Mathematics Middle School

Adding and Subtracting Fractions. Solve each problem.Write your answer as a mixed number if possible.

1.4 2/7 - 2 1/5
2.5 7/8 + 11/4
3.5/8 - 2/5
4.16/5 + 2 1/2

Answers

Answer 1
1. 6 17/35
2. 16 116/32
Answer 2

The answers are 2 3/35, 8 5/8, 9/40, and 5 7/10 respectively.

Here are step-by-step solutions to your problems:

4 2/7 - 2 1/5:

convert to improper fractions (30/7 - 11/5),

find a common denominator (150/35 - 77/35),

subtract to get 73/35, which simplifies to 2 3/35.

5 7/8 + 11/4:

convert to improper fractions (47/8 + 11/4),

find a common denominator (47/8 + 22/8),

add to get 69/8, which simplifies to 8 5/8.

5/8 - 2/5:

find a common denominator (25/40 - 16/40),

subtract to get 9/40.

16/5 + 2 1/2:

convert to improper fractions (16/5 + 5/2),

find a common denominator (32/10 + 25/10),

add to get 57/10, which simplifies to 5 7/10.

Related Questions

3.3k≤9.9 k=? Also what does the solution look like on a graph?

Answers

3.3 k ≤ 9.9
/divide by 3.3:
k ≤ 3

Our product is equal to 6+2 what factors are we

Answers

The factors you would use would be 2 and 4
The you will use is 2 and 4

How many solutions will this system of equations have? y = 3.5x − 3.5 y = −3.5x + 3.5 No solution Infinite solutions One solution Two solutions\

Answers

It will not have any possible solutions

Step-by-step explanation:


this would actually have some solutions because

y=3.5x−3.5

Step: Substitute 3.5x−3.5 for y in y=−3.5x+3.5:

y=−3.5x+3.5

3.5x−3.5=−3.5x+3.5

3.5x−3.5+3.5x=−3.5x+3.5+3.5x(Add 3.5x to both sides)

7x−3.5=3.5

7x−3.5+3.5=3.5+3.5(Add 3.5 to both sides)

7x=7

7x

7

=

7

7

(Divide both sides by 7)

x=1

Step: Substitute 1 for x in y=3.5x−3.5:

y=3.5x−3.5

y=(3.5)(1)−3.5

y=0(Simplify both sides of the equation)

x=1 and y=0

Why is an increase 20-40 100% but a decrease of 40-20 is 50%

Answers

the increase of 20-40 is one hundred percent because it takes one hundred percent of the first number (20) and adds it to itself. but 40-20 is a fifty percent decrease because it takes half (50%) of 40 and subtracts it from itslef
When 20 changes to 40, it is being increased by 20, which in percent is 100% of the starting number, resulting in a 100% change.  This leaves 200% of the starting number left. This is the same thing as multiplying by 2, and 200% is 2!
When 40 changes to 20, it is being decreased by 20, which in percent is only 50% of the starting number.  This leaves 50% of the original number left.  This is the same thing as dividing by two, and 50% is 1/2!

Hope this helps!

Please answer pic provided

Answers

For number 1, the answer is 3/2, 6/4, 12/8, 18/12, and 30/20. For number 2, the answer is Eve.

There are 25 students in Ms.Morris's class. She wants to divide the class into 3,4,or 5 equal teams with all students on a team. Which number of teams can Ms.Morris make? Explain.

Answers

Ms. Morris can divide the class into 5.
5 times 5 equal 25. 

The number of teams Ms.Morris can make would be 5-students groups.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have been given that there are 25 students in Ms.Morris's class. She wants to divide the class into 3,4,or 5 equal teams with all students on a team.

If Ms. Morris wants to divide all the students in 3, 4 or 5 equal teams, then apply a division to know the number of students per group.

If she makes 3-students groups, it would be;

25/3

If she considers 4-students groups, then it would be;

25/4

Thus, it can be seen that she cannot divide a students in parts to have equal groups.

Therefore, she has to make 5-students groups,

25/5 = 5

This means that she can make groups of 5 students each, and she would have equal groups.

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Convert 3/5 to a percent

Answers

3/5 as a percent is 75%
Hope this helped!!
3/5 to a percent is 60% because if you make the fraction bigger, with the denominator as 100, it would be 60/100, so 60%

what what what is an equation for 2 1/4 + 6 2/10

Answers

please make your question clearer so that I can help you. What do you mean? Write the whole question below and see what I can do for you.
1/2 + 6 1/5
= 1/2 + 6/5
= 5+12/10
=17/10
Alternative form :
1 7/10 , 1.7

Suppose f(x) = 4x – 2 and g(x) = -2x + 1. Find the value of f(g(3)).

