Grades 9-10 Video Solutions 2014-Grades 9-10 Video Solutions 2014 problem4

Video Transcription

Question number four, which number lies halfway in between of two-thirds and four-fifths? What the question is asking for is for us to compute the average.  The average lies halfway in between, and this is the number that we obtain by adding our two numbers together, two-thirds plus four-fifths, and then dividing by two.  So in the numerator, let's leave the two in the denominator here for now, we can cross-multiply,  and with a common denominator of 15, we have 10 plus 12 here, and that gives us 22 over 15, then still divided by 2, which is the same thing as 22 divided by 2 and 15, they're  a product. Now we can cancel, common factor, we can divide by 2 and obtain 11 over 15, which does not  simplify anymore because 11 is a prime number, so we have found our average, and that number lies exactly halfway between the two original numbers, so the answer here is A.

Video Summary

Question number four, which number lies halfway in between of two-thirds and four-fifths? What the question is asking for is for us to compute the average. The average lies halfway in between, and this is the number that we obtain by adding our two numbers together, two-thirds plus four-fifths, and then dividing by two. So in the numerator, let's leave the two in the denominator here for now, we can cross-multiply, and with a common denominator of 15, we have 10 plus 12 here, and that gives us 22 over 15, then still divided by 2, which is the same thing as 22 divided by 2 and 15, they're a product. Now we can cancel, common factor, we can divide by 2 and obtain 11 over 15, which does not simplify anymore because 11 is a prime number, so we have found our average, and that number lies exactly halfway between the two original numbers, so the answer here is A.

Keywords

average

fractions

common denominator

cross-multiply

prime number