Box of 2000 paper clips,120 are defective. Express non-defective as a ratio of the defctive in its simplest form

To express the ratio of non-defective to defective paper clips in its simplest form, we need to follow these steps:

1. **Total number of paper clips**: 2000  
2. **Number of defective paper clips**: 120  

First, calculate the number of **non-defective** paper clips:

\[
\text{Non-defective paper clips} = \text{Total paper clips} - \text{Defective paper clips} = 2000 - 120 = 1880
\]

Now, find the **ratio** of non-defective to defective paper clips:

\[
\text{Ratio of non-defective to defective} = \frac{1880}{120}
\]

To simplify this ratio, we need to divide both the numerator and the denominator by their greatest common divisor (GCD). Let's find the GCD of 1880 and 120.

The prime factorization of each number is:
- \(1880 = 2^3 \times 5 \times 47\)
- \(120 = 2^3 \times 3 \times 5\)

The common factors are \(2^3 \times 5 = 40\). Thus, the GCD is 40.

Now, divide both the numerator and the denominator by their GCD (40):

\[
\frac{1880 \div 40}{120 \div 40} = \frac{47}{3}
\]

Therefore, the simplified ratio of non-defective to defective paper clips is **47:3**.

Would you like further details or have any questions?

Here are 5 related questions that expand on this topic:

1. What percentage of the paper clips in the box are non-defective?
2. How would the ratio change if there were 30 more defective paper clips?
3. How do you determine the greatest common divisor (GCD) of two numbers using their prime factors?
4. If the box originally had 2500 paper clips and 150 were defective, what would be the simplified ratio of non-defective to defective?
5. How can you calculate the defective to non-defective ratio instead?

**Tip:** When calculating ratios, always double-check the total number and defective count to ensure accuracy before simplifying.

Learn how to calculate and simplify the ratio of non-defective to defective paper clips in a box of 2000 paper clips, where 120 are defective. Understand the process of finding the greatest common divisor (GCD) and simplifying ratios. Suitable for students in Grades 6-8.

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