Answers

g(3) = -2(3) + 1
g(3) = -6 + 1 = -5
f(-5) = 4(-5) - 2 
f(-5) = -20 -2
f(-5) = -22
Hence, the value of f(g(3)) is equal to -22.

Value of f(g(3)) is -22.

What is a function?

Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given

f(x) = 4x – 2

g(x) = -2x + 1

Value of f(g(3))

g(x) = -2x + 1

g(3) = -2(3) + 1

g(3) = -6 + 1

g(3) = -5

f(g(3)) = f(-5)

f(x) = 4x – 2

f(-5) = 4(-5) - 2

f(g(3)) = -20 -2

f(g(3)) = -22

Hence, value of f(g(3)) is -22.

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Explain how mental math can be used to estimate a 15% tip on a taxi ride that costs $23.25

Plz explain, and plz show work

Answers

10%=2.33 + half that is 1.17= 3.50 23.25×.15= 3.4875

Answer: 3.4875

Step-by-step explanation:

Here, According to the question,

Total amount is $23.25

[tex]100\% = 23.25[/tex]

⇒[tex]1\% = \frac{23.25}{100}[/tex]

⇒[tex]1\%= \frac{0.95}{8}[/tex]

⇒ [tex]15\%= 15\times \frac{0.95}{8}[/tex] ( By multiplying 15 on both sides)

⇒ [tex]15\%= \frac{14.25}{8}[/tex]

⇒  [tex]15\%= 3.4875 [/tex]

Thus, 15% of $23.25 is $3.4875



What is the equation of the line in slope-intercept form?

Answers

y=mx+b
m=slope
b=y intercept

slope=rise/run

we can see that if we look at the portion of the line that is bounded by the 2nd quadrant, we see it rises 5 units up and runs 2 units to the right
5/2
m=5/2

yintercept is where the line crosses the y axis
it crosses at y=5

the equation is [tex]y= \frac{5}{2} x+5[/tex]

Bob makes 4% commission on his sales as a real estate agent. If Bob sells a house for $249,000, How much money does he get to keep?

Answers

Bob will keep $9,960 if i am not mistaking.

$9,960

You can find this by multiplying the price od the house by the decimal version of 4% (.04).

on saturday, a minor league baseball team gave away baseball cards to each person entering the stadium. one group received 28 baseball cards. a second group received 68 baseball cards. if each person entering the stadium received the same number of cards, what was the greatest possible number of baseball cards that each person could have received?

Answers

Only one because u don't know how many people are in each group

Answer:

Step-by-step explanation:use the greatest common factor of 28 and 68 would give you 4

using 3.14 for pi, what is the volume of the sphere to the nearest tenth

Answers

You need to post a picture or tell us something about the sphere to be able to answer.  The formula for the volume of a sphere is (4/3)pi(r^3)

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where π can be approximated as 3.14 for simpler calculations. Volume is proportional to the cube of the radius, so if the radius changes significantly, the volume adjusts correspondingly by the cube of the factor of change.

To calculate the volume of a sphere using the value 3.14 for pi, you can apply the formula V = (4/3)πr³. If the radius of the sphere is 'r', you would plug in the value of 'r' into this formula. Next, you would multiply the result by 4/3 and then by 3.14 in place of π to get the volume. It's important to note that the volume of the sphere increases proportionally to the cube of the radius, meaning if the radius changes by a factor of 10, the volume changes by a factor of 10³ or 1000.

Adding 3/8 to a number increases it by 5% of its original value. What is the original number?

Answers

The original number would be 7.5

If the mean (average) of five consecutive numbers is 21, the smallest of three five numbers will be...

Answers

consecutive numbers are 1 apart
they are
x,x+1,x+2,x+3,x+4

average is 21
(x+x+1+x+2+x+3+x+4)/5=21
(5x+10)/5=21
times both sides by 5
5x+10=105
minus 10 both sides
5x=95
divide both sides by 5
x=19
x+1=20
x+2=21
x+3=22
x+4=23


the smallest number is 19

Bo has 23 video games for sale. He plans to donate the money he makes from each sale to a local charity. What is the least amount of money in whole dollars Bo should charge for each game in order to raise $100? Explain

Answers

She should sell each game for $4.34 since 4.34 times 23 is around $100.

In  order to raise $100, Bo should charge $5 for each game. In mathematics, "at least one" refers to one or more.

How to calculate least amount of money?

He provided the least amount of money of any donor, whether in size, quantity, degree, etc. lowest in importance, standing, or consideration. noun. The smallest possible quantity, degree, or other attribute.

In mathematics, "at least one" refers to one or more. It is frequently employed when existence can be proved but there is no way to know how many possible solutions there are.

Given ,

Let x represent the lowest price per video game.

The number of games available is 23.

Selling video games will need to raise $100 as the minimum amount.

The necessary inequality follows:

total number of games need minimum sum

i.e.[tex]23x\geq 100[/tex]

23 divided by both sides gives us

[tex]x\geq 4.24782608696[/tex]≈5

So, in order to raise $100, Bo should charge $5 for each game.

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a can of juice contains 175 calories per 2.5 servings which of the following is not an equivalent number of calories per serving

Answers

Final answer:

To find the equivalent number of calories per serving based on that a can of juice contains 175 calories for 2.5 servings, divide 175 by 2.5 to get 70 calories per serving. Any amount other than 70 calories per serving would not be equivalent.

Explanation:

The question is asking to find an equivalent number of calories per serving based on the information that a can of juice contains 175 calories per 2.5 servings. To calculate the calories per serving, we divide the total number of calories by the number of servings, so:

Calories per serving = Total calories ÷ Number of servings = 175 calories ÷ 2.5 servings = 70 calories per serving.

Now, let's say we have several options that represent the number of calories per serving:

70 calories per serving (correct equivalent)60 calories per serving (not an equivalent)75 calories per serving (not an equivalent)80 calories per serving (not an equivalent)

From this list, every option except for the first one (70 calories per serving) is not an equivalent number of calories per serving as our calculated 70 calories per serving.

carlos has a string that is 24 inches long. he wants to divide it into 3 equal parts. write an equation to find how long each part will be. use ? to represent the unknow number. then solve your equation.

Answers

is 8 the answer ?
just divide the given number by 3 . you will get the answer 8 


Final answer:

Carlos can divide his 24-inch string into 3 equal parts by solving the equation 3x = 24, which gives each part a length of 8 inches.

Explanation:

Carlos has a string that is 24 inches long and wants to divide it into 3 equal parts. To find how long each part will be, we can represent the unknown length of each part by the variable ? (which we will replace with x for the equation). The equation we can write for this scenario is 3x = 24.

To solve for x, we divide both sides of the equation by 3:

3x / 3 = 24 / 3x = 8

So, each part of the string will be 8 inches long.

Sarah is keeping up with how many miles her car gets per gallon. She starts with a full tank. After 448 miles, she fills up with 14 gallons. If she plots the points (0,0) and (14,448) on a coordinate plane, what would be the y-value of the point (1,y)?

Answers

For starters, determine what the x and y coordinates mean. In this case, you have two numbers (not counting 0), 14 and 448. In the question, we can see that 14 is the number of gallons and 448 is the number of miles. As the point is (14,448) and points are set up as (x,y), we can determine that your x is your number of gallons and y is your number of miles. Now, we set up a ratio, which will be set up as [tex] \frac{miles_1}{gallons_1} = \frac{miles_2}{gallons_2} [/tex]. Using your known values as miles1 and gallons1 and your known x that is paired with the unknown y as miles2 and gallons2, we get [tex] \frac{448}{14} = \frac{y}{1} [/tex]. Now, as we have one in the denominator for our second ratio, we can simplify to [tex] \frac{448}{14} =y[/tex]. Now, we divide 448 by 14 to get 32, meaning our y value is 32 miles.

Using a linear function, it is found that the value is: y = 32.

A linear function has the following format:

[tex]y = mx + b[/tex]

In which:

m is the slope, which is the rate of change.b is the y-intercept, which is the value of x when y = 0.

In this problem, when [tex]x = 0, y = 0[/tex], and thus, the y-intercept is [tex]b = 0[/tex].

Then

[tex]y = mx[/tex]

She also plots the point (14, 448), which means that when [tex]x = 14, y = 448[/tex], and this is used to find m.

[tex]14m = 448[/tex]

[tex]m = \frac{448}{14}[/tex]

[tex]m = 32[/tex]

Hence, the linear function is:

[tex]y = 32x[/tex]

Then, when x = 1, the point is (1,y), and:

[tex]y = 32(1) = 32[/tex]

The y-value is y = 32.

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there are threee spider on the wall.There are six ladybugs on the wall.how many spider and ladybugs legs are there on the wall

Answers

Spiders have 8 legs
Ladybugs have 6 legs
3 spiders * 8 legs = 24 spider legs
6 ladybugs * 6 legs = 36 ladybug legs
24 spider legs + 36 ladybug legs = 60 total legs.

But my question is, why are there so many insects on the wall?
1 spider has 8 legs
=> 8*3=24 legs
1 ladybug has (6 I assume) legs
=> 6*6=36 legs
Total 24+36=60 (legs, not insects)

The school purchased 100 trophies to give to the honor roll students. If one trophy cost $4.32, how much would it cost for all of the trophies

Answers

all trophies combined will estimate to $432 .  
100 * 4.32 = $432.00

Create two whole number division problems that have a quotient of 9 and a remainder of 5. Justify which is greater using decimal division.

Answers

86/9=9.55555555556
95/10=9.5

Answer and explanation;

If we choose two whole numbers; 8 and 10

We want to divide certain numbers by 8 and 10 to get 9 remainder 5.

In this case; 77 divided by 8 is equal to 9 rem 5

and 95 divided by 10 is equal to 9 rem 5

To justify which is greater, we use decimal division;

= 77 divided by 8 we get 9.625 ( 77 ÷ 8 = 9.625)

and

= 95 divided by 10 is equal to 9.5 (95 ÷10 = 9.5)

Therefore; the first case is greater since 9.625 is greater than 9.5

That is; 9 rem 5 got after dividing 77 by 8 is greater than 9 rem 5 got after dividing 95 by 10.

A store sells 12-packs of ballpoint pens for $1.09 each and composition books for $2.79 each. Cindy buys m packs of ballpoint pens and n composition books. The store offers a 5% discount for every 50th customer who makes a purchase. If Cindy gets the 5% discount, which expression will represent Cindy’s bill?

A. 0.05 − 1.09m + 2.79n
B. 1.05 + 1.09m + 2.79n
C. 1.05(1.09m + 2.79n)
D. 0.95(1.09m + 2.79n)

Answers

A 5% discount indicates that her total purchase amount will be decreased by 5%. Paying full price could be shown as 1.00, so we must subtract 0.05 from the full price to represent the discounted total (1.00-0.05 = 0.95).
Only one choice, D, contains this multiplier so we can be certain of this answer. 


The expression that will represent Cindy’s bill is 0.95(1.09m + 2.79n). Hence, the correct option is D. 0.95(1.09m + 2.79n).

What are equivalent expressions?

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

It is given that store sells 12-packs of ballpoint pens for $1.09 each.

The store also sells composition books for $2.79 each.

Cindy buys 'm' packs of ballpoint pens and 'n' composition books.

So, the equation for this becomes

1.09m + 2.79n

Cindy gets a 5% discount, so she has to pay 95% of the regular price.

Then the expression that will represent Cindy’s bill,

0.95(1.09m + 2.79n)

Hence, the correct option is D. 0.95(1.09m + 2.79n).

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The lemonade stand at the county fair sells the lemonade at a price of two cups for $3.60. Complete the table at right to find what Paula’s family will pay to buy lemonade for all eight members of the family.

Answers

i cant really help you with the table but she will need $14.40 to pay for it. This is because since two cups cost $3.60 you multiply 3.60 by 4. I got the 4 by dividing 8 into 2 because 8 people and 2 cups each

The cost of 8 cups of lemonade would be $14.40

Calculating the price for the table given

Price of lemonade :

2 cups = 3.60

price per cup:

3.6 / 2 = 1.80

for 3 cups:

1.8 × 3 = 5.40

for 4 cups:

1.8 × 4 = 7.20

for 5 cups:

1.8 × 5 = 9

for 6 cups:

1.8 × 6 = 10.8

for 7 cups:

1.8 × 7 = 12.60

for 8 cups:

1.8 × 8 = 14.40

Therefore , the cost of 8 cups of lemonade is $14.40

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A car wash detailed 272 cars in 8 hours. At what rate did the car wash detail cars in cars per hour.

Answers

272/8 = 34 cars an hour
34 cars per hour. 272c/8h 

clydesdale horse weighs as much a shetland pony and an american saddledred combined

Answers

That's 1550 pounds. A Shetland pony weighs 450 pounds and an American saddlebred weighs 1200 pounds so the Clydesdale horse weighs around 1550 pounds.

A mountain climber climbed down a cliff 50 feet at a time.He did this 5 times in one day.What was the overall change in his elevation

Answers

Answer:

The overall change is -250 feet. 50 times 5 is 250 feet, and the mountain climber descended. Therefore, the change is -250 feet in elevation.

Step-by-step explanation:

Answer:

the overall changes is -250 its descended 50×5=250

Step-by-step explanation:

a number y is no more than -8 what is the inequality

Answers

y<-8 because the number y is no less

Y is less than or equal to -8

10-5y=1x
Please show work on how to solve for Y

Answers

10-5y=1x
-10       -10
-5y= 1x -10
/-5     /-5
y= -1/5x +2
10-5y=1x
-10      -10
-5y=1x-10
/5       /5

y= 1x/5 -(-2)
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