What is the correct equation to calculate the net decimal equivalent (NDE) of a 45% and a 60% discount?

To calculate the **Net Decimal Equivalent (NDE)** of two successive discounts, you multiply the complements of the discounts (in decimal form). The complement of a discount is \( 1 - \text{discount fraction} \).

Here’s how to calculate the NDE for a 45% and 60% discount:

1. Convert each discount into its complement:
   - For 45%: \( 1 - 0.45 = 0.55 \)
   - For 60%: \( 1 - 0.60 = 0.40 \)

2. Multiply the complements together:
   \[
   \text{NDE} = 0.55 \times 0.40 = 0.22
   \]

3. Subtract the NDE from 1 to find the equivalent single discount:
   \[
   \text{Equivalent Discount} = 1 - 0.22 = 0.78 \, \text{or} \, 78\%
   \]

So, the **Net Decimal Equivalent** (NDE) is **0.22**, and the combined discount is **78%**.

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Would you like me to explain this further or apply it to a similar scenario?

Here are 5 questions related to this topic:
1. How does the NDE change if the discounts are smaller, such as 10% and 20%?
2. How do you calculate the final price of an item using the NDE?
3. What happens if you have more than two successive discounts?
4. Can the NDE method be extended to percentages greater than 100% (e.g., markups)?
5. How does the order of applying discounts affect the result?

**Tip:** Always ensure discounts are expressed in decimal form before

Learn how to calculate the Net Decimal Equivalent (NDE) for two successive discounts of 45% and 60%. Understand the step-by-step process, including converting percentages to complements, multiplying decimals, and determining the equivalent discount. Suitable for students in Grades 8-10.

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