Question

Hi my name is is Morgen and I need help with this question.

Answer 1

Bhavesh walked 3 1/8 miles.

Alana walked 4 3/4 miles.

To determine how many more miles did Alana walk, you have to calculate the difference between the distance walked by Alana and the distance walked by Bhavesh:

`4(3)/(4)-3(1)/(8)`

First, you have to express both mixed numbers as fractions:

Let's start with 4 3/4:

- Divide the whole number by 1 to express it as a fraction and add 3/4:

`4(3)/(4)=(4)/(1)+(3)/(4)`

- To sum both fractions, they must be expressed using the same denominator. To express 4/1 as the equivalent fraction with denominator 4, you have to multiply the denominator and numerator by four:

`(4\cdot4)/(1\cdot4)+(3)/(4)=(16)/(4)+(3)/(4)`

-Now you can add them:

`(16)/(4)+(3)/(4)=(16+3)/(4)=(19)/(4)`

Repeat to express 3 1/8 as a fraction:

- Divide the whole number by 1 and add 1/8:

`3(1)/(8)=(3)/(1)+(1)/(8)`

- Multiply the first fraction by 8 so that both are expressed with the same denominator:

`(3\cdot8)/(1\cdot8)+(1)/(8)=(24)/(8)+(1)/(8)`

-Add both fractions

`(24)/(8)+(1)/(8)=(24+1)/(8)=(25)/(8)`

So, you can rewrite the difference as follows:

`4(3)/(4)-3(1)/(8)=(19)/(4)-(25)/(8)`

As well as when you have to sum two fractions, to be able to subtract them, they have to be expressed with the same denominator.

The fractions have the denominators "4" and "8", a common factor between both numbers is "8". So, you have to multiply the first fraction by a number, so that it is expressed in its equivalent fraction with denominator 8.

Multiply the numerator and denominator of the first fraction by 2:

`(19\cdot2)/(4\cdot2)-(25)/(8)=(38)/(8)-(25)/(8)`

Now that both fractions are expressed with the same denominator, you can subtract them:

`(38)/(8)-(25)/(8)=(38-25)/(8)=(13)/(8)=1.625`

Finally, you have to express the result as a mixed number.

13/8 expressed as a decimal value is 1.625. The number behind the decimal dot represents the whole number of the mixed number and the numbers after the decimal dot represent the fraction of the mixed number.

There are 3 digits after the decimal dot, to express this as a fraction, divide it by 1000

`0.625=(625)/(1000)`

Next, you have to simplify this fraction, the numbers "625" and "1000" are divisible by 125, so you can simplify the fraction as follows:

`(625/125)/(1000/125)=(5)/(8)`

The result expressed as a mixed number is:

`(13)/(8)=1(5)/(8)\text{ miles}`

Alana walked 1 5/8 more miles than Bhavesh. The correct option is B.