Section 2.3 2.4 mult div rational (algebra)
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Rational numbers include fractions, integers, whole numbers, and numbers that can be written as fractions. To multiply fractions, multiply the numerators and denominators. To divide fractions, change the division to multiplication and take the reciprocal of the second fraction. Examples are provided for multiplying and dividing fractions and mixed numbers.
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The document provides examples of solving two-step algebraic equations using multiplication, division, addition and subtraction. It includes 16 examples of equations with steps shown to solve for the variable. The examples cover a variety of equation types including multiplication with subtraction/addition, division with addition, the distributive property, and combining like terms.Section 3.8 solving equations and formulas (alg)
Section 3.8 solving equations and formulas (alg)Algebra / Mathematics
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The document provides instructions for solving equations and formulas by working backwards. It lists 5 examples of equations and identifies the variable to solve for in each case. For each equation, it notes to look at the equation as having two terms and reads out the terms starting with the second term and working to the first term. This provides the steps for isolating the variable of interest when solving each type of equation.Section 3.7 percent of change (Algebra)
Section 3.7 percent of change (Algebra)Algebra / Mathematics
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The document provides examples of calculating percentages of quantities and finding the percent of change between two amounts. It explains how to calculate percentages by multiplying the original amount by the decimal equivalent of the percentage. It also shows how to calculate the percent of change by taking the difference between the new and original amounts and dividing it by the original amount. Common mistakes in the calculations are identified and corrected with the right approach.Section 3.6 ratios and proportions (Algebra)
Section 3.6 ratios and proportions (Algebra)Algebra / Mathematics
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This document outlines ratios, proportions, and how to solve ratio and proportion problems. It discusses:
- What a ratio is and how ratios are expressed and simplified by reducing to lowest terms.
- Properties of proportions including the cross product property (ad = bc) and reciprocal property.
- Examples of setting up and solving proportions for an unknown variable using the cross product property.
- An example problem walking through setting up and solving a multi-step ratio and proportion word problem about how many gallons of gas Mr. Yu uses in a week for his commute to school.Section 3.5 solv eqnvarbothside (algebra)
Section 3.5 solv eqnvarbothside (algebra)Algebra / Mathematics
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The document provides examples for solving equations with variables on both sides, including the steps to isolate the variable. It includes 7 examples of solving different types of equations, with the key steps being combining like terms, adding/subtracting the same quantity to both sides, and then isolating the variable. It concludes with two challenge problems asking for the value of x given specific equations.Chapter 1 review (algebra) (UPDATED for A.C.)
Chapter 1 review (algebra) (UPDATED for A.C.)Algebra / Mathematics
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The Algebra I Chapter 1 test will cover sections 1.1 through 1.6 and 1.8, including topics like solving equations, properties of equality, perimeter, the distributive property, ordered pairs, exponents, evaluation of expressions, and more. Several example problems are provided testing concepts like finding solutions to inequalities, identifying properties, simplifying expressions, interpreting graphs, and writing expressions in words.Section 3.4 solving multi step equations (algebra)
Section 3.4 solving multi step equations (algebra)Algebra / Mathematics
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Johnny took some rope on a camping trip. He used 32 feet to tie his canoe, then gave 1/3 of the remaining rope to others. He later used half the rope left to secure his tent. On the last day, he used 7 feet as a fish stringer. After the trip he had 9 feet left. The question is: how much rope did he have to begin with?Section 2.8 3.1 powers and exponents - squ root (math)
Section 2.8 3.1 powers and exponents - squ root (math)Algebra / Mathematics
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The document outlines lessons and sections covering rational numbers, exponents, square roots, and ratios and rates. It includes topics such as comparing fractions and square roots, powers and exponents, the real number system, and properties of exponents including the product of powers rule and power of a product rule. Examples are provided to demonstrate evaluating expressions with exponents and finding square roots.Section 4.1 ratios and rate (math)
Section 4.1 ratios and rate (math)Algebra / Mathematics
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This document discusses ratios, rates, and unit rates. It provides examples of ratios comparing two quantities like boys to girls in a class. Rates compare quantities with different units, like miles per hour. Unit rates express a rate with the second quantity being 1. The document gives examples of unit rates and discusses using unit rates to compare costs per item, like the cost of one lime. It includes practice problems for ratios, rates, and unit rates.Section 3.3 the real number system (math)
