Podcast
Questions and Answers
3 x (-5) = ______.
3 x (-5) = ______.
-15
Applying the rules for multiplying integers in word problems is a great way to solidify your understanding of multiplying integers with ______ signs.
Applying the rules for multiplying integers in word problems is a great way to solidify your understanding of multiplying integers with ______ signs.
different
To multiply two positive integers, you can use the following rule: multiply the ______ values and keep the sign positive.
To multiply two positive integers, you can use the following rule: multiply the ______ values and keep the sign positive.
absolute
When multiplying a positive integer with a negative integer, multiply the positive integer's absolute value by the negative integer's absolute value, and then change the sign of the product to ______.
When multiplying a positive integer with a negative integer, multiply the positive integer's absolute value by the negative integer's absolute value, and then change the sign of the product to ______.
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To multiply two negative integers, multiply the ______ values and keep the sign negative.
To multiply two negative integers, multiply the ______ values and keep the sign negative.
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When multiplying integers with different signs, multiply the absolute values and change the sign of the product to ______.
When multiplying integers with different signs, multiply the absolute values and change the sign of the product to ______.
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For example, \( -2 imes 3 = ______ \).
For example, \( -2 imes 3 = ______ \).
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For instance, \( -5 imes -4 = ______ \).
For instance, \( -5 imes -4 = ______ \).
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Study Notes
Multiplying Integers
When it comes to arithmetic, the concept of multiplying integers might seem deceptively simple at first glance, but a closer look reveals some interesting and important rules to remember. Let's delve into these rules and explore how they apply in various situations.
Rules for Multiplying Positive Integers
To multiply two positive integers, you can use the following rule: multiply the absolute values and keep the sign positive. In other words, if you're multiplying 2 and 3, you'd get (2 \times 3 = 6).
Rules for Multiplying Negative Integers
When dealing with negative integers, the rules are a bit more nuanced. To multiply two negative integers, multiply the absolute values and keep the sign negative. For instance, if you're multiplying (-2) and (-3), you'd get ((-2) \times (-3) = 6) (with a negative sign). Conversely, when multiplying a positive integer with a negative integer, multiply the positive integer's absolute value by the negative integer's absolute value, and then change the sign of the product to negative. For example, (-2 \times 3 = -6).
Multiplying Integers with Different Signs
When multiplying integers with different signs, you can use the following rule: multiply the absolute values and change the sign of the product to negative. For instance, (-2 \times 3 = -6). This rule holds true for all possible combinations of signs.
Word Problems Involving Multiplying Integers
While the rules above are essential, a solid understanding of multiplying integers comes from applying them in real-world situations and word problems. Here's a simple example:
A person takes three steps forward and five steps backward. How many steps are taken overall?
To solve this problem, we'll multiply the number of steps taken forward ((3)) and the number of steps taken backward ((-5)): (3 \times (-5) = -15). Since the person took steps in opposite directions, the overall number of steps is negative, meaning they took 15 steps backward.
In summary, multiplying integers is a fundamental arithmetic concept, and understanding the rules for multiplying positive and negative integers is essential. The rules for multiplying integers with different signs can be derived from the rules for positive and negative integers alone. Applying these rules in word problems is a great way to solidify your understanding of multiplying integers.
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Description
Delve into the rules for multiplying integers, including how to handle positive and negative integers and different sign combinations. Learn through examples and word problems, such as determining the direction of steps taken based on positive and negative values. Applying these rules is crucial for mastering arithmetic with integers.
