Add or subtract as indicated. Write answers in lowest terms as ne...

Question

Add or subtract as indicated. Write answers in lowest terms as needed. 4(3/4) - 1(2/5)

Accepted Answer

Hello. Today we're going to be subtracting the two given mixed fractions. So what we are given is five and 2/ minus three and one third. Now before we perform any type of operation we always want to change our mixed fractions to improper fractions. So in order to do that you're going to go ahead and change the numerator of the mixed fraction. And in order to change the numerator you're gonna multiply your denominator with the whole number and you're going to add that value to the current numerator which is to and on the right hand side we're gonna go ahead and do the same thing. We're going to multiply this denominator with the whole number and then we're gonna add that value to the current numerator. So on the left hand side seven times five is going to give us 35 plus two is going to give us 37. So the new numerator on the left hand fraction is going to be 37 we're going to keep the same denominator which is seven. So that's going to be five and two sevens from the form of a mixed fraction to an improper fraction. Now let's go ahead and do the same thing with the right hand side three times three is going to give us nine and nine plus one is going to give us 10. So on the right hand side, the numerator of the improper fraction is going to be 10 and we're going to keep the same denominator which is three. Now in order to add and subtract fractions. We want to go ahead and have the same denominator in any fraction we're working with here, we have seven in the denominator and we have three in the denominator. So we're going to need to find the lowest common denominator between seven and three, while seven and three share the common factor of 21. So the lowest common denominator is going to be 21. In order to get 21 in both the left hand and right hand fraction, we're going to multiply the right hand fractions denominator by seven. And if we multiply the denominator by seven we need to multiply the numerator by seven as well. And on the left hand side to change 7 to 21 we're going to multiply seven by three and doing this to the denominator we must also due to the numerator. So we're going to multiply 37 by three. So multiplying this, 37/7 by 3/3 is going to give us 111 over 21. And on the right hand side we're going to be subtracting 10/3 by 7/7 and that's going to give us 70/21. Now that both of these fractions have the same denominator, we can go ahead and perform the subtraction. So subtracting these two fractions together is going to give us -70/21 and 111 -70 is going to give us 41. So what we are left with is 41/21. Now you need a check to make sure that this is in the simplest form and if it's in the simplest form it won't be divisible by any common factor between 41 and 21. While 41 and 21 don't have any common factors. Mean that there's no common number that you can divide the numerator and denominator by to reduce the fraction further. So 41/21 is going to be the simplest form of the subtraction. And with that being said, the answer to this problem is going to be d. So I hope this video helps you in understanding how to approach this type of problem. And I'll go ahead and see you all in the next video.

Add or subtract as indicated. Write answers in lowest terms as needed. 4(3/4) - 1(2/5)

Key Concepts

Multiplication of Fractions

Subtraction of Fractions

Simplifying Fractions

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