Question

Please help me out with this question

Answer 1

Answer:

D.  A major 6th

Step-by-step explanation:

The ratio of the interval is question is 480 : 800.   Reduce this ratio to see which ratio it matches up with.   This is similar to reducing fractions, find the common factors and divide them out from both terms...here is one example

Step 1:  480 : 800      (Both are multiples of 10, so divide both by 10)

     You get 48 : 80

Step 2:  48 : 80         (both are even, so they are multiples of 2, so divide by 2)

    You get  24 : 40

Step 3:  24 : 40       (both are even again, divide by 2)

    You get   12 : 20

Step 4:  12 : 20       (both are multiples of 4, divide by 4)

    You get   3 : 5

This matches up with the ratio for a major sixth.

***You can reduce this ratio faster if you recognize larger common factors

Answer 2

Answer:

Step-by-step explanation:

Givens

f1 = 480

f2 = 800

Solution

Method One: Step by Step

f1 / f2 = 480/ 800

Start by dividing both top and bottom on the right by 10

f1/f2 = 480/10 // 800 / 10

f1 / f2 = 48 / 80

The next thing to notice is that both 48 and 80 are divisible by 8. Divide top and bottom on the right by 8

f1 / f2 = 48 / 8// 80/ 8 =  6 / 10

f1 / f2 = 6/10

Last, divide top and bottom on the right by 2

f1 / f2 = 6/2 // 10 / 2

f1 / f2 = 3 / 5

Method Two Highest Common Factor.

Could you have done this a short way? Yes if we say it. The short way would have been to  divide by 10 * 8 * 2 = 160 right away. We might have done it by factoring 480 and 800 into prime factors.

480: 2  * 2 * 2 * 2 * 2 * 5 * 3

800: 2 * 2 * 2 * 2 * 2 * 5 * 5

The highest common factor is what is in bold.

The highest common factor is 2^5 * 5 = 32 * 5 = 160

The answer in both cases is 3/5 which I think is D.

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