Section 3.3 the real number system (math)Algebra / Mathematics
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This document discusses the real number system and square roots. It defines square roots as the number that when multiplied by itself equals the original number. Only perfect squares have whole number square roots. Most numbers are not perfect squares and have irrational square root values that are decimals that do not terminate or repeat. The document provides examples of finding square roots of numbers and identifying which two consecutive whole numbers a given square root falls between.Section 2.7 square roots (algebra)
Section 2.7 square roots (algebra)Algebra / Mathematics
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The document discusses square roots and real numbers. It defines square roots as the number that when multiplied by itself equals the original number. Numbers with whole number square roots are called perfect squares. Most numbers are not perfect squares and have irrational square root values that are non-terminating decimals. The combination of rational and irrational numbers make up the set of real numbers. The document provides examples of finding square roots with and without a calculator and identifying the whole number a square root lies between.Section 2.1 rational numbers (algebra)
Section 2.1 rational numbers (algebra)Algebra / Mathematics
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The document discusses rational numbers and their representation on a number line. It defines rational numbers as numbers that can be expressed as a/b, where a and b are integers and b 0. It also discusses integers, absolute value, and evaluating expressions involving absolute value.Chapter 1 test corrections (algebra)
Chapter 1 test corrections (algebra)Algebra / Mathematics
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This document contains corrections to problems on a chapter 1 test. It provides the work and solutions to problems involving fractions, solving equations, simplifying algebraic expressions, identifying counterexamples, and writing verbal expressions algebraically and vice versa.Section 1.8 solving add sub equations (math)
Section 1.8 solving add sub equations (math)Algebra / Mathematics
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This document provides instructions for solving addition and subtraction equations. It explains that an equation contains an equal sign and variables can be used to represent unknown numbers. To solve equations, the opposite operation of what is shown must be applied to both sides so they remain balanced, just as items on both sides of a scale must be equal. Examples are provided of solving equations by identifying the operation, applying the opposite to both sides, solving for the variable, and checking the solution.Section 1.7 writing expressions and equations (math)
Section 1.7 writing expressions and equations (math)Algebra / Mathematics
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The document provides information about expressions and equations, including definitions of key terms like sum, difference, product, and quotient. It explains that expressions do not contain equals signs, while equations do. It outlines that students will practice writing verbal expressions and equations from algebraic forms, and vice versa. It emphasizes using words like "more than", "less than", and "product of" rather than symbols like plus, minus, and equals.Ad
Section 2.3 2.4 mult div rational (algebra)
- 1. Section 2.3 2.4 Multiplying and Dividing Rational Numbers
- 2. The term Rational Numbers refers to any number that can be written as a fraction. This includes fractions that are reduced, fractions that can be reduced, mixed numbers, improper fractions, and even integers and whole numbers. An integer, like 4, can be written as a fraction by putting the number 1 under it. Rational Numbers
- 3. When multiplying fractions, they do NOT need to have a common denominator. To multiply two (or more) fractions, multiply across, numerator by numerator and denominator by denominator. If the answer can be simplified, then simplify it. Example: Example: Multiplying Fractions
- 4. When multiplying fractions, we can simplify the fractions and also simplify diagonally. This isnt necessary, but it can make the numbers smaller and keep you from simplifying at the end. From the last slide: An alternative: Simplifying Diagonally You do not have to simplify diagonally, it is just an option. If you are more comfortable, multiply across and simplify at the end. 1 1
- 5. To multiply mixed numbers, convert them to improper fractions first. Mixed Numbers 1 1
- 6. Remember, when multiplying signed numbers... Sign Rules Positive * Positive = Negative * Negative = Positive * Negative = Positive. Positive. Negative.
- 7. Multiply the following fractions and mixed numbers: Try These: Multiply
- 9. Solutions (alternative): Multiply Note: Problems 1, 2 and 4 could have been simplified before multiplying. 1 2 2 1 1 2 1 3 1 3
- 10. When dividing fractions, they do NOT need to have a common denominator. To divide two fractions, change the operation to multiply and take the reciprocal of the second fraction (flip the second fraction). Keep-Change-Change. Dividing Fractions Change Operation. Flip 2nd Fraction.
- 11. Finish the problem by following the rules for multiplying fractions. Dividing Fractions
- 12. Divide the following fractions & mixed numbers: Try These: Divide
- 14. 2-1: Rational Numbers on the Number Line (including absolute value)油 2-7: Square Roots and Real Numbers (different types of numbers) 2-2: Adding and Subtracting Rational Numbers 2-3 & 4: Multiplying and Dividing Rational Numbers Chapter 2 Test