How To Add Fractions With Variables And Whole Numbers

tommy is studying forfinal exams this weekend. he will spend 1/5 ofthe weekend studying. what fraction ofthe weekend will he spend studying foreach of his 4 subjects if he spends the same amount oftime studying for each subject?

How To Add Fractions With Variables And Whole Numbers, so the total amountof time he's going to spend studying thisweekend is 1/5 of the weekend. and he has to divide thatinto 4 equal sections. and he's going to spend thatmuch time on each subject.

so he's going todivide this by 4. now, we've already seenthat dividing by a number is the same thing asmultiplying by its reciprocal. you might say, hey, well,what's the reciprocal of 4? you just have toremind yourself that 4 is the same thing as 4/1. so 1/5 divided by 4/1 is thesame thing as 1/5 times 1/4. and you could also viewthis as 1/4 of 1/5 or 1/5 of 1/4, either way.

but here we multiplyour numerators to get 1. and then we multiply ourdenominators, 4 times 5 is 20. so you get 1/20 ofthe weekend will be spent studyingfor each subject. now, let's also try tothink about this visually. let's imagine that thisis his entire weekend. and i've divided itinto 5 equal sections. and so we already knowthat the total amount of his weekend spentstudying is 1/5.

so that's the totalamount studying for the weekend is 1/5. now, he has to divide thisinto 4 equals section. so let's do that. he's got four subjects,and he's going to spend the same amount oftime on each of the 4 subjects. so he's going to dividethis into 4 equal sections. so how much time doeshe spend on one subject? well, in each subject, thatwould be this little area

that i'm doing inyellow right over here. and what is that? well, that's 1 over-- howmany equal sections are there of that size in the weekend? well, i've justdrawn out the grid. you had 5 rows, andnow you have 4 columns. so 5 rows times 4 columns,you have 20 equal sections. so once again, lookingat it visually, he's spending 1/20of his weekend

on each of the 4 subjects. and then if you do thisfor 4 subjects, that means that in thiswhole weekend, 1/5 will be spent studying. but the questionthat they're asking, he's spending 1/20 of theweekend on each subject.