Question

The Hendersons went on a driving vacation. They decided to travel 1/3 of the distance on the first day. Owing to bad weather, they had to stop for the night having gone only 1/4 of the distance to the one-third point.

What fraction of the total distance did they travel the first day? Show your work and reduce to lowest terms.


Howie works at a petting zoo. He fed a piglet 1/5 of a bottle of milk, then gave 3/4 of what was left to a calf.
How much of the bottle of milk did the calf drink? Show your work and reduce to lowest terms.

Nathan used 2(5/6) loaves of bread to make sandwiches for a lunch. He made equal numbers of 4 different types of sandwiches.
What fraction of a loaf of bread did Nathan use for each type of sandwich?

Answer 1

A)

`\displaystyle (1)/(12)`

B)

`\displaystyle (3)/(5)`

C)

`\displaystyle (17)/(24)`

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:

`\displaystyle (1)/(4)*(1)/(3)=(1)/(12)`

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:

`\displaystyle 1-(1)/(5)`

Of the bottle left.

Making common denominators and subtracting yields:

`\displaystyle =(5)/(5)-(1)/(5)=(4)/(5)`

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:

`\displaystyle (3)/(4)*(4)/(5)`

Multiply:

`\displaystyle =(12)/(20)=(3)/(5)`

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:

`\displaystyle 2(5)/(6)=(12+5)/(6)=(17)/(6)`

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:

`\displaystyle (17)/(6)*(1)/(4)=(17)/(24)`

So, Nathan used 17/24 loaves of bread per sandwich.