Operations with Integers - Flash Cards
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What are integers?
Integers are whole numbers that can be positive, negative, or zero. Examples include -3, -2, -1, 0, 1, 2, 3.
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How do you add two integers?
To add two integers, simply combine their values. For example, \(5 + (-2) = 3\).
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How do you subtract integers?
Subtracting an integer is the same as adding its additive inverse. For example, \(5 - 3 = 5 + (-3) = 2\).
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What is the additive inverse of an integer?
The additive inverse of an integer \(a\) is \(-a\). For example, the additive inverse of 7 is -7.
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What does a number line represent?
A number line is a visual representation of integers in order. Positive integers are to the right of 0, and negative integers are to the left.
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Calculate: \(4 + (-5)\)
The result is \(4 + (-5) = -1\). You move 4 units right and then 5 units left.
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Calculate: \(7 - 12\)
The result is \(7 - 12 = 7 + (-12) = -5\).
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What is the total of two numbers if their difference is 11?
If their sum is \(S\) and difference is \(D\), the two numbers are: \(x + y = S\) and \(x - y = D\). Solve for \(x\) and \(y\).
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What is the formula for the final position after two strikes?
If the first strike moves the coin 'a' units and the second 'b' units, the final position \(P = a + b\).
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How are movements modeled on a number line?
Rightward movements are positive, while leftward movements are negative.
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What's a common mistake when adding integers?
Neglecting the signs of the integers. Always remember to consider whether the integers are positive or negative.
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What happens when you subtract a negative integer?
Subtracting a negative integer is the same as adding its positive. For example, \(5 - (-3) = 5 + 3 = 8\).
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If the first movement is -4 and final is 5, what is the second movement?
Use the formula \(P = a + b\). Hence, \(5 = -4 + b\) implies \(b = 9\).
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How can you practice integers with a partner?
One person thinks of two integers, gives their sum and difference, and the other finds the integers. It's a fun way to review.
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How are tokens used to represent integers?
Use one type of token for positive integers and another for negative integers to visualize addition and subtraction.
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How do sum and difference differ?
Sum combines values, while difference finds how far apart the values are. For example, \(x + y\) vs. \(x - y\).
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What are the two integers if their sum is 25 and difference is 11?
The numbers are 18 and 7. \(18 + 7 = 25\) and \(18 - 7 = 11\).
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What role does zero play in integers?
Zero is an integer that acts as a neutral element in addition: \(a + 0 = a\).
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