Verified Answer :
- Problem 1: The fraction of the pie Johnny ate is \(\frac{3}{6} = \boxed{\frac{1}{2}}\).
- Problem 2: The total fraction of the sweets eaten is \(\frac{1}{5} + \frac{3}{5} = \boxed{\frac{4}{5}}\).
- Problem 3: The fraction of the relay Thabiso ran is \(1 - (\frac{2}{8} + \frac{1}{8} + \frac{3}{8}) = \boxed{\frac{1}{4}}\).
Explanation
- Solving Problem 1: Johnny's Pie Consumption
To solve the first problem, we are given that there are 6 total slices of pie, and Johnny ate 3 of them. The fraction of the pie that Johnny ate is represented by the ratio of the slices eaten to the total number of slices. Therefore, the fraction is \(\frac{3}{6}\). We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3. Thus, \(\frac{3 \div 3}{6 \div 3} = \frac{1}{2}\). Johnny ate \(\frac{1}{2}\) of the pie.
- Solving Problem 2: Thando and Her Brother's Sweets Consumption
For the second problem, Thando ate \(\frac{1}{5}\) of a packet of sweets, and her brother ate \(\frac{3}{5}\) of the same packet. To find the total fraction of the packet they ate together, we add these two fractions: \(\frac{1}{5} + \frac{3}{5} = \frac{1+3}{5} = \frac{4}{5}\). So, they ate \(\frac{4}{5}\) of the packet of sweets in total.
- Solving Problem 3: The Relay Race Distance
In the third problem, a relay race is completed by four people, and the total distance represents 1 whole. Aanu ran \(\frac{2}{8}\) of the distance, Rowland ran \(\frac{1}{8}\), and Nala ran \(\frac{3}{8}\). To find the fraction Thabiso ran, we first calculate the sum of the portions covered by the other three: \(\frac{2}{8} + \frac{1}{8} + \frac{3}{8} = \frac{2+1+3}{8} = \frac{6}{8}\). Simplifying \(\frac{6}{8}\) by dividing by 2, we get \(\frac{3}{4}\). Since the total relay is represented by 1, Thabiso's portion is \(1 - \frac{3}{4} = \frac{4}{4} - \frac{3}{4} = \frac{1}{4}\). Therefore, Thabiso ran \(\frac{1}{4}\) of the relay.
Examples
Fractions are used in everyday life to divide resources fairly. For instance, when sharing a pizza among friends, if a pizza is cut into 8 equal slices and you eat 2, you have consumed \(\frac{2}{8} = \frac{1}{4}\) of the pizza. Similarly, when working on a project with colleagues, dividing tasks into portions like \(\frac{1}{3}\) or \(\frac{1}{4}\) helps manage the workload efficiently, ensuring that everyone knows their contribution relative to the whole project. Understanding how to add and subtract these parts allows us to track progress and plan effectively.