Fractions are a massive part of our day-to-day lives. Measurements of ingredients in the kitchen are possible and decipherable only because of the existence of fractions. Do you get confused and cannot interpret which of the two given fractions is greater or lesser than the other? Is it one of the reasons you are scoring low on your fractions test?
Fractions can get a little bit technical when it comes to comparing them. You may have difficulty recalling the correct method and reaching the appropriate answer. Worry not; get ready to score well and learn about solving such problems. If you need to learn how to see which fraction is more significant, this article is for you.
Dive into this article to know various ways in which you can understand and solve which of the two given fractions is greater.
How do I solve this problem?
Whether ⅜ is greater than ¼ or vice versa can be concluded using one of the below-mentioned methods.
⅜ is greater than ¼. How? Read on to know.
This is one of the most commonly used methods for this type of question. You can convert the given fractions into decimals and compare the resulting decimals. The corresponding fraction to the greater decimal would obviously be more significant. For the fractions in question, all you have to do is divide the numerator (3 for the first fraction)with the denominator(8 in the first fraction)
Similarly, divide 1 by 4 to obtain the decimal for the fraction ¼
Now, when we compare the two resulting decimals, i.e., 0.375 and 0.25, it is clear that 0.375 is more significant than 0.25 (look at the number in the tenths position)
Thus, ⅜ ＞¼
Cross Multiplication Method
This is a relatively simplified and sought-after method as well. In the cross multiplication method, as self-explanatory, you multiply the numerator of one fraction to the denominator of the other fraction, multiplying diagonally.
The products or results on both sides are then compared to know which fraction is more significant. For instance, for the given fractions ⅜ and ¼, in order to multiply diagonally, you are to solve like this:-
4(the denominator of one fraction)x3(the numerator of other fraction)=12
12 ⅜ ⃞ ¼
Likewise, multiply 8(denominator of one fraction) by the 1(numerator of the other fraction)
12 ⅜ ⃞ ¼ 8
Comparing 12 and 8, we know that 12＞8. Thus, ⅜ ＞¼.
Comparing by making the bases common
Another way you can determine which of the two fractions is greater is by making the denominators/bases of both the fractions common and then comparing their numerators. This is further be done in 2 ways:-
- By taking the L.C.M(lowest common multiple):- For this problem, taking the L.C.M. of 8 and 4, we get 8. Solving it further with the fractions, we get 2 new factions, that is, ⅜ and 2/8, like so:-
⅜,¼ =3,2, which becomes ⅜, and 2/8, respectively.
Now that the bases are the same, i.e., 8, we can decide which fraction is more significant by looking at the numerators. Hence, it is very clearly visible that 3＞2, hence ⅜ ＞¼.
- Another method of making the bases or denominators common is by multiplying one denominator with the other fraction and vice versa. For example, for the fractions in question, if ⅜ is multiplied by 4/4 and ¼ is multiplied by 8/8, the denominators of both the fractions become equal, i.e., 32, while the numerator becomes 12 and 8, respectively. In this case, too, it is seen that 12＞8(comparing the numerators) and so ⅜ ＞¼.
Using one of these methods, you can conclude and come to the correct answer.
So, yes, ⅜ is bigger than ¼. The methods mentioned above make calculating the more significant fraction much easier and quicker. Using one of the three given methods, you can swiftly solve the questions asked on these grounds and answer them correctly and move to the next question.
These methods involve basic mathematics and hence are easy to decipher and keep in mind. Now that you are aware of these techniques, you can even find solutions to these questions orally, thus saving your time and enhancing your pace.
These simple tricks can help you bring laurels to your exams. Not only that, this concept will be highly and excessively used in your daily life as well.
- Q) What is a fraction?
In mathematics, a fraction is a numerical value representing the part of a whole. It is a portion of any quantity out of its whole. For example, when an apple is cut into 4 parts, each part represents ¼ of the part of the entire apple.
Remember, every fraction contains two parts:- a numerator and a denominator. There are various kinds of fractions:- like, unlike, unit, proper, improper, mixed, equivalent fractions. For example:-⅔,4/6,5/9 are fractions with 2,6,5 as numerators and 3,6,9 as denominators, respectively.
- Q) What are the properties of fractions?
Fractions show the associative property of addition and multiplication, commutative property of addition and multiplication, as well as distributive property. Besides that, fractions also show the properties of identity and inverse.