How do I multiply, subtract, add, and divide fractions?
Answers
Step 1: How to multiply Fractions
Fractions are number that have two-part numerator and denominator e.g
\(\frac{3}{4},\frac{5}{4\text{ }}\)To multiply fractions, you multiply the numerator and denominator
Examples:
\(\frac{5}{7}\times\frac{3}{4}=\frac{5\times3}{7\times4}=\frac{15}{28}\)Then you reduce the result to the lowest form if possible.
Step 2: How to Divide fractions
Dividing a fraction is very similar to the multiplication of fractions. Just that you are to change the division symbol to multiplication and then you take the reciprocal of the fraction.
Example:
5/8 ÷ 3/4
This will become
\(\frac{5}{8}\times\frac{4}{3}=\frac{5}{2}\times\frac{1}{3}=\frac{5}{6}\)Note that the 4 at the numerator is used to divide 8 at the denominator
Step; How to Add and Subtract Fractions
To add or subtract fraction, you make use of the LCM of the denominators
Examples:
\(\begin{gathered} \frac{5}{8}+\frac{4}{5} \\ \text{The denominators are 8 and 5 whose LCM is 40} \\ \frac{5}{8}+\frac{4}{5} \\ =\frac{25+32}{40}=\frac{57}{40}=1\frac{17}{40} \end{gathered}\)Note that: Divide the denominator by the LCM and multiply the result by the numerator
Similarly for subtraction
\(\begin{gathered} \frac{5}{6}-\frac{3}{4} \\ \text{The LCM of the denominators is 24} \\ \frac{5}{6}-\frac{3}{4} \\ =\frac{20-18}{24}=\frac{2}{24}=\frac{1}{12} \end{gathered}\)Note that you can also use a similar approach to Mixed Fractions
For mixed fractions, you can convert the fraction to an improper fraction and follow the approach above.
Alternatively, you can use this
Example
\(\begin{gathered} 4\frac{3}{5}-2\frac{1}{3} \\ \text{The mixed fraction has two part, the whole number and proper fraction} \\ 4\frac{3}{5}-2\frac{1}{3}=(4-2)(\frac{3}{5}-\frac{1}{3}) \end{gathered}\)\(\begin{gathered} \text{Then we have} \\ 2(\frac{9-5}{15})=2\frac{4}{15} \end{gathered}\)A similar method also goes for addition.
Related Questions
Find the x values of x in the parallelogram
Answers
Answer:
No idea
Step-by-step explanation:
You need to show the parallelogram in order for your question to make sense.
Find the slope of the line graphed below. m=(
Answers
Answer:
m = 2
Step-by-step explanation:
Rise:4 and run=2
4/2 = 2
The box is a rectangular prism. He covered all the sides with the of the box with special wallpaper that cost a total of $504. How much wallpaper cost per square foot length is 6 feet width is 5 feet and height is 3 feet.
Answers
The cost of the wallpaper per square foot is $4.
To find the cost per square foot of the wallpaper, we first need to calculate the total surface area of the box. A rectangular prism has six faces, and each face is a rectangle.
The front and back faces have dimensions 6 feet by 3 feet, so their combined area is 6 ft * 3 ft * 2 = 36 square feet.
The top and bottom faces have dimensions 5 feet by 3 feet, so their combined area is 5 ft * 3 ft * 2 = 30 square feet.
The left and right faces have dimensions 6 feet by 5 feet, so their combined area is 6 ft * 5 ft * 2 = 60 square feet.
The total surface area of the box is 36 + 30 + 60 = 126 square feet.
Since the cost of the wallpaper is $504, we divide the total cost by the total surface area to find the cost per square foot: $504 / 126 sq ft = $4 per square foot.
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Patel made a deposit into an account that earns 5%simple interest. After 10 years Patel had earned $1500 in interest. How much was Patel’s initial deposit?
Answers
Answer:
Patel’s initial deposit was $3000
Step-by-step explanation:
Given:
Simple interest (S.I.) = 5%
Time period (t) = 10 years
Interest earned (r) = $1500
To find: Patel’s initial deposit
Solution:
Simple interest is a method of calculating the interest charged on the principal, or original amount of a loan.
