as a ____________ , where n and d ared
n
____________ and d 0.=/
The goal of simplifying fractions is to make the numerator and the denominator relatively prime. Relatively prime numbers have no ____________ ____________ other than 1.
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Examples: Simplifying Fractions
Simplify:
8016
- 2918
2718
- 3517
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Decimals that ____________ or ____________ are rational numbers.
Examples: Writing Decimals as Fractions
Write each decimal as a fraction in simplest form.
5.37
0.622
8.75
0.2625
To write a fraction as a decimal, divide the ____________ by the ____________. You can use ____________ division.
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Examples: Writing Fractions as Decimals Write the fraction as a decimal
911
720
915 940
Lesson 1-2
Multiplying Rational Numbers
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Warm-Up
Examples: Multiplying a Fraction and an Integer
Multiply. Write the answer in simplest form.
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-8( )76
2(5 )31
-3( )85
4(9 )52
Caution: A fraction in lowest terms, or simplest form, when the numerator and denominator
have no ____________ ____________.
Examples: Multiplying Fractions
Multiply. Write the answer in simplest form.
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( )81
76
- ( )32
29
( )53
85
- ( )87
74
Examples: Multiplying Decimals
Multiply.
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2(-0.51)
(-0.4)(-3.75)
3.1 (0.28)
(-0.4)(-2.53)
Examples: Application
Joy completes of her painting each day. How much of her painting does she complete in a 7120
day week?
Mark runs mile each day. What is the total distance he runs in a 5-day week?71
Lesson 1-3
Dividing Rational Numbers
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Warm-Up
Vocabulary
A number and its reciprocal have a product of 1. To find the reciprocal of a fraction,
____________ the numerator and the denominator. Remember that an ____________ can be
written as a fraction with a denominator of 1.
*** Flip the second fraction and multiply ***
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Examples: Dividing Fractions
Divide. Write the answer in simplest form.
511 ÷ 2
1
2 283 ÷
715 ÷ 4
3
4 352 ÷
When dividing a decimal by a decimal, multiply both numbers by a ____________ of 10 so you
can divide by a __________ number. To decide which power of 10 to multiply by, look at the
denominator. The number of decimal places is the number of zeros to write after the 1.
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Examples: Dividing Decimals
Find 0.384 0.24÷
Find 0.585 0.25÷
Examples: Evaluating Expressions with Fractions and Decimals
Evaluate the expression for the given value of the variable.
for n = 0.15n5.25
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k for k = 5÷ 54
for b = 0.75b2.55
u for u = 9÷ 74
Examples: Problem Solving Application
A cookie recipe calls for cup of oats. You have cup of oats. How many batches of cookies21
43
can you bake using all of the oats you have?
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A ship will use of its total fuel load for a typical round trip. If there is of a total fuel61
85
load on board now, how many complete trips can be made?
Lesson 1-4
Adding and Subtracting with Unlike Denominators
Warm-Up
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There are two methods that can be used to add and subtract rational numbers with
____________ denominators.
Method 1 - Find a common denominator by ____________ one denominator by the other
denominator.
Method 2 - Find the ____________ ____________ denominator (LCD).
Examples: Adding and Subtracting Fractions with Unlike Denominators
Add using method 1.
+ 81
72
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Subtract using method 2.
1 - 161
85
Add using method 1.
+ 31
85
Add using method 2.
2 +61
43
Examples: Evaluating Expressions with Rational Numbers
Evaluate t - for t = 54
65
Evaluate - h for h = -54 7
12
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Examples: Consumer Application
Two dancers are making necklaces from ribbon for their costumes. They need pieces
measuring 13 inches and 12 inches. How much ribbon will be left over after the pieces are43
87
cut from a 36-inch length?
Fred and Jose are building a treehouse. They need to cut a 6 foot and a 4 foot piece of43 5
12
wood from a 12 foot board. How much of the board will be left?.
Lesson 1-5
Solving Equations with Rational Numbers
Warm-Up
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Examples: Solving Equations with Decimals Solve and Check.
m + 4.6 = 9
8.2p = -32.8
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= 15x1.2
m + 9.1 = 3
5.5b = 75.9
= 90y4.5
Examples: Solving Equations with Fractions
Solve and Check
n + = -72
73
y - =61
32
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x =65
85
n + = -91
95
y - =21
43
x =83 6
19
Examples: Solving Word Problems Using Equations
Mr. Rios wants to prepare a dessert, but only has 2 tablespoons of sugar. If each serving32
has tablespoon, how many servings can he make for the party?32
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Rick’s car holds the amount of gas as his wife’s van. If the car’s gas tank can hold32
231
gallons, how much gas can the tank in the minivan hold?
Lesson 1-6
Solving Two-Step Equations
Warm-Up
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Sometimes more than one ____________ operation is needed to solve an equation. Before
solving, ask yourself, “What is being done to the ____________, and in what order?” Then
work backward to ____________ the operations.
Examples: Problem Solving Application
The mechanic’s bill to repair Mr. Wong’s car was $650. The mechanic charges $45 per hour for labor, and the parts that were used cost $443. How many hours did the mechanic work on the car?
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The mechanic’s bill to repair your car was $850. The mechanic charges $35 per hour for labor, and the parts that were used cost $275. How many hours did the mechanic work on your car?
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Examples: Solving Two-Step Equations
Solve and Check
+ 7 = 223n
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= 93y−4
+ 8 = 184n
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= 72y−7