Compare Two Fractions With Large Numerators – Denominators Math Quiz Online

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Comparing two numbers is altogether a different picture when it comes to a fraction. A lot of things have to be considered before drawing a conclusion. Between two given fractions it is important to notice both the behaviors of numerator and denominator. To let a number be bigger than the other, the numerator has to be larger comparing to its counterpart and the denominator has to be smaller. This quiz attempts to normalize the pain that is involved in comparing fractions through practice. 

Learn to compare two fractions with large numerator or denominator

When comparing two fractions, it’s important to make sure that both fractions have the same denominator (the bottom number). If the denominators are different, you’ll need to find a common denominator before you can compare the fractions. A common denominator is a number that both denominators can be divided by evenly.

For example, let’s say you want to compare the fractions 3/4 and 5/6. The denominators are 4 and 6, which are not the same. To find a common denominator, you can think of the smallest number that is a multiple of both 4 and 6, which is 12. This means that you’ll need to multiply both the numerator and denominator of the first fraction by 3, and the numerator and denominator of the second fraction by 2, so that both fractions have a denominator of 12. So the first fraction becomes 9/12, and the second becomes 10/12. Now you can compare the fractions because they have the same denominator.

Another way to find a common denominator is by finding the least common multiple (LCM) of the denominators. To find the LCM you can use prime factorization method, where you write down both denominators as the product of prime numbers and then take the highest exponent of each prime in both numbers and multiply the primes together.

For example, 4 = 2 x 2 and 6 = 2 x 3, so the LCM of 4 and 6 is 2^2 * 3 = 12.

Once the fractions have the same denominator, you can compare the numerators (the top numbers) directly. Whichever numerator is larger, that fraction is larger. For example, in the case of 9/12 and 10/12, 10/12 is the larger fraction because 10 is greater than 9.

It’s also important to keep in mind that when comparing large numerators and denominators, you could simplify the fractions by dividing both the numerator and denominator by the greatest common factor, which is the largest number that divides into both numbers without leaving a remainder, it will make it easier to compare them.

For example, when comparing the fractions 48/72 and 42/56, the GCD of 48 and 72 is 24, so the first fraction can be simplified to 2/3 and the GCD of 42 and 56 is 14 so the second fraction can be simplified to 3/4.

In short, when comparing two fractions with large numerators and denominators, first you need to find a common denominator by either multiplying the numerator and denominator of each fraction by different number or by finding the least common multiple (LCM) of the denominators. Then you can compare the fractions by comparing the numerators directly. And lastly, simplify the fraction to make it easier to compare them.