CSSS Identify Structure Explain how to use the Multiplication Property of Equality o solve $$ \frac{2}{5} y=6 $$. Then explain how to solve the equation using the Division Property Equality.

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To solve the equation $$ \frac{2}{5} y = 6 $$ using the Multiplication Property of Equality and the Division Property of Equality, we will follow these steps:

### Step 1: Multiplication Property of Equality

The Multiplication Property of Equality states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal.

1. **Identify the equation**: 
   $$
   \frac{2}{5} y = 6
   $$

2. **Multiply both sides by the reciprocal of $$ \frac{2}{5} $$**, which is $$ \frac{5}{2} $$:
   $$
   \frac{5}{2} \cdot \frac{2}{5} y = \frac{5}{2} \cdot 6
   $$

3. **Simplify the left side**:
   $$
   y = \frac{5}{2} \cdot 6
   $$

4. **Calculate $$ \frac{5}{2} \cdot 6 $$**:
   $$
   y = \frac{5 \cdot 6}{2} = \frac{30}{2} = 15
   $$

So, using the Multiplication Property of Equality, we find that:
$$
y = 15
$$

### Step 2: Division Property of Equality

The Division Property of Equality states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal.

1. **Start with the original equation**:
   $$
   \frac{2}{5} y = 6
   $$

2. **Divide both sides by $$ \frac{2}{5} $$**:
   $$
   y = 6 \div \frac{2}{5}
   $$

3. **Dividing by a fraction is the same as multiplying by its reciprocal**:
   $$
   y = 6 \cdot \frac{5}{2}
   $$

4. **Calculate $$ 6 \cdot \frac{5}{2} $$**:
   $$
   y = \frac{6 \cdot 5}{2} = \frac{30}{2} = 15
   $$

So, using the Division Property of Equality, we also find that:
$$
y = 15
$$

### Conclusion

In both methods, we arrive at the same solution: $$ y = 15 $$. The Multiplication Property of Equality allows us to eliminate the fraction by multiplying, while the Division Property of Equality allows us to isolate $$ y $$ by dividing by the fraction. Both properties are fundamental in solving equations effectively.
To solve $$ \frac{2}{5} y = 6 $$: 1. **Multiplication Property of Equality**: - Multiply both sides by $$ \frac{5}{2} $$: $$ y = 15 $$ 2. **Division Property of Equality**: - Divide both sides by $$ \frac{2}{5} $$: $$ y = 15 $$ Both methods give $$ y = 15 $$.

CSSS Identify Structure Explain how to use the Multiplication Property of Equality o solve \( \frac{2}{5} y=6 \). Then explain how to solve the equation using the Division Property Equality.

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