**Which One of the Following Statements Expresses a True Proportion?**

Determining the validity of a proportion is crucial in various mathematical applications. Understanding the concept of true proportions empowers us to analyze data effectively and draw accurate conclusions. In this blog post, we will explore which of the following statements represents a true proportion:

**Statement 1:**2/3 = 4/6**Statement 2:**1/2 = 3/4**Statement 3:**5/7 = 10/14

**Grasping the Essence of True Proportions**

Proportions express the equality of two ratios. A true proportion holds when the cross-products of its numerators and denominators are equal. Recognizing true proportions is essential for tasks such as solving equations, scaling measurements, and converting units.

**Identifying the True Proportion**

After careful examination, we find that **Statement 1: 2/3 = 4/6** is a true proportion. The cross-product of its numerators (2 x 4 = 8) is equal to the cross-product of its denominators (3 x 6 = 18). Conversely, Statements 2 and 3 are not true proportions because their cross-products do not equate.

**Summary: True Proportions and Their Significance**

In conclusion, **Statement 1: 2/3 = 4/6** represents a true proportion, demonstrating the equality of two ratios. Understanding true proportions enables us to analyze data with precision and derive meaningful results. By grasping the concept, we enhance our problem-solving abilities and deepen our mathematical comprehension.

## Determining True Proportions

### 1. Statement 1: **a/b = c/d**

If the cross-products are equal, i.e., `ad = bc`

, then the statement expresses a true proportion.

### 2. Statement 2: **a/b = d/c**

This statement is not necessarily true. The cross-products may not be equal.

### 3. Statement 3: **a + b/b = c + d/d**

To determine if this statement is true, simplify both sides:

```
a/b + 1 = c/d + 1
a/b = c/d
```

Therefore, the statement expresses a true proportion.

### 4. Statement 4: **a/b = c/b + d**

This statement is not necessarily true. The expression on the right-hand side can be simplified further, and the cross-products may not be equal.

### 5. Statement 5: **a + b/b = c**

This statement is not necessarily true. The expression on the left-hand side can be simplified further, and the cross-products may not be equal.

### 6. Statement 6: **a/b + c = d/b**

This statement is not necessarily true. The cross-products may not be equal.

### 7. Statement 7: **a/b = b/c + d**

This statement is not necessarily true. The expression on the right-hand side can be simplified further, and the cross-products may not be equal.

### 8. Statement 8: **a + b/b = c + b/d**

This statement is not necessarily true. The expression on the left-hand side can be simplified further, and the cross-products may not be equal.

### 9. Statement 9: **a – b/b = c – d/d**

To determine if this statement is true, simplify both sides:

```
a/b - 1 = c/d - 1
a/b = c/d
```

Therefore, the statement expresses a true proportion.

### 10. Statement 10: **a/b = c – d/b**

This statement is not necessarily true. The expression on the right-hand side can be simplified further, and the cross-products may not be equal.

### Conclusion

To determine if a statement expresses a true proportion, you need to verify whether the cross-products are equal. If they are equal, then the statement is true. Otherwise, it is not necessarily true.

## FAQs

**1. What is the cross-product of two fractions?**

The cross-product of two fractions `a/b`

and `c/d`

is `ad`

.

**2. How do you solve a proportion?**

To solve a proportion, you can use cross-multiplication, i.e., `ad = bc`

.

**3. Which of the following statements expresses a true proportion?**

The following statements express true proportions:

`a/b = c/d`

`a + b/b = c + d/d`

`a - b/b = c - d/d`

**4. How do you determine if a statement is a true proportion without cross-multiplication?**

In some cases, it is possible to determine the truthfulness of a proportion by simplifying both sides of the equation.

**5. What is the difference between a proportion and an equation?**

A proportion expresses the equality of two ratios, while an equation expresses the equality of two expressions.

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