2.2 Answer The Following Increasing And Decreasing Ratios:a) Increase $11.47 , \text Kg}$ In The Ratio Of $11 7$. { \square$ $b) Decrease R2 980 In The Ratio Of $5:6$. { \square$}$
Understanding Increasing and Decreasing Ratios in Mathematics
What are Increasing and Decreasing Ratios?
In mathematics, ratios are used to compare the size of two or more quantities. An increasing ratio is a comparison of two quantities where the second quantity is larger than the first. On the other hand, a decreasing ratio is a comparison of two quantities where the second quantity is smaller than the first. In this article, we will explore how to increase and decrease given quantities in a specific ratio.
Increasing a Quantity in a Given Ratio
To increase a quantity in a given ratio, we need to multiply the original quantity by the ratio of the increase. The ratio of the increase is calculated by dividing the increase by the original quantity. Let's consider the first problem:
a) Increase 11.47 kg in the ratio of 11:7
To increase 11.47 kg in the ratio of 11:7, we need to calculate the ratio of the increase. The ratio of the increase is 11/7.
# Define the original quantity and the ratio of the increase
original_quantity = 11.47
ratio_increase = 11/7
increase = original_quantity * ratio_increase
Now, we can calculate the increase by multiplying the original quantity by the ratio of the increase.
# Calculate the increase
increase = original_quantity * ratio_increase
print(increase)
The increase is 19.29 kg. Therefore, the new quantity is 11.47 kg + 19.29 kg = 30.76 kg.
b) Decrease R2 980 in the ratio of 5:6
To decrease R2 980 in the ratio of 5:6, we need to calculate the ratio of the decrease. The ratio of the decrease is 5/6.
# Define the original quantity and the ratio of the decrease
original_quantity = 980
ratio_decrease = 5/6
decrease = original_quantity * ratio_decrease
Now, we can calculate the decrease by multiplying the original quantity by the ratio of the decrease.
# Calculate the decrease
decrease = original_quantity * ratio_decrease
print(decrease)
The decrease is 816.67. Therefore, the new quantity is R2 980 - R2 816.67 = R2 163.33.
Conclusion
In this article, we have explored how to increase and decrease given quantities in a specific ratio. We have used the concept of ratios to calculate the increase and decrease of the quantities. The ratio of the increase is calculated by dividing the increase by the original quantity, and the ratio of the decrease is calculated by dividing the decrease by the original quantity. We have used Python code to calculate the increase and decrease of the quantities.
Frequently Asked Questions (FAQs) on Increasing and Decreasing Ratios
Q: What is a ratio in mathematics?
A: A ratio is a comparison of two or more quantities. It is a way of expressing the relationship between two or more numbers.
Q: What is an increasing ratio?
A: An increasing ratio is a comparison of two quantities where the second quantity is larger than the first.
Q: What is a decreasing ratio?
A: A decreasing ratio is a comparison of two quantities where the second quantity is smaller than the first.
Q: How do I increase a quantity in a given ratio?
A: To increase a quantity in a given ratio, you need to multiply the original quantity by the ratio of the increase. The ratio of the increase is calculated by dividing the increase by the original quantity.
Q: How do I decrease a quantity in a given ratio?
A: To decrease a quantity in a given ratio, you need to multiply the original quantity by the ratio of the decrease. The ratio of the decrease is calculated by dividing the decrease by the original quantity.
Q: What is the formula for increasing a quantity in a given ratio?
A: The formula for increasing a quantity in a given ratio is:
New Quantity = Original Quantity x (Increase / Original Quantity)
Q: What is the formula for decreasing a quantity in a given ratio?
A: The formula for decreasing a quantity in a given ratio is:
New Quantity = Original Quantity x (Decrease / Original Quantity)
Q: Can I use a ratio of more than two numbers?
A: Yes, you can use a ratio of more than two numbers. For example, if you want to increase a quantity in the ratio of 3:4:5, you would multiply the original quantity by the ratio of the increase, which is 3/4.
Q: How do I calculate the increase or decrease of a quantity in a given ratio?
A: To calculate the increase or decrease of a quantity in a given ratio, you need to multiply the original quantity by the ratio of the increase or decrease. You can use a calculator or a computer program to perform the calculation.
Q: Can I use a ratio of fractions?
A: Yes, you can use a ratio of fractions. For example, if you want to increase a quantity in the ratio of 1/2:3/4, you would multiply the original quantity by the ratio of the increase, which is 1/2 divided by 3/4.
Q: How do I simplify a ratio?
A: To simplify a ratio, you need to find the greatest common divisor (GCD) of the two numbers and divide both numbers by the GCD.
Q: Can I use a ratio to compare quantities that are not numbers?
A: No, you cannot use a ratio to compare quantities that are not numbers. Ratios are used to compare quantities that are expressed in numerical terms.
Q: How do I use ratios in real-life situations?
A: Ratios are used in many real-life situations, such as cooking, building, and finance. For example, if you want to make a recipe that serves 4 people, and you want to increase the quantity to serve 6 people, you would use a ratio of 6:4 to calculate the increase.
Q: Can I use a ratio to compare quantities that are expressed in different units?
A: No, you cannot use a ratio to compare quantities that are expressed in different units. You need to convert the quantities to the same unit before you can compare them using a ratio.