To review, rational number is any number that can be written as a fraction of integers. We shall understand by using example, 3 and 4 are the integers so 3 divided by 4 would be considered as a rational number. Fractions as we know are rational numbers and so are whole numbers. Let us take 3 divided by 1 is 3 and is the same thing so dividing rational numbers using the multiplicative inverse.
Dividing Rational Numbers or How to Divide Rational Numbers – Rational numbers are divided using the multiplicative inverse. When we divide fractions, we find the multiplicative inverse of the divisor; often it is also known as reciprocal. Reciprocal is when we replace the numerator by denominator and denominator by numerator then the resultant fraction. For example: - For a fraction 7/8, its reciprocal will be 8/7.
To Divide Rational Numbers, we find the multiplicative inverse or reciprocal of divisor. For example, if we have to divide 2/5 by ¾ then ¾ is considered as dividend and 2/5 as the divisor. So in this case reciprocal of divisor will be 5/2. Now instead of dividing we will directly multiply 5/2 by 3/4. Therefore in simple words 3/4 is multiplied by the multiplicative inverse of 2/5. When we multiply fractions we multiply straight across the top, 3 times 5 is 15 and 4 times 2 is 8. Thus 15/8 is the solution.
We also understand that in Division of Rational Numbers, we have to turn the fraction upside down and then multiply the first fraction by the resulted reciprocal. If we have two rational numbers 2 /3 and 3/4 and we need to divide ¾ by 2/3 so ¾ will be called as divisor, its reciprocal will be 4/3, which is nothing but done upside down. Then next step will be multiplying the first fraction with the reciprocated fraction. That is 2/3 multiplied by 4/3. Here we shall multiply 2 by 4 and divided by 3 multiplied by 3 and get 8/9 as the solution. We also will understand how we simplify the fractions, 48/108 we simplify by 2 the whole fraction as it is divisible by 2 we get 24/54. Another simplification by 2 gives us 12/27. Here we understand that 12 and 27 will not be simplified by 2 anymore as it’s not divisible by 2, thus which could be another number, 3 is the other number which is divisible so we get 4/9. Thus we simplify the fractions.
