Question

Caleb has 2 1/5 yards of rope. He uses 3/4 of rope to make a dog leash. Which expression can be used to represent 3/4 of 2 1/5? Pick all that apply.

A. 3/4 x 2 x 1/5
B. 3/4 x 11/5
C. 3/4 x 2 + 3/4 x 1/5
D. 3/4 x 3/4 + 1/5

Answer 1

B 3/4 x 11/5

Explanation:

We can rewrite 2 1/5. This number is 2 + 1/5, which can be written as:

2 + 1/5 = 10/5 + 1/5

Because 2 = 10/5, what we do is multiply and divide 2 by 5. And if we simplify:

2 + 1/5 = 10/5 + 1/5 = 11/5

So, caleb has initially 11/5 yards of rope.

He uses 3/4 of the rope, or 75%. We need to see how much is 3/4 (or 75%) of 11/5. We do this by simply multiplying 11/5 by 3/4 (or 0.75):

11/5 * 3/4 = [11*3] / [5*4]

As in multiplying fractions we multiply numerator by numerator and denominator by denominator.

11/5 * 3/4 = [11*3] / [5*4] = 33/20

For comparing we need to rewrite 11/5 with 20 as denominator. We do this by multiplying and dividing 11/5 by the number that, when multiplied by 5 gives us 20. This is 4. So

11/5= (11*4)/(5*4) = 44/20

So, caleb had 44/20 yards of rope and used 33/20 yards for his dog. He kept 11/20 yards.

Correct option: B