Multiplying A Quantity By Which Of The Following Will Result In A Decrease In That Quantity?1. $\frac{7}{8}$2. 1.053. $\frac{9}{4}$4. 2.89

Multiplying a Quantity by Which of the Following Will Result in a Decrease in That Quantity?

Understanding the Concept of Multiplication and Decrease

Multiplication is a fundamental operation in mathematics that involves the repeated addition of a number. When we multiply a quantity by a number, we are essentially adding that number a certain number of times, equal to the multiplier. However, the outcome of this operation can be either an increase or a decrease in the original quantity, depending on the value of the multiplier. In this article, we will explore the concept of multiplying a quantity by a number and determine which of the given options will result in a decrease in that quantity.

The Role of Multipliers in Multiplication

A multiplier is a number that is used to multiply another number. In the context of this discussion, we are interested in finding a multiplier that will result in a decrease in the original quantity. To understand this concept, let's consider an example. Suppose we have a quantity of 100 units, and we want to multiply it by a number to decrease it. If we multiply 100 by 0.5, we get 50 units, which is a decrease of 50 units from the original quantity.

Analyzing the Options

Now, let's analyze the given options to determine which one will result in a decrease in the original quantity.

Option 1: $\frac{7}{8}$

Multiplying a quantity by $\frac{7}{8}$ will result in a decrease in that quantity. This is because $\frac{7}{8}$ is a fraction less than 1, which means it is a decimal value between 0 and 1. When we multiply a quantity by a decimal value between 0 and 1, we are essentially reducing the quantity.

Option 2: 1.05

Multiplying a quantity by 1.05 will result in an increase in that quantity. This is because 1.05 is a decimal value greater than 1, which means it is a percentage increase. When we multiply a quantity by a decimal value greater than 1, we are essentially increasing the quantity.

Option 3: $\frac{9}{4}$

Multiplying a quantity by $\frac{9}{4}$ will result in an increase in that quantity. This is because $\frac{9}{4}$ is a fraction greater than 1, which means it is a decimal value greater than 1. When we multiply a quantity by a decimal value greater than 1, we are essentially increasing the quantity.

Option 4: 2.89

Multiplying a quantity by 2.89 will result in an increase in that quantity. This is because 2.89 is a decimal value greater than 1, which means it is a percentage increase. When we multiply a quantity by a decimal value greater than 1, we are essentially increasing the quantity.

Conclusion

In conclusion, the only option that will result in a decrease in the original quantity is option 1: $\frac{7}{8}$. This is because $\frac{7}{8}$ is a fraction less than 1, which means it is a decimal value between 0 and 1. When we multiply a quantity by a decimal value between 0 and 1, we are essentially reducing the quantity.

Key Takeaways

• Multiplication is a fundamental operation in mathematics that involves the repeated addition of a number.
• A multiplier is a number that is used to multiply another number.
• Multiplying a quantity by a decimal value between 0 and 1 will result in a decrease in that quantity.
• Multiplying a quantity by a decimal value greater than 1 will result in an increase in that quantity.

Real-World Applications

The concept of multiplying a quantity by a number to decrease it has numerous real-world applications. For example, in finance, a company may want to reduce its expenses by multiplying its current expenses by a certain percentage. In engineering, a designer may want to reduce the size of a component by multiplying its current dimensions by a certain factor. In medicine, a doctor may want to reduce the dosage of a medication by multiplying the current dosage by a certain factor.

Final Thoughts

In conclusion, multiplying a quantity by a number can result in either an increase or a decrease in that quantity, depending on the value of the multiplier. By understanding the concept of multiplication and the role of multipliers, we can make informed decisions in various fields, such as finance, engineering, and medicine.
Multiplying a Quantity by Which of the Following Will Result in a Decrease in That Quantity? - Q&A

Frequently Asked Questions

In the previous article, we discussed the concept of multiplying a quantity by a number and determined which of the given options will result in a decrease in that quantity. In this article, we will answer some frequently asked questions related to this topic.

Q: What is the difference between multiplying a quantity by a number and adding a number to a quantity?

A: Multiplying a quantity by a number involves the repeated addition of that number, whereas adding a number to a quantity involves the simple addition of that number. For example, multiplying 100 by 0.5 is equivalent to adding 50 to 100, but multiplying 100 by 0.5 is a more efficient way to reduce the quantity.

Q: Can you give an example of a real-world application of multiplying a quantity by a number to decrease it?

A: Yes, consider a company that wants to reduce its energy consumption by 20%. If the company's current energy consumption is 100 units, it can multiply this quantity by 0.8 (1 - 0.2) to reduce it to 80 units.

Q: How do you determine whether multiplying a quantity by a number will result in an increase or a decrease?

A: To determine whether multiplying a quantity by a number will result in an increase or a decrease, you need to check the value of the multiplier. If the multiplier is a decimal value between 0 and 1, it will result in a decrease. If the multiplier is a decimal value greater than 1, it will result in an increase.

Q: Can you explain the concept of a multiplier in more detail?

A: A multiplier is a number that is used to multiply another number. In the context of this discussion, we are interested in finding a multiplier that will result in a decrease in the original quantity. A multiplier can be a fraction, a decimal, or a percentage.

Q: How do you handle negative multipliers?

A: When you have a negative multiplier, it will result in an increase in the original quantity. For example, multiplying 100 by -0.5 will result in an increase of 50 units.

Q: Can you give an example of a situation where multiplying a quantity by a number is not the best approach?

A: Yes, consider a situation where you want to reduce a quantity by a certain percentage, but the quantity is already very small. In this case, multiplying the quantity by a decimal value between 0 and 1 may result in a very small decrease, which may not be significant.

Q: How do you choose the best multiplier for a given situation?

A: To choose the best multiplier for a given situation, you need to consider the specific requirements of the situation. You need to determine the desired outcome and choose a multiplier that will achieve that outcome.

Q: Can you explain the concept of percentage increase and decrease?

A: A percentage increase is a multiplier that is greater than 1, whereas a percentage decrease is a multiplier that is between 0 and 1. For example, a 20% increase is equivalent to multiplying a quantity by 1.2, whereas a 20% decrease is equivalent to multiplying a quantity by 0.8.

Q: How do you handle multipliers with decimal places?

A: When you have a multiplier with decimal places, you need to multiply the quantity by the decimal value. For example, multiplying 100 by 0.5 is equivalent to multiplying 100 by 0.5 (which is 0.5 x 100).

Q: Can you give an example of a situation where multiplying a quantity by a number is used in finance?

A: Yes, consider a situation where a company wants to reduce its expenses by 10%. If the company's current expenses are 100 units, it can multiply this quantity by 0.9 (1 - 0.1) to reduce it to 90 units.

Q: How do you handle multipliers with fractions?

A: When you have a multiplier with fractions, you need to multiply the quantity by the fraction. For example, multiplying 100 by 3/4 is equivalent to multiplying 100 by 0.75 (which is 3/4 x 100).

Conclusion

In conclusion, multiplying a quantity by a number can result in either an increase or a decrease in that quantity, depending on the value of the multiplier. By understanding the concept of multiplication and the role of multipliers, we can make informed decisions in various fields, such as finance, engineering, and medicine.