For each of these terms, give an example and a non-example.
Example
- Multiple of 10
Non-example - Product of 10
- Quotient of 10
Use Vocabulary in Writing
The Correct answer and Explanation is:
Let’s break down each term with examples and non-examples, followed by a detailed explanation.
1. Multiple of 10
- Example: 30
- Non-example: 12
A multiple of 10 means any number that results from multiplying 10 by an integer. For example, 30 is a multiple of 10 because it can be expressed as 10×3=3010 \times 3 = 3010×3=30. On the other hand, 12 is a non-example because there is no whole number that can be multiplied by 10 to result in 12.
2. Product of 10
- Example: 50
- Non-example: 7
The product of 10 refers to the result of multiplying 10 by another number. For example, 50 is the product of 10 and 5, since 10×5=5010 \times 5 = 5010×5=50. Conversely, 7 is not the product of 10 because no multiplication of 10 will result in 7.
3. Quotient of 10
- Example: 2
- Non-example: 15
The quotient of 10 is the result when 10 is divided by another number. For example, the quotient of 10 divided by 5 is 2, since 10÷5=210 \div 5 = 210÷5=2. However, 15 is a non-example because dividing 10 by any number will not yield 15.
Explanation (300 Words)
Understanding these mathematical terms helps to clarify different operations involving the number 10. A multiple of 10 means any number that can be formed by multiplying 10 by an integer. Common multiples of 10 include 20, 30, 40, and so on. These numbers all share the property of being divisible by 10 without leaving a remainder. A non-example, such as 12, does not satisfy this condition since dividing 12 by 10 does not result in a whole number.
In contrast, a product of 10 is a specific result of multiplying 10 by another number. For example, 10×4=4010 \times 4 = 4010×4=40, making 40 a product of 10. Any number that cannot be expressed as 10×10 \times10× some other number is a non-example, like 7.
The quotient of 10 refers to the outcome when 10 is divided by another number. For instance, dividing 10 by 2 results in a quotient of 5. A non-example, like 15, arises when the division of 10 by any number does not result in 15.
These concepts are essential for recognizing mathematical relationships. Knowing whether a number is a multiple, product, or quotient of another number helps in problem-solving, particularly when dealing with factors and divisibility. Multiples and products are often used in multiplication and pattern recognition, while quotients are important in division and fractions.