Castor brought 6 3/4 cakes to share with 26 students. Did Castor bring enough for each student to have 1/4 of a cake? Explain your thinking and show your work
6 3/4 ÷ 26
= 27/4 ÷ 26
= mmmh, what do you think?
each student is to have 26 quarters = 26/4 and
we have 27/4 of them.
(I'll take the extra piece)
26 students and each gets 1/4 cake.
26 x 1/4 = 6 1/2 cales and Castor brought 6 3/4 cakes; therefore, he brought enough. There will be 1/4 cake left (enough for 1 more student).
To determine if Castor brought enough cake for each student to have 1/4 of a cake, we need to calculate the total amount of cake brought and then divide it by the number of students.
Castor brought 6 3/4 cakes. To add a mixed number to a whole number, we need to convert the mixed number to an improper fraction. The improper fraction form of 6 3/4 is (6 * 4 + 3) / 4 = 27/4.
Now, we can add the cakes:
Total amount of cake = 27/4
Next, we divide the total amount of cake by the number of students (26):
Division: (27/4) ÷ 26
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(27/4) * (1/26)
Multiplication: (27 * 1) / (4 * 26) = 27/104
So, each student will receive 27/104 of a cake.
To determine if this is equivalent to 1/4 of a cake, we can find the common denominator and compare the fractions:
The common denominator of 27/104 and 1/4 is 104.
Multiplying the numerator and denominator of 1/4 by 26, we get 26/104.
Now we can compare:
27/104 = 26/104
Since the fractions are equal, each student will have exactly 1/4 of a cake.
Therefore, Castor brought enough cake for each student to have 1/4 of a cake.