Fractions In Real Life Calculating Gas Usage And Heights

This article dives into two intriguing mathematical problems that involve fractions and their applications in real-world scenarios. We'll explore how to calculate the fraction of a tank of gas used during a journey and how to determine a person's height relative to another, providing step-by-step solutions and insightful explanations. These types of problems are fundamental to understanding proportional reasoning and can be applied in various everyday situations, from cooking and measuring to financial calculations and travel planning. By mastering these concepts, you'll gain a stronger foundation in mathematical problem-solving and enhance your ability to tackle similar challenges with confidence.

Problem 1: Calculating Fuel Consumption

Fraction calculations are crucial in everyday life, particularly when it comes to managing resources. In this problem, Jenny has rac7}{8} of a tank of gas, and she estimates that she will use rac{2}{3} of that amount to get home. The question is What fraction of the entire tank of gas will she actually use? This is a classic problem of multiplying fractions, where we need to find a fraction of another fraction. To solve this, we multiply the two fractions together. Let's break down the process step-by-step. First, we identify the given fractions: rac{78} representing the initial amount of gas in the tank, and rac{2}{3} representing the fraction of that gas Jenny expects to use. Next, we multiply the numerators (the top numbers) together 7 multiplied by 2 equals 14. Then, we multiply the denominators (the bottom numbers) together: 8 multiplied by 3 equals 24. This gives us the fraction rac{14{24}. Now, we need to simplify this fraction to its simplest form. Both 14 and 24 are divisible by 2. Dividing both the numerator and the denominator by 2, we get rac{7}{12}. Therefore, Jenny will use rac{7}{12} of the tank of gas to get home. This problem highlights the importance of understanding fraction multiplication and simplification in practical scenarios, such as estimating fuel consumption for a trip. Being able to perform these calculations accurately helps in making informed decisions about resource management and planning.

Solution:

To find the fraction of the tank of gas Jenny uses, we need to multiply the fraction of the tank she has by the fraction she will use:

${ \frac{7}{8} \times \frac{2}{3} = \frac{7 \times 2}{8 \times 3} = \frac{14}{24} }$

Now, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

${ \frac{14}{24} = \frac{14 \div 2}{24 \div 2} = \frac{7}{12} }$

Answer: Jenny uses rac{7}{12} of the tank of gas.

Problem 2: Comparing Heights Using Fractions

Understanding height comparisons using fractions is another practical application of mathematical concepts. In this problem, Robert's height is given as 168 cm, and his sister Marie is rac5}{8} as tall as him. The objective is to determine Marie's height. This involves finding a fraction of a whole number, which is a common type of problem in proportional reasoning. To solve this, we multiply Robert's height by the fraction representing Marie's height relative to his. We start by identifying the given information Robert's height is 168 cm, and Marie's height is rac{5{8} of Robert's height. The next step is to multiply 168 by rac{5}{8}. This can be done by first multiplying 168 by the numerator, 5, which gives us 840. Then, we divide this result by the denominator, 8. So, we have rac{840}{8}. Performing this division, we get 105. Therefore, Marie is 105 cm tall. This problem demonstrates how fractions can be used to represent and calculate proportions, allowing us to compare quantities and determine relative values. Such skills are essential in various real-life situations, such as scaling recipes, adjusting measurements in construction, or understanding proportions in statistics. By mastering these fractional calculations, we enhance our ability to interpret and solve problems involving comparative quantities.

Solution:

To find Marie's height, we need to multiply Robert's height by the fraction representing Marie's height relative to Robert's:

${ 168 \times \frac{5}{8} = \frac{168 \times 5}{8} = \frac{840}{8} }$

Now, we divide 840 by 8:

${ \frac{840}{8} = 105 }$

Answer: Marie is 105 cm tall.

Through these two problems, we've explored the practical applications of fractions in everyday scenarios. Fractional arithmetic is not just an abstract mathematical concept; it's a powerful tool for solving real-world problems related to resource management and comparative measurements. In the first problem, we calculated the fraction of a tank of gas used during a trip, demonstrating the importance of understanding fraction multiplication and simplification in estimating fuel consumption. This skill is crucial for planning journeys and managing resources effectively. In the second problem, we determined a person's height relative to another, showcasing how fractions can be used to represent proportions and make comparisons. This concept is widely applicable in various fields, from scaling recipes in cooking to understanding statistical data. By mastering these types of problems, we enhance our ability to apply mathematical concepts in practical situations and make informed decisions based on proportional reasoning. The ability to work with fractions empowers us to solve a wide range of challenges, fostering a deeper understanding of the mathematical principles that govern our daily lives. Continued practice and application of these skills will further solidify your understanding and confidence in tackling similar problems in the future. Ultimately, these mathematical skills contribute to a greater sense of competence and preparedness in navigating the complexities of the world around us.