Let p denotes original amount of a loan
\(S.I.=\frac{p\times r\times t}{100}\\\Rightarrow 1500=\frac{p\times 5\times 10}{100}\\\Rightarrow p=\frac{1500\times 100}{5\times 10}\\=3000\)
So, Patel’s initial deposit was $3000
In the data set below, what is the interquartile range?
26 42 52 61 75 85 93 96
Answers
Answer:
the iqr is 42
Step-by-step explanation:
Give two ways to write the algebraic expression p + 26 in words the product
Answers
Answer:
para lara
Step-by-step explanation:
pere culu ana lletere
A student determines the density of a chunk of metal to be 5.1 g/cm3. She then repeats the measurement four more times on the same chunk of metal and obtains values of 5.0, 4.9, 5.4, and 5.2 g/cm3 for the density. What is the standard deviation of the five measurements?
A. 0.148
B. 0.19
C. 0.037
D. 0.22
E. 0.17
Answers
Answer:
E. 0.17
Step-by-step explanation:
Mean:
Sum of all values divided by the number of values, so:
\(\overline{x} = \frac{5.1 + 5 + 4.9 + 5.4 + 5.2}{5} = 5.12\)
Standard deviation:
Square root of the sum of the difference squared between each value and the mean, divided by the sample size, so:
\(s = \sqrt{\frac{(5.1-5.12)^2 + (5-5.12)^2 + (4.9-5.12)^2 + (5.4-5.12)^2 + (5.2-5.12)^2}{5}} = 0.172\)
Thus the correct answer is given by option E.
2 Mabaso has R140, Thabo has R70 and Ally has R35. What is the ratio of the amount of money Mabaso has, to the amount of money Thabo has and to the amount of money Ally has? Write the ratios in simplest form. The price of a steel table is R750. On Black Friday the table could be bought for R600. Calculate the percentage discount? Show ALL your calculations. Convert 125 g to kilograms. (1 kg = 1 000 grams) A green grocer packs 12 apples in a plastic bag. Calculate the number of bags he w need if he has 285 apples. The scale of a map is 1 500 000. Determine the actual distance in km if measurement on the map is 23,7 cm. Hint: 1 km = 100 000 cm
Answers
The actual distance represented by 23.7 cm on the map is 355.5 km.
To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.
Mabaso has R140, Thabo has R70, and Ally has R35.
The ratio of Mabaso's money to Thabo's money is:
R140 ÷ R35 = 4
The ratio of Mabaso's money to Ally's money is:
R140 ÷ R35 = 4
Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.
To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.
Original price: R750
Discounted price: R600
Discount: R750 - R600 = R150
Percentage discount: (R150 ÷ R750) × 100 = 20%
So, the table has a 20% discount on Black Friday.
To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).
125 g ÷ 1,000 = 0.125 kg
Therefore, 125 grams is equal to 0.125 kilograms.
If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.
Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags
Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.
If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.
1 cm on the map represents 1,500,000 cm in reality.
23.7 cm on the map represents x cm in reality.
x = 23.7 cm × 1,500,000 cm = 35,550,000 cm
To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).
35,550,000 cm ÷ 100,000 = 355.5 km
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Evaluate the expression 4w² + w-6, when w = -4
a.) 54
b.) 22
c.) -54
d.) 74
Answers
\( \huge \pink{ \underline \mathfrak{ \green{Answer}}} \: \\ \\ \: \: \rightarrow \fbox{ a). \blue{ \: 54 \: }}\)
Step-by-step explanation:
\( \bf{Given} \: \colon 4w² + w-6, when \: \: w = -4 \\ \\ \tt \underline \red{Solution} \colon \\ \\ \rightarrow \: 4w {}^{2} + w \: - 6 \\ \\ \: put \: \: value \: \: of \: \: w \: \: in \: \: given \: \: equation \\ \\ \rightarrow \: 4( - 4) {}^{2} + \: (- 4 )\: - 6 \\ \\ \rightarrow \: 4(16) \: - 4 \: - 6 \\ \\ \rightarrow \: 64 \: - 10 \\ \\ \bf \rightarrow54\)
Help please having a little trouble
Answers
Answer:
A) you do 2 