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Questions and Answers
What is the value of $15 - 5$?
What is the value of $15 - 5$?
Which property states that $a - b$ does not equal $b - a$?
Which property states that $a - b$ does not equal $b - a$?
What is the identity element for subtraction?
What is the identity element for subtraction?
In the word problem, 'John has 10 stamps and Tom has 8 stamps. How many more stamps does John have?', what type of subtraction is being used?
In the word problem, 'John has 10 stamps and Tom has 8 stamps. How many more stamps does John have?', what type of subtraction is being used?
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When using compensation subtraction, how would you adjust the problem $87 - 28$?
When using compensation subtraction, how would you adjust the problem $87 - 28$?
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Which of the following represents a breakdown method for $98-36$?
Which of the following represents a breakdown method for $98-36$?
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Which option illustrates the relationship between subtraction and addition?
Which option illustrates the relationship between subtraction and addition?
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What does the Distributive Property allow you to do with subtraction?
What does the Distributive Property allow you to do with subtraction?
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Study Notes
Subtraction
- Subtraction is an arithmetic operation that represents the removal of objects from a collection.
- It is the inverse of addition, as adding the result back to the difference will recover the original value.
- Subtraction is denoted by the minus sign (-)
- Example: 10 - 5 = 5
Number Properties in Subtraction
- Commutative Property: Does not apply. For example 5 - 3 ≠ 3 - 5
- Associative Property: Does not apply. For example (10 - 5) - 2 ≠ 10 - (5 - 2)
- Identity Property: The only identity element in subtraction is subtracting 0 from a number, which results in that same number. For example, 10 - 0 = 10
- Distributive Property: Can be used in some cases; for example, 100 - (30 + 20) = (100 - 30) - 20 or 100 - 50 = 70
Word Problems
- Word problems involving subtraction frequently involve taking away, comparisons, or finding differences.
- Key words often indicate subtraction: minus, less, difference between, fewer than, taken away, left
- Example: Mary has 15 apples and gives 5 to her friend. How many apples does Mary have left? Problem type: Take Away problem, answer is 10 apples. Example: John has 10 stamps and Tom has 8 stamps. How many more stamps does John have? Problem type: Comparison problem. Answer is 2 extra stamps.
Mental Math Techniques
- Compensation Subtraction: Adjust numbers to make subtraction easier by adding or subtracting values from both numbers by the same amount to get a "nice" number. Example: 87 - 28 ≈ (87+2) - (28+2) = 89 - 30 = 59
- Using Compatible Numbers: Use pairs of numbers that are easy to subtract mentally. Example: 65 - 23 ≈ 65-20 -3 = 45-3 = 42
- Break-down Method: Separating a subtraction problem into simpler ones. Example: 98-36 can be separated into 98-30-6=68-6=62
Basic Operations - Relationship
- Subtraction and addition are inverse operations.
- Knowing the basic addition facts greatly helps in accurate subtraction.
- Memorisation of subtraction facts is important to speed up basic calculations. For example: being able to instantly know the difference between quantities can create huge time savings.
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Description
This quiz covers the concept of subtraction, its properties, and its relationship to addition. It also explores how subtraction is applied in word problems and includes various examples to illustrate key principles. Test your understanding of this fundamental arithmetic operation!
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