Question

Pepita and francisco each spend a equal amount of time on homework. The table shows the fraction of time they spend on each subject. Complete the table by determining the missing fraction for each student

Fraction 1/2, math,2/3 english,1/6,3/8 science

Answer 1

`\begin{array}{ccc}\text{Homework}&\text{Pepita}&\text{Francisco}\\ \\\text{Math}&(1)/(6)&(1)/(2)\\ \\\text{English}&(2)/(3)&(1)/(8)\\ \\\text{Science}&(1)/(6)&(3)/(8)\end{array}`

Explanation:

Pepita and Francisco each spend a equal amount of time on homework. he table shows the fraction of time they spend on each subject.

`\begin{array}{ccc}\text{Homework}&\text{Pepita}&\text{Francisco}\\ \\\text{Math}&&(1)/(2)\\ \\\text{English}&(2)/(3)&\\ \\\text{Science}&(1)/(6)&(3)/(8)\end{array}`

We know Pepita spent

`(2)/(3)+(1)/(6)=(2\cdot 2+1\cdot 1)/(6)=(5)/(6)`

on English and Science.

Hence, Pepita spent

`1-(5)/(6)=(6)/(6)-(5)/(6)=(1)/(6)`

on Math.

Francisco spent

`(1)/(2)+(3)/(8)=(1\cdot 4+3\cdot 1)/(8)=(7)/(8)`

on Math and Science, so he spent

`1-(7)/(8)=(8)/(8)-(7)/(8)=(1)/(8)`

on English.

The table is

`\begin{array}{ccc}\text{Homework}&\text{Pepita}&\text{Francisco}\\ \\\text{Math}&(1)/(6)&(1)/(2)\\ \\\text{English}&(2)/(3)&(1)/(8)\\ \\\text{Science}&(1)/(6)&(3)/(8)\end{array}`