Ascending Order of Fractions: 1/4, 1/3, 1/2

1. Introduction:
In this question, we are asked to arrange the given fractions in ascending order using the symbol less than (<). the="" fractions="" given="" are="" 1/2,="" 1/3,="" and="" 1/4.="" to="" arrange="" these="" fractions="" in="" ascending="" order,="" we="" need="" to="" compare="" their="">

2. Understanding Fractions:
Before we begin, let's understand what fractions are. Fractions represent a part of a whole. They consist of a numerator (the number above the fraction line) and a denominator (the number below the fraction line). The numerator represents the number of parts we have, while the denominator represents the total number of equal parts in the whole.

3. Comparing Fractions:
To compare fractions, we need to find a common denominator. In this case, the common denominator is 12 since it is a multiple of all the denominators (2, 3, and 4).

4. Converting Fractions to a Common Denominator:
To convert the fractions to a common denominator, we need to multiply the numerator and denominator of each fraction by the same number so that the denominator becomes 12.

- 1/2 becomes 6/12 (multiplied numerator and denominator by 6)
- 1/3 becomes 4/12 (multiplied numerator and denominator by 4)
- 1/4 remains 1/4 (already has a denominator of 4)

5. Arranging Fractions in Ascending Order:
Now that we have converted the fractions to a common denominator, we can compare their numerators to arrange them in ascending order.

- 4/12 is the smallest fraction (1/3)
- 6/12 is the middle fraction (1/2)
- 1/4 is the largest fraction

Therefore, the fractions arranged in ascending order using the symbol less than are 1/3 < 1/2="" />< />

6. Conclusion:
In conclusion, we have successfully arranged the fractions 1/2, 1/3, and 1/4 in ascending order using the symbol less than. By converting the fractions to a common denominator and comparing their numerators, we determined that the correct order is 1/3 < 1/2="" />< 1/4.="" />