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This document introduces the next chapter on integers in a math workbook. It explains that the chapter will provide an in-depth understanding of integers, including the different types of integers, how they are used in math, and their real-world applications. It notes that integers are a fundamental part of high school math and that the reader has mastered the foundational whole number operations to now move on to applying those same operations with integers.
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1) When adding integers with the same sign, add their absolute values and use the same sign for the result.
2) When adding integers with opposite signs, take the absolute values, subtract the smaller from the larger, and use the sign of the integer with the larger absolute value for the result.
3) The sum of any integer and its opposite integer is always zero.
032 lesson 20
The document defines integers as natural numbers including zero and their negatives. It explains that positive integers are whole numbers greater than zero, while negative integers are the opposites of positive integers. The number line is used to demonstrate that integers increase from left to right and how the absolute value of a number is always positive or zero.
030 unit ii
This unit overview discusses fundamental integer operations, including the four basic arithmetic operations (addition, subtraction, multiplication, division) and order of operations. The objectives are for students to discuss integers, perform the four operations on integers, appreciate integers, gain knowledge about integers to prepare for algebra, and discuss order of operations. This unit contains lessons to skillfully perform integer operations and critically think through exercises to solve.
029 lesson 19
The ski resort sold a total of 111,359 day ski tickets in January. To calculate the average number of tickets sold per day, the total number of tickets was divided by 31, the number of days in January. The average number of tickets sold per day was 3,589.
028 lesson 18
The document provides instructions on dividing whole numbers using the method of cancelling insignificant zeros. It defines cancelling insignificant zeros as removing the same number of trailing zeros from both the dividend and divisor when performing long division. The document includes examples of cancelling zeros when dividing numbers such as 300/100, 2500/100, and 38175/638175. It then provides a 20 question worksheet for students to practice dividing numbers using this method.
027 lesson 17
The document discusses different methods for dividing whole numbers, including division with remainders where the answer is not a whole number. It provides examples and steps to show how to calculate division problems and expresses the answer as a quotient with a remainder. Mental division strategies are also described, emphasizing knowing multiplication tables and the order of operations.
026 lesson 16
This document defines division and its key components. It discusses division as the inverse of multiplication, with division being described as repeated subtraction and multiplication as repeated addition. Examples are provided to illustrate division with a dividend, divisor, and quotient. Special cases of division by 1 and 0 are also explained. Division by 0 is said to be impossible.
025 chapter iv
Division is one of the fundamental mathematical operations that is explained in this chapter. It will cover the different parts of division and how it can be used to solve word problems. Mastering division is an important part of learning mathematics.
024 lesson 15
The document provides examples of word problems involving multiplication to calculate quantities over time or between groups. It gives step-by-step work for problems such as calculating the number of screws a machine can produce in an hour given its 1-minute rate, or the number of radios a store has if it bought a certain number of crates each containing a set quantity. The document includes practice problems for students to solve using multiplication, such as calculating total seats in a stadium based on the number of sections and rows.
022 lesson 13
This lesson introduces the "99 multiplier" shortcut for multiplying whole numbers mentally. It works by annexing zeros to the multiplicand equal to the number of 9s in the multiplier, then subtracting the original multiplicand. Examples show 999×364 equals 364,000 minus 364, which is 369,636. The lesson aims to help students appreciate exploring multiplication and the multiplication operation.
023 lesson 14
This lesson teaches students about multiplying numbers with factors that are powers of ten. It explains that when multiplying numbers where one factor is a power of ten, such as 10, 100, 1000, students should multiply the non-zero digits and add the appropriate number of zeros to the product based on the power of ten. Some examples are provided. It also notes that when both factors end in zeros, students should multiply the significant digits and use the total number of zeros in both factors for the product. A worksheet with practice problems is included for students.
021 lesson 12
Lesson 12 aims to teach students how to multiply whole numbers quickly and correctly. It introduces multiplication as a shortcut for repeated addition and shows students how to use a multiplication table to solve problems efficiently. Students are given examples and a worksheet to practice their multiplication skills. The objectives are for students to multiply whole numbers easily, develop speed in multiplication, and perform multiplication accurately.
021 lesson 11
The document discusses various properties of multiplication, including:
1) The identity property where multiplying any number by 1 leaves the number unchanged.
2) The zero property where multiplying any number by 0 equals 0.
3) The commutative property where changing the order of factors does not change the product.
It provides examples to illustrate each property and a worksheet for students to practice applying the properties.
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031 chapter v
- 1. -914400-914400<br />IntroductionYou have finished Unit 1 of this modular workbook. You now already reviewed what you have taken in your Elementary level .Now, you are ready to proceed to the next chapter of this modular workbook, the INTEGERS. This chapter will give you a deep understanding about integers, the different kinds of integers, the uses of integers in Mathematics and the functions of integers in our real world. In studying high school math, integers are always present. It seems that you have already mastered the fundamental operations in whole numbers you may now proceed to the next chapter which is the application of the four fundamental operations that you have mastered.<br />