Question

A boy goes to school by first taking a bus for 1 3/4 km and then by walking 1/3 km. Find the distance of his house from the school.

Answer 1

The boy goes to school by bus for 1 3/4km, then he walks 1/3 km.

To determine the total distance he traveled you have to add both distances:

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

To solve this sum, add the fractions first and then add the result to the whole number:

- Add both fractions:

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

To add both fractions you have to express them using the same denominator first. A common multiple between the denominators "4" and "3" is "12". Multiply the first fraction by 3 and the second by 4 to express them as their equivalent fractions with denominator 12. Then proceed to add them:

`(3\cdot3)/(4\cdot3)+(1\cdot4)/(3\cdot4)=(9)/(12)+(4)/(12)=(9+4)/(12)=(13)/(12)`

The result is 13/12, as you can see the numerator is greater than the denominator, which indicates that this is an improper fraction, i.e. its value is greater than 1. You can write this fraction as a mixed number as follows:

- Solve the division:

`13/12=1.08\bar{3}`

The mixed number will have the whole number "1".

- To express the decimal value as a fraction, multiply it by 12

`0.08\bar{3}\cdot12=1`

The result is the numerator of the fraction, and the denominator will be 12, so:

`0.08\bar{3}=(1)/(12)`

And the resulting mixed number is:

`(13)/(12)=1(1)/(12)`

Finally, add the remaining whole number from the first sum to determine the distance between his house and the school:

`1+1(1)/(12)=2(1)/(12)`

The distance he traveled from home to school is 2 1/12 km.