Answer:
A)
[tex]\displaystyle \frac{1}{12}[/tex]
B)
[tex]\displaystyle \frac{3}{5}[/tex]
C)
[tex]\displaystyle \frac{17}{24}[/tex]
Step-by-step explanation:
Part A)
The Hendersons were traveling 1/3 of the distance on the first day.
However, they had to stop, having only traveled 1/4 of the 1/3 distance.
So, we can multiply the two fractions together.
Therefore, the fraction of the total distance they traveled is given by:
[tex]\displaystyle \frac{1}{4}\times\frac{1}{3}=\frac{1}{12}[/tex]
The Hendersons traveled 1/12 of the total distance.
Part B)
We are assuming the bottle of milk was full at the beginning.
So, at the beginning, there were 1/1 bottle of milk left.
Howie fed a piglet 1/5 of the bottle. So, there is now:
[tex]\displaystyle 1-\frac{1}{5}[/tex]
Of the bottle left.
Making common denominators and subtracting yields:
[tex]\displaystyle =\frac{5}{5}-\frac{1}{5}=\frac{4}{5}[/tex]
So, after feeding the piglet, 4/5 of the bottle of milk was still there.
3/4 of the remainder was fed to a calf.
So, the amount that was fed to the calf is 3/4 times 4/5. Therefore:
[tex]\displaystyle \frac{3}{4}\times\frac{4}{5}[/tex]
Multiply:
[tex]\displaystyle =\frac{12}{20}=\frac{3}{5}[/tex]
So, the calf drank 3/5 of the bottle of milk.
Part C)
Nathan used 2 (5/6) loaves of bread to make 4 sandwiches.
First, convert 2 (5/6) to an improper fraction. So:
[tex]\displaystyle 2\frac{5}{6}=\frac{12+5}{6}=\frac{17}{6}[/tex]
Nathan made 4 sandwiches using this. So, we will divide this by 4. Note that this is the same as multiplying by 1/4. Therefore:
[tex]\displaystyle \frac{17}{6}\times\frac{1}{4}=\frac{17}{24}[/tex]
So, Nathan used 17/24 loaves of bread per sandwich.
