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Basic Operations, Fractions, Decimals, and Percentages in Mathematics

This chapter covers fundamental mathematical concepts, including essential operations such as addition, subtraction, multiplication, and division. It introduces key topics such as order of operations (PEMDAS), area, volume, and the application of formulas. The chapter further explores advanced topics like fractions (equivalent, mixed numbers), decimals (conversion and arithmetic), and percentages (conversion among formats). Through various examples and practice problems, students will build a solid foundation in these core areas of mathematics.

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Basic Operations, Fractions, Decimals, and Percentages in Mathematics

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  1. Chapter 1 Basic Concepts

  2. §1.1 – Basic Operations • Addition and Subtraction • Example 3, p. 4 • Multiplication • Different forms (×, dot, parenthesis) • Ohm’s law: E = I × R (voltage = amps × ohms) • Division • Divisor, dividend, quotient, remainder • Different forms (÷, / , fractions) • Ex: 204 ÷ 4 • Ex: 534 / 24

  3. §1.2 – Order of Operations • Exponents • PEMDAS • Examples

  4. §1.3 – Area and Volume • General discussion: Length and Area • Rectangles: L = W × H • Problem 1.3 #12 • General Discussion: Volume • Problems 1.3 #24, 34

  5. §1.4 – Formulas • Handout and discuss formula sheet • Problems 1.4 #6, 12, 24, 32 • Graded Activity #1

  6. §1.6 thru 1.8 – Fractions • Fractions • Equivalent fractions and simplifying • Mixed numbers and converting • Addition and subtraction • Multiplication and division • Problems 1.7 #18, 46, 86 • Problems 1.8 #30, 56, 80

  7. §1.9 – English System • Distance • Inches, feet, yards, miles • Time • Seconds, minutes, hours • Weight • Ounces, pounds • Problems 1.9 #22, 34

  8. §1.10 thru 1.12 – Decimals • Converting fractions to decimals • Arithmetic with decimals • Problems 1.10 #58, 64 • Problems 1.12 #46, 62 • Rounding • Ex: Round 527.8914 to: • Hundreds, tens, ones, tenths, hundredths

  9. §1.13 – Percent • Figure 1.33 (p. 69) • Conversions • Percent to decimal • Decimal to percent • Percent to fraction • Fraction to percent • Problem 1.13 #81 – students do on printout

  10. §1.14 – Part, Base, and Rate • Percentage applications • P = part (percentage) • B = base • R = rate (percent) • Formulas • Examples • Find 90% of 200 • 700 is 43% of what amount • What percent of 12.05 is 7.26 • Graded Activity 2

  11. §1.15 – Powers and Roots • Discuss powers • Calculating • By hand • On calculator • Discuss roots • Calculating • By hand • On calculator

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