in essence, how many times does 1¾ go into 15?
first off, let's convert the mixed fraction to improper, and then divide them.
![\bf \stackrel{mixed}{1\frac{3}{4}}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}} \\\\\\ \cfrac{\quad 15\quad }{\frac{7}{4}}\implies \cfrac{\quad \frac{15}{1}\quad }{\frac{7}{4}}\implies \cfrac{15}{1}\cdot \cfrac{4}{7}\implies \cfrac{60}{7}\implies 8\frac{4}{7}](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cstackrel%7Bmixed%7D%7B1%5Cfrac%7B3%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B1%5Ccdot%204%2B3%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B7%7D%7B4%7D%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B%5Cquad%2015%5Cquad%20%7D%7B%5Cfrac%7B7%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B%5Cquad%20%5Cfrac%7B15%7D%7B1%7D%5Cquad%20%7D%7B%5Cfrac%7B7%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B15%7D%7B1%7D%5Ccdot%20%5Ccfrac%7B4%7D%7B7%7D%5Cimplies%20%5Ccfrac%7B60%7D%7B7%7D%5Cimplies%208%5Cfrac%7B4%7D%7B7%7D%20)
Answer:
36
Step-by-step explanation:
Total students un the contest = 84
<u>Number of students who gave their speech yesterday:- </u>
![\frac{1}{4} \: of \: total \\ = \frac{1}{4} \times 84 \\ = 21](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20%20%5C%3A%20of%20%5C%3A%20total%20%5C%5C%20%20%3D%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%5Ctimes%2084%20%5C%5C%20%20%3D%2021)
so 21 students gave their speech yesterday
- remaining students = 84 - 21
= 63
<u>Number of students who gave their speech today:-</u>
![\frac{3}{7} \: of \: remaining \\ = \frac{3}{7} \times 63 \\ = 27](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B7%7D%20%20%5C%3A%20of%20%5C%3A%20remaining%20%5C%5C%20%20%3D%20%20%5Cfrac%7B3%7D%7B7%7D%20%20%5Ctimes%2063%20%5C%5C%20%20%3D%2027)
<u>Number of students who have given their speech</u>:-
= 21 + 27
= 48
<u>Number of students who still haven't given their speech :-</u>
= total - 48
= 84 - 48
<u>= 36</u>