We have 105males and 100 females write it as a ratio and show the steps of writing it in the lowest terms

To express the given number of males (105) and females (100) as a ratio and reduce it to its lowest terms, follow these steps:

### Step 1: Write the ratio
The ratio of males to females is written as:

\[
\text{Ratio of males to females} = 105 : 100
\]

### Step 2: Find the greatest common divisor (GCD)
To simplify this ratio, we need to find the greatest common divisor (GCD) of 105 and 100. The GCD is the largest number that divides both 105 and 100 evenly.

- **Prime factors of 105**:  
  105 = \( 3 \times 5 \times 7 \)

- **Prime factors of 100**:  
  100 = \( 2^2 \times 5^2 \)

The only common factor between 105 and 100 is **5**.

Thus, the GCD of 105 and 100 is **5**.

### Step 3: Divide both numbers by the GCD
Now, divide both numbers in the ratio by the GCD (which is 5):

\[
\frac{105}{5} : \frac{100}{5} = 21 : 20
\]

### Step 4: Write the simplified ratio
The simplified ratio of males to females is:

\[
21 : 20
\]

### Final Answer:
The ratio of 105 males to 100 females, in its lowest terms, is **21:20**.

---

Do you want more details or have any questions?

Here are 5 related questions to consider:
1. How do you find the GCD of two numbers using the Euclidean algorithm?
2. What if the ratio were given as 210 males and 200 females? What would the simplified ratio be?
3. How can you express a ratio as a fraction and simplify it?
4. What are some real-life examples of ratios in everyday situations?
5. How do you simplify ratios with more than two numbers, such as 105 males, 100 females, and 50 children?

**Tip:** Always check for common factors in both numbers when simplifying ratios to their lowest terms.

We have 105 males and 100 females. Write it as a ratio and show the steps of writing it in the lowest terms.

Learn how to simplify the ratio of 105 males to 100 females. This problem explains prime factorization and finding the greatest common divisor (GCD) to reduce the ratio to its lowest terms. Ideal for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation