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:

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.

What is the slope of the line that contains these points?

Select the three true statements.

1. pi is the area of a circle of radius 1.

2. pi is the area of a circle of diameter 1.

3. pi is the circumference of a circle of radius 1.

4. pi is the circumference of a circle of diameter 1.

5. pi is the constant of proportionality relating the diameter of a circle to its circumference.

6. pi is the constant of proportionality relating the radius of a circle to its area.

Given that x^2+(1/x^2) = 7, what is the value of x^4+(1/x^4)

A circular swimming pool measures 79 feet around. What is the diameter?
A. about 200 ft
B. about 25 ft
C. about 50 ft
D. about 100 ft

What is the slope of the line that passes through the points (-8, -3)(−8,−3) and (-12, -3) ?(−12,−3)? Write your answer in the simplest form.

help me please thank you!​

What is the slope of this line? −3/2 −2/3 2/3 3/2

Need help on
These 2 questions

pls help me! (question is in the picture)

What value of w makes the equation 145 = w + 27 true?

rick serves his community as a firefighter. he works for a full 24 hours and then is off for the next 48 hours before his next 24-hour shift. last month, he earned $4,665.60, before taxes, and worked twelve 24-hour shifts. how much money does rick make per hour?
A. $8.10
B. $194.40
C.16.20
D.$24.30

Select all that apply.

Which of the following are equivalent?

The mouse covered 15 I’m sorry haha

the world record for the 100 m sprint is 9.77 s. How long would it take to run 1 m at this speed?

what is 7,563 ÷ 4

Please help and please put remainder

Daniel decides to use the method of proportions and similar
triangles to find the height of a tower. He measures the length of the
tower's shadow and finds it is 72 feet long. Then he holds a 12-inch
ruler perpendicular to the ground and finds that it casts an 24-inch
shadow. How tall is the tower?
a. 3 ft c. 36 ft
b. 4 ft d. 144 ft

At Supply World, 4 pens cost $10.00. How much do 3 pens cost if the price per pen is the same?

Which expression is equivalent to 2(d + 7)? ASAP PLEASE

What is the answer:

8x9x0x9x8 divided by 340 times 700 plus 500?????

another brainliest if its right :D

this is a khan academy question

A linear equation should have points that graph in a _____________ line.

Which of the following is a unit rate?

30 POINTS FOR THIS...Bus Stop: A graph has time (minutes) on the x-axis, and distance (miles) on the y-axis. A line goes through points (0, 5), (6, 8), and (12, 11). Friend's house: A 2-column table with 3 rows. Column 1 is labeled Time (minutes) with entries 3, 6, 9. Column 2 is labeled Distance (miles) with entries 4, 6, 8.
Seth is comparing scenarios to determine which starting point he should get dropped off at to get him to school faster. Seth's house is 17 miles from school.



In which scenario does Seth start closer to school?


In which scenario does Seth travel at a greater speed, and what was the rate?

I haven't done this in so long. I forgot how. Please help!

The sum of the length and width of a rectangle is 37. The length is 1 more than 2 times the width. Find the length. Note: Complementary angles are angles whose measures sum to 90°. find angle 1 and angle 2

What is the solution of the equation −14+2x+3=4x−13−7x?

I need help know!!!!!

Barb needs to run a total of 9 miles each week. So far, she has run 4 miles this week. How much father does she need to run? Write an equation and solve to figure out how many miles she needs to run.

Step by step

Rewrite the equation A = 3B in terms of “B =”.