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. 8(2/9)-4(2/3)

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression three and 5/ minus two and one half. And were asked to evaluate this and reduce our final answer to the lowest terms possible. Well, before we can start subtracting, we need to do two things first. We need to convert our mixed numbers here to improper fractions. And after we've done that we are going to need to ensure that we have common denominators before we can subtract. So converting mixed numbers into improper fractions we recall from previous lessons on converting mixed numbers to improper fractions that we're going to take our whole number and we're going to multiply it by our denominator. So for the 1st 13 times eight. That's 24 for the 2nd 12 times two, that's four. And then we are going to take that product and add it to the numerator. Z. And those sums will become our new enumerators. So 24 plus five is 29 and four plus one is five. So rewriting these fractions with our new enumerators For the first fraction, the numerator is 29 it's over the same denominator, eight. So 29 8th minus the second fraction are new, numerator is five divided by the same denominator which is two, So minus five halves. All right, we've got the first step done. But now we need to get common denominators. What is our common denominator? Going to be what number to Both eight and to go into well eight and two. Both go into eight. So that is our target here. So we want something over eight minus something over eight. Well, the 1st 1, 29/8. That's already over eight. So that remains 29/8. How about five halves? How do we get the denominator of eight? What do we multiply that to buy to get eight? Well, two times four equals eight. And what? We multiply the denominator by. We need to multiply the numerator by as well because then we're multiplying it by 4/4. We're multiplying it by one. So that's why we're allowed to do that. All right. What is five times four? Five times four is 20 and two times four is the eight that we want? Great. Now we've got a common denominator and we can go ahead and subtract. We are only going to subtract the numerator. The denominator is going to remain the same. It's going to remain eight when we are subtracting fractions. So 29 minus 20 in the numerator, 29 minus 20 is nine. And so that gives us 9/8. Now the last thing we need to do is check and make sure that our answers in the lowest terms possible. So is there anything that both nine and eight are divisible by? Well nine? That's three times three and eight. That's two times 44 is two times two. They do not share any common factors. So this cannot reduce anymore. 9/8 is our final answer. We look at our answer choices in this matches with answer choice, a well done, we'll catch you on the next one.

Add or subtract as indicated. Write answers in lowest terms as needed. 8(2/9)-4(2/3)

Key Concepts

Fraction Operations

Multiplication of Fractions

Simplifying Fractions

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