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7th Grade Pre-algebra Chapter 5 Notes 1
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5.1 Writing Fractions as Decimals
Vocabulary Terminating Decimal: a decimal which ends (non-repeating) Ex Repeating Decimal: a decimal which repeats one or more digits Ex Bar notation: used to indicate a repeating number in a decimal. Ex. Period: the digit that repeats in a repeating decimal Mixed Number: a fraction written as the sum of whole number and a fraction. 2
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Writing a Fraction as a Decimal
Write a a decimal Write as a decimal
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Writing Repeating Decimals
Write as a decimal Write as a decimal
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Writing Mixed Numbers as Decimals
Write as a decimal Write as a decimal
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Comparing Fractions and Decimals
To compare Fractions and Decimals, change the fractions to decimals and compare using <, >, or =
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5.2 Rational Numbers Vocabulary
Rational Numbers: a number that can be written as a fraction. Ex can be written as 7
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Writing Mixed Numbers and Integers as Fractions
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Writing Terminating Decimals as Fractions
0.48 3.375
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Write Repeating Decimals and Fractions
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5.3 Multiplying Rational Numbers
Vocabulary Dimensional Analysis: the process of including units of measurement when you compute. Used to check whether an answer is reasonable. 11
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Multiplying Fractions
To multiply fractions, multiply the numerators and multiply the denominators. Simplify.
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You Try…
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Multiplying Negative Fractions
To multiply negative fractions, attach the negative sign to the numerator of the fractions, then multiply.
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Simplifying BEFORE Multiplying
When multiplying you can cross cancel first
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Multiplying Algebraic Fractions
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5.4 Dividing Rational Numbers
Vocabulary Multiplicative Inverse: Two numbers whose product is one. Reciprocal: Two numbers whose product is one. * To find the multiplicative inverse or reciprocal of a number, write it as a fraction and ‘flip’ the fraction 17
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Find Multiplicative Inverses
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Dividing by a Fractions
To divide by a fraction, multiply by its multiplicative inverse
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You Try…
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Dividing by a Whole Number
To divide by a whole number, first rename the whole number as a fraction, then multiply by the reciprocal.
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Dividing by Mixed Numbers
To divide by a mixed number, rename the mixed numbers as improper fractions, multiply by the multiplicative inverse.
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5.5 Adding and Subtracting Like Fractions
To add fractions with like denominators, add the numerators and write the sum over the denominator. To subtract fractions with like denominators, subtract the numerators and write the difference over the denominator. 23
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Adding and Subtracting Fractions
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Adding and Subtracting Mixed Numbers
To add or subtract mixed numbers with common denominators, first add the whole numbers, then add the fractions. Simplify.
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Adding and Subtracting Algebraic Fractions
Follow the same rules as adding fractions
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5.6 Least Common Multiple (LCM)
Vocabulary Multiple: the multiple of a number is a product of that number and a whole number. Common Multiples: when two or more numbers share the same multiple Least Common Multiple: The smallest non-zero multiple that two or more numbers share Least Common Denominator: the LCM of the denominators of two or more fractions. 27
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Common Multiples List the first 10 multiples of each number, then find any multiples the numbers share Find the common multiples of 4 and 6
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Least Common Multiples
Method 1: List out multiples List the first 10 multiples of each number, then determine which common multiple is the smallest. Find the least common multiples of 4 and 6
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Least Common Multiples
Method 2: Use prime factorization Write the prime factorization of each number, write in exponent form. Find the greatest power of each number between the numbers and circle them. Multiply these circled numbers together to find the LCM. Find the LCM of 108 and 240 180 = ∙ 2 ∙ 3 ∙ 3 ∙ 3 = ∙ 33 240 = ∙ 2 ∙ 2 ∙ 2 ∙ 3 ∙ 5 = ∙ 3 ∙ 5 LCM = 33 ∙ 24 ∙ 5 = 2160
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LCM Find the LCM of 24 and 32 Find the LCM of 45, 30, 35
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LCM of Monomials Find the LCM of 18xy2 and 10y
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Least Common Denominator
Step 1: find the LCM of the denominators Step 2: rewrite the fractions using the LCD Step 3: compare the numerators.
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LCD
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LCD of Algebraic Fractions
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5.7 Adding and Subtracting Unlike Fractions
To add or subtract fractions with unlike denominators, rename the fractions with common denominators, usually the LCD. Then add and simplify. 37
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Adding Unlike Fractions
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Subtracting Unlike Fractions
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Adding and Subtracting Mixed Numbers
To add or subtract mixed numbers, write the mixed numbers as improper fractions, then rename using the LCD, add or subtract, simplify.
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Practice…
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5.8 Measures of Central Tendency
Vocabulary Measures of Central Tendency: using one or more numbers to represent a whole set of data 42
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Finding the Mean Find the Mean of the data set
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Find the Median Find the Median of the data set
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Find the Mode Find the Mode of the data set
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You Try…
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Finding Extreme Values
Extreme Values are numbers in a set that are much greater or much less than the rest of the data. Extreme values can affect the mean of the data and overall the usefulness of the data.
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Extreme values
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Problem Solving
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5.9 Solving Equations with Rational Numbers
Review Solve the following equations: 1. 3x + 4 = 52
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Solving Addition and Subtraction Equations
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5.10 Arithmetic and Geometric Sequences
Vocabulary Sequence: an order list of number Arithmetic sequence: a sequence in which the difference between any two consecutive terms is the same Geometric sequence: a sequence in which the quotient of any two consecutive terms is the same. Term: each number in a sequence Common Difference: the differences in a arithmetic sequence Common Ratio: the quotient in a geometric sequence 56
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You Try… Determine whether each sequence is arithmetic, geometric, or neither. If it is arithmetic or geometric, state the common difference or common ratio and write the next three terms of the sequence. 2, 5, 8, 11, …. 4, 1, ¼, 1/16, …. 25, 22, 19, 16, … 2, 6, 18, 54
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