Which area model correctly represents the expression 2/3(1/4+3/5)
The area model that correctly represents the expression (2/3)(1/4+3/5) is:
```
_______________
| | |
| 1/4 | 3/5 |
| | |
|_______|_______|
| |
| 2/3 |
| |
|_______________|
```
In this model, the rectangle on the left represents 1/4, the rectangle on the right represents 3/5, and the larger rectangle represents 2/3. The area of the larger rectangle is divided into two parts - one part represents 1/4 and the other part represents 3/5.
To correctly represent the expression 2/3(1/4+3/5) using an area model, we can follow these steps:
Step 1: Find the common denominator for 1/4 and 3/5. The common denominator is 20.
Step 2: Convert 1/4 and 3/5 into fractions with a denominator of 20.
1/4 is equal to 5/20 (multiply numerator and denominator by 5).
3/5 is equal to 12/20 (multiply numerator and denominator by 4).
Step 3: Add the fractions: 5/20 + 12/20 = 17/20.
Step 4: Multiply the sum from step 3 by 2/3.
(17/20) * (2/3) = (17 * 2) / (20 * 3) = 34/60.
So the correct area model for the expression 2/3(1/4+3/5) would involve a rectangle divided into 60 equal parts, with 34 of those parts shaded.