A wall of a building is 22 inches wide. Ten inches is concrete, 8 inches is brick, and 4 inches is limestone. What fraction of the wall is brick? (Type a whole number or a simplified fraction. )
The correct answer and explanation is:
The fraction of the wall that is brick is 8/22, which simplifies to 4/11.
Explanation:
To find what fraction of the wall is made of brick, start by understanding the total thickness of the wall and the thickness of the brick portion.
The total thickness of the wall is 22 inches. This is made up of three materials:
- Concrete: 10 inches
- Brick: 8 inches
- Limestone: 4 inches
To find the fraction of the wall that is brick, divide the thickness of the brick by the total thickness of the wall: thickness of bricktotal thickness=822\frac{\text{thickness of brick}}{\text{total thickness}} = \frac{8}{22}
Next, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD of 8 and 22 is 2.
Divide numerator and denominator by 2: 8÷222÷2=411\frac{8 \div 2}{22 \div 2} = \frac{4}{11}
So, the brick makes up 411\frac{4}{11} of the wall.
Additional notes:
Fractions represent parts of a whole. Here, the whole is the entire wall thickness (22 inches), and the part is the brick thickness (8 inches). Simplifying fractions helps express the part-to-whole relationship in the simplest form, which is easier to understand and compare.
In summary, the fraction of the wall that is brick is 411\boxed{\frac{4}{11}}.