Express 4.75 as a fraction in lowest form. 2. What will be the reciprocal of a proper fraction? Give an example. 3. Find 7/8 of a day.
The Correct Answer and Explanation is:
Answers and Explanation:
- Express 4.75 as a fraction in lowest form:
To convert 4.75 into a fraction:
- 4.75 = 4 + 0.75
- 0.75 = 75/100
- Simplify 75/100 by dividing both numerator and denominator by 25:
75 ÷ 25 = 3, and 100 ÷ 25 = 4
So, 0.75 = 3/4 - Therefore, 4.75 = 4 + 3/4 = 19/4
Answer: 4.75 = 19/4
- What will be the reciprocal of a proper fraction? Give an example.
A proper fraction is a fraction where the numerator is less than the denominator, meaning its value is less than 1. The reciprocal of a proper fraction is obtained by interchanging its numerator and denominator.
For example:
Consider the proper fraction 3/5. Its reciprocal is 5/3.
Answer: The reciprocal of a proper fraction is an improper fraction. Example: The reciprocal of 3/5 is 5/3.
- Find 7/8 of a day.
One full day is 24 hours.
To find 7/8 of a day, multiply 24 by 7/8:
24 × 7/8 = (24 ÷ 8) × 7 = 3 × 7 = 21 hours
Answer: 7/8 of a day is 21 hours
Explanation
Understanding fractions and their applications is an important part of mathematics. To begin with, converting a decimal like 4.75 to a fraction involves separating the whole number and the decimal part. The number 4.75 can be seen as 4 + 0.75. Since 0.75 is equivalent to 75/100, simplification is needed to express it in lowest terms. Dividing both 75 and 100 by their greatest common divisor, which is 25, gives 3/4. Thus, 4.75 becomes 4 + 3/4, which is an improper fraction written as 19/4.
Next, when dealing with proper fractions, it is important to understand that they represent parts of a whole. A proper fraction has a numerator smaller than the denominator. The reciprocal of a number is what it must be multiplied by to get 1. For a fraction, this means flipping the numerator and denominator. For instance, the reciprocal of 3/5 is 5/3. It is important to note that the reciprocal of a proper fraction is always an improper fraction because the numerator becomes greater than the denominator after flipping.
Finally, applying fractions to time provides practical insight into how fractions work in everyday life. Since there are 24 hours in a day, finding 7/8 of a day means calculating a portion of those 24 hours. Multiplying 24 by 7/8 gives 21. This tells us that 7/8 of a day is equivalent to 21 hours, which is helpful when dealing with schedules, time management, or work planning. Understanding these operations allows learners to see the connection between numerical concepts and real-world applications.
