Subtracting integers
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The document discusses subtracting integers using number lines, algebra tiles, and the rule for subtracting integers. It provides examples of subtracting integers with each method and asks students to practice subtracting integers using the different approaches. The document also includes a section connecting subtracting integers to concepts of poverty, hunger, and righteousness from the Beatitudes in the Gospel of Matthew.
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- For subtraction, change a negative number to its positive equivalent by changing the sign, then add. This allows subtraction to follow the same rules as addition.
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- For division of integers, the quotient is positive if the signs are the same and negative if the signs are different, with examples like 12 ÷ -4 =
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Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
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1. To subtract integers, add the opposite of the second number instead of subtracting.
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The document defines integers and provides rules for adding and subtracting integers:
- Integers include all positive whole numbers and their opposites, including zero.
- For addition, if signs are the same, add the numbers and keep the sign; if different, subtract the smaller number from the larger and keep the sign of the number with the larger absolute value.
- For subtraction, change a negative number to its positive equivalent by changing the sign, then add. This allows subtraction to follow the same rules as addition.
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This document provides information and examples about integer operations:
- Addition of integers follows the same rules as normal addition, such as 20 + 10 = 30 and -40 + -60 = -100.
- Subtraction of integers is performed similarly to addition, such as -3 - 7 = -10 and 15 - 9 = 6.
- When multiplying integers, the product is positive if the signs are the same and negative if the signs are different, exemplified as -2 × 6 = -12 and 2 × -3 = -6.
- For division of integers, the quotient is positive if the signs are the same and negative if the signs are different, with examples like 12 ÷ -4 =
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This document contains instructions and examples for subtracting numbers without regrouping. It includes step-by-step explanations and examples of subtracting 3-digit and 4-digit numbers, identifying the minuend and subtrahend, and representing numbers using place value (thousands, hundreds, tens, ones). Practice problems are provided for students to subtract various 3-digit and 4-digit numbers.
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The document discusses patterns and sequences in mathematics. It explains that a sequence is the proper term for a pattern of numbers, with each number in the sequence having a term name (first term, second term, etc.). It provides examples of number sequences and instructs readers to look for the relationship between each term to predict the next number in the sequence. Several practice sequences are presented for readers to identify the patterns.
Subtraction of Integers
For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
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At the end of the lesson, the learner will be able to:
divide integers (with non-zero divisor)
interpret quotients of rational numbers by describing real-world contexts
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Algebra Expressions in Word Problems
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The document provides an overview of adding integers and examples worked through step-by-step. It discusses the rules for adding integers with the same sign versus different signs. Specifically, it states that for the same sign you add the numbers and keep the sign, and for different signs you subtract the numbers and keep the sign of the number with the larger absolute value. Examples are provided to demonstrate applying these rules to evaluate integer expressions.
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The document discusses basic rules of algebra. It recaps terms like algebraic expressions and equations from the previous class. It then explains that the rules of addition and subtraction of algebraic terms are similar to numerical addition and subtraction, but the terms must be "like" terms, meaning they have the same variables. Unlike terms, with different variables, cannot be added or subtracted. It provides several examples to illustrate how to combine like terms through addition and subtraction.
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This document provides instruction on the order of operations for solving mathematical expressions. It explains that there are specific rules to follow when solving expressions, known as the order of operations. These rules are: 1) complete all operations within parentheses first, 2) perform all exponents next, 3) multiply and divide from left to right, and 4) add and subtract from left to right. The document provides examples of solving expressions using the proper order of operations and encourages remembering the order using the acronym PEMDAS.
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This document introduces addition and subtraction of integers. It explains that for addition, if the signs are the same you add the numbers and keep the sign, and if the signs are different you subtract the numbers and use the sign of the larger number. For subtraction, you change it to addition by making the subtrahend positive and follow the addition rule. Examples are provided to illustrate adding and subtracting integers using tiles or numbers. A rhyme is also presented to help remember the addition rule.
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The document defines integers and their properties like positive and negative numbers. It introduces rules for adding and subtracting integers, such as adding numbers with the same sign and subtracting numbers with different signs. It also explains how to use a number line to demonstrate adding integers and proves that subtracting a negative number is the same as adding a positive number.
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The document defines integers as numbers on the number line that include whole numbers and their opposites. Positive integers are whole numbers to the right of zero, while negative integers are whole numbers to the left of zero. Zero is neither positive nor negative. The sum of two positives or two negatives is either positive or negative, respectively. The document provides examples and links to interactive games and practice problems for adding, subtracting, and understanding integers on a number line.
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Rational numbers can be used to solve equations that cannot be solved using only natural numbers, whole numbers, or integers. Rational numbers are numbers that can be expressed as fractions p/q where p and q are integers and q is not equal to 0. Rational numbers are closed under addition, subtraction, and multiplication, but not division. They are commutative for addition and multiplication, but not for subtraction or division. Addition is associative for rational numbers, but subtraction is not.
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This document is a chapter from a Greek first year high school mathematics textbook. It covers the topics of positive and negative real numbers, absolute value, opposites, and comparing real numbers. Some key points covered include: defining positive and negative numbers, their placement on the number line; absolute value as the distance from zero; opposites having the same absolute value but different signs; and the absolute value of positive numbers being themselves and negatives being their opposites. Examples are provided to illustrate these concepts along with exercises for students to practice.
CBSE-Class-8-NCERT-Maths-Book-Rational-Numbers-chapter-1.pdf
Rational numbers are numbers that can be written as fractions p/q, where p and q are integers and q ≠ 0. Some key properties of rational numbers are:
1) Rational numbers are closed under addition, subtraction, and multiplication but not division. For any two rational numbers a and b, a + b, a - b, and a × b are rational, but a ÷ b may not be rational if b = 0.
2) Addition and multiplication of rational numbers are commutative but subtraction and division are not.
3) Addition and multiplication of rational numbers are associative but subtraction and division are not.
1059331.pdf
Rational numbers are numbers that can be written as fractions p/q, where p and q are integers and q ≠ 0. Some key properties of rational numbers are:
1) Rational numbers are closed under addition, subtraction, and multiplication but not division. For any two rational numbers a and b, a + b, a - b, and a × b are rational, but a ÷ b may not be rational if b = 0.
2) Addition and multiplication of rational numbers are commutative but subtraction and division are not.
3) Addition and multiplication of rational numbers are associative but subtraction and division are not.
Aditya Class 8th
Rational numbers can be used to solve equations that cannot be solved using only natural numbers, whole numbers, or integers. Rational numbers are numbers that can be expressed as fractions p/q where p and q are integers and q ≠ 0.
Rational numbers are closed under addition, subtraction, and multiplication, but not division. Addition, subtraction and multiplication of rational numbers are commutative, but division is not. Addition of rational numbers is associative, but subtraction is not.
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Subtracting integers
- 2. Observe the following pictures and then match the pictures opposite to each other. Bad Mourn Hungry Rich Good Dirty Poor New born Bow Clean
- 3. Study the following patterns.
- 4. CONCLUSION: The patterns in the mathematical sentences above show that subtracting a number gives the same results as adding its opposite.
- 5. Using the Number Line Express the subtraction problem to addition problem.
- 6. Examples: a. -4-3 b. 4-(-3) c. -8 - (-12)
- 7. -4-3 = -4 + (-3)-
- 9. 4 – (-3) = 4 + 3
- 11. -8 – (-12) = -8 + 12
- 14. Examples: (+5) – (+2) = Remove or take away +2 of the tiles: So,….What’s left? (+1) – (+1) = (-4) – (-3) = (-7) – (-2) =
- 15. (+3) – (-5) = +3 “remove” -5, but you do not have any negatives to remove. Add zero pairs!
- 16. Zero pair (+3) – (-5) = Now you can remove -5 And, your left with…… Now, try: (-4) – (+1) =
- 17. Zero pair (-4) – (+1) = Add a zero pair. Now you can remove +1 And, your left with…… (-8) – (+3) = 4 – (-7) = -6 – (+9) =
- 18. What are the disadvantages of using number line and algebra tiles in subtracting integers?
- 19. Rule in Subtracting Integers In subtracting integer from another integer, add the opposite of the subtrahend to the
- 20. Use the number line to subtract the following integers. Grp. 1–5 -1 – (-6) Grp. 6–10 -2 - 7
- 21. -1 – (-6) = 5
- 22. -2 – 7 = -9
- 23. Subtract by using the algebra tiles. Grp. 1–5 4- (-3) Grp. 6 –10 -5 – (-2)
- 24. Grp. 1–5 4- (-3) = 7 Grp. 6–10 -5 – (-2) = -3
- 25. Subtract. Use the rule for subtracting integers. Grp. 1-4 -11 – 14 Grp. 5-7 18 - 22 Grp. 8-10 41- (-25)
- 26. Let’s Check: Grp. 1-4 -11 – 14 = 4 Grp. 5-7 18 – 22 = -4 Grp. 8-10 41- (-25) = 66
- 27. Let us work in group! Use the number line to subtract the following integers. a. 11 – (-5) b. -6 – (-9)
- 28. Let’s check: a. 11 – (-5) = 15 b. -6 – (-9) = 3
- 29. Subtract by using algebra tiles. c. 5 – (-3) d. (-3) – (-8)
- 30. Let’s check: c. 5 – (-3) = 8 d. (-3) – (-8) = 5
- 31. Subtract. Use the rule for subtracting integers. e. -29 - 45 f. 18 - 24 g. -20 – (-4)
- 32. Let’s check: e. -29 – 45 = -74 f. 18 – 24 = -6 g. -20 – (-4) = -16
- 34. Matthew 5:3-10 “The BeaTiTudes” Blessed are the poor in spirit, for theirs is the kingdomRichheaven. of Poor
- 35. Blessed are they who mourn, for they will be comforted. New born baby Mourn
- 36. Blessed are the meek, for they will inherit the land. Good Bad
- 37. Blessed are they who hunger and thirst for righteousness, for they will be satisfied. Bow Hungry
- 38. Blessed are the merciful, for they will be shown mercy.
- 39. Blessed are the clean of heart, for they will see God. Dirty Clean
- 41. Assignment: Answer page 48-49 of The Next Century Mathematics I (Elementary Algebra) Written Math, A numbers 1-10