Question

Question #6d808

Answer 1

`2 3/8`

Explanation:

One way of solving the problem is to change the fraction to an improper fraction and then multiplying by 1/2.

`4 3/4 = 19/ 4`

`1 = 4/4`

Multiply `4 xx 1 = 4 xx 4/4 = 16/4`

Now `16/4` can be added to `3/4`

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

Now multiply `19/4` by `1/2`

`19/4 xx 1/2 = 19/8`

`19/8 = 2 3/8`

Answer 2

The distance he jogged on the boardwalk and park is `17/4" mi"`, or `4 1/4" mi"`.

Explanation:

If you meant, "How many miles were jogged on the boardwalk and park?", then the following is the answer.

Subtract `1/2` mi from `4 3/4` mi.

First convert the the mixed fraction `4 3/4` into an improper fraction. To do this, multiply the denominator by the whole number and add the numerator. Place the result over the denominator.

`4 3/4=(4xx4+3)/4=19/4`

Now subtract `1/2` from `19/4`.

`19/4-1/2`

In order to add or subtract fractions, they must have the same denominator. Multiply `1/2` by `2/2` to convert the denominator to `4`. Since `2/2=1`, the numbers change, but the value does not.

`19/4-1/2xxcolor(magenta)(2/2)=`

`19/4-2/4=`

`17/4`

The boardwalk and park are `17/4" mi"`.

We can convert the improper fraction back to a mixed number by dividing the numerator by the denominator by long division to get the whole number as the quotient, and the numerator as the remainder.

`"17-:4=4` `"R1"`

The mixed fraction is `4 1/4`. So `17/4" mi"` `=` `4 1/4" mi"`.

We can reason this out by mentally taking away `2/4`, which is the same as `1/2` from `4 3/4` to get `4+3/4-2/4=4+1/4=4 1/4`.