Subtracting Fractions with Unlike Denominators

We ensure the fractions have the same denominator by multiplying each fraction by an appropriate form of 1 that converts its denominator to the desired common denominator.

To subtract two fractions, we need to get common denominators. A simple way to find a common denominator is to multiply the two denominators.

A common denominator is a number that both denominators can divide into without leaving a remainder.

To get the same denominator, we multiply the first fraction by the denominator of the second fraction over itself, and the second fraction by the denominator of the first fraction over itself.

No, multiplying by the denominator over itself does not change the value of the fraction, as it is equivalent to multiplying by 1.

After finding a common denominator, we subtract the numerators of the two fractions.

Sure, let's subtract 7/8 by 3/5. The common denominator is 8 * 5, which is 40. We then multiply the first fraction by 5/5 and the second fraction by 8/8 to get the same denominator, then subtract the numerators to get 11/40.

The result of subtracting 7/8 by 3/5 is 11/40.

After subtraction, if the fraction is not in its simplest form, we can simplify it by dividing both the numerator and the denominator by their greatest common divisor.

To simplify a fraction, we find the greatest common divisor of the numerator and the denominator, and then divide both by that number.

The result of subtracting 4/9 by 1/7 is 19/63.

Certainly, let's subtract 4/9 by 1/7. The common denominator is 9 * 7, which is 63. We then multiply the first fraction by 7/7 and the second fraction by 9/9 to get the same denominator, then subtract the numerators to get 19/63.

The greatest common divisor of 11 and 40 is 1, as 11 is a prime number and does not divide evenly into 40.

The greatest common divisor of 19 and 63 is 1, as 19 is a prime number and does not divide evenly into 63.

It is important to have the same denominator when subtracting fractions because it allows us to directly subtract the numerators without having to convert anything.

The least common denominator is the smallest common multiple of the denominators of the fractions being subtracted. It is the smallest number into which both denominators can divide evenly.

No, it is not always necessary to find the least common denominator. Any common denominator will work, but using the least common denominator can simplify the process and the result.

We ensure the fractions have the same denominator by multiplying each fraction by an appropriate form of 1 that converts its denominator to the desired common denominator.

To subtract two fractions, we need to get common denominators. A simple way to find a common denominator is to multiply the two denominators.