b) multiplication of improper fractions: 4/3 x 4/3
expressed as improper fraction: 16/3
product expressed as mixed number: 5 1/3
why: 4 x 4 = 16, keeping the denominator (3) is 16/3. 16 isn't a multiple of 3, the closest is 15, and 15 / 3 is 5, but we since we have 16, we have one left, so it'd be 5 1/3
c) multiplication of improper fractions: 7/3 x 3/2
expressed as improper fraction: 21/6
product expressed as mixed number: 3 3/6 = 3 1/2
why: 7 x 3 = 21, 2 x 3 is 6, combine it, 21/6. multiple of 6 that is closest to 21 is 18. 18 / 6 = 3. we have 3 numbers left over. (21 - 18 = 3) so it's the 3 that we get, plus the 3 that we have left, is 3 3/6
d) multiplication of improper fractions: 11/6 x 7/5
expressed as improper fraction: 77/30
product expressed as mixed number: 2 17/30
why: 11 x 7 = 77, 6 x 5 = 30, combine it, 77/30. 77 goes into 30 twice. (30 x 6 = 60, can't add another 30, because its more than 77) we have 17 numbers left over, (77 - 60 = 17) so it's 2 17/30. can't reduce 17/30 because 17 doesn't have any common factors with 30. hope i helped!