find the lowest form of the following fractions 18 upon 42 step by step for class 5th.
The correct answer and explanation is:
To simplify the fraction 18/42 to its lowest form, follow these steps:
- Find the Greatest Common Divisor (GCD):
The first step is to find the GCD of 18 and 42. This can be done by listing the factors of each number:
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 The common factors between 18 and 42 are 1, 2, 3, and 6. The greatest of these common factors is 6.
- Divide both the numerator and denominator by the GCD:
Now, divide both the numerator (18) and the denominator (42) by their GCD, which is 6.
- Numerator: 18 ÷ 6 = 3
- Denominator: 42 ÷ 6 = 7 So, 18/42 simplifies to 3/7.
- Check your work:
To ensure the fraction is in its simplest form, check if the new numerator and denominator (3 and 7) have any common factors. Since 3 and 7 are both prime numbers and have no common factors other than 1, the fraction 3/7 is in its lowest form.
Thus, the fraction 18/42 simplified to its lowest form is 3/7.
Explanation:
In mathematics, simplifying fractions means reducing them to their simplest form, where the numerator and denominator have no common factors other than 1. The GCD is used to divide both parts of the fraction to achieve this simplest form. This makes the fraction easier to understand and work with in further calculations or comparisons. For example, 18/42 simplified to 3/7 is much easier to handle in problems like addition, subtraction, or comparison.