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

Question

Add or subtract as indicated. Write answers in lowest terms as needed. $7 \frac{5}{12} - 4 \frac{5}{6}$

Accepted Answer

welcome back. I am so glad you're here. We are given this expression three and 5/16 minus two and 7 30 seconds. We are asked to evaluate this expression and to reduce our final answer to the lowest terms. Alright before we can start subtracting we need to do two things first. We've got mixed numbers and in order to subtract them we need to change our mixed numbers into improper fractions. The second thing we need to do before we can subtract is we need to have a common denominator between our fractions. So once we've done those two things then we can subtract. Alright, improper fractions were calling previous lessons on changing mixed numbers to improper fractions. We're going to take our whole number And we are going to multiply it by the denominator. So for the 1st 13 times 16 gives us 48 And for the 2nd 12 times 32 gives us 64 and then we take those products and we are going to add them to our enumerators and those will become Our new enumerators. So for the 1st 1, 48 plus five, that is 53. And for the 2nd 1, 64 plus seven is 71. So now rewriting our fractions are new numerator for the first one is we keep the old denominator 16 53 16th minus. And our new numerator for the second fraction is 71 divided by the same denominator from the previous which is 30 to 30 seconds. Alright. So 53 16th minus 71. 30 seconds. Well we can't do that yet because we need to have a common denominator. So what would our common denominator b? What's the lowest number that both 16 and 32 go into? That would be 32. So our common denominator is going to be 32. That's what we're aiming for. But how do we get 16 to become 32? Will we multiply it by two? And what we do to the denominator? We need to do to the numerator as well. So that multiplying it by two halves. That's just one. We're really only multiplying it by one. That's why we're allowed to do it. All right. So what is two times 53 for our numerator? Two times 53 is 106 and then two times 16 is 32 for the denominator. The second one already has our common denominator for its denominator so that one remains 71, 30 seconds. And now we can do the subtraction and recall, we only subtract the numerator as for fractions. So 106 -71. That will give us 35 and the denominators stay the same. 30 seconds. So that's our final answer. 35 30 seconds. Were asked to reduce it to the lowest terms possible. So really quickly we check and we see if there are any factors that 32 both have in common 35. Well, that's five times 7, 32. Well that doesn't have any fives in it or any sevens going into it, so they have nothing in common. 35. 30 seconds is as low as it gets. So we look at our answer choices and that matches with answer choice B. Well done, we'll catch you on the next one.

Add or subtract as indicated. Write answers in lowest terms as needed. $7 \frac{5}{12} - 4 \frac{5}{6}$

Key Concepts

Multiplication of Whole Numbers and Fractions

Subtraction of Fractions

Simplifying Fractions to Lowest Terms

Watch next

Add or subtract as indicated. Write answers in lowest terms as needed. 7512−4567\(\frac{5}{12}\) - 4\(\frac{5}{6}\)

Key Concepts

Multiplication of Whole Numbers and Fractions

Subtraction of Fractions

Simplifying Fractions to Lowest Terms

Watch next

Add or subtract as indicated. Write answers in lowest terms as needed. $7 \frac{5}{12} - 4 \frac{5}{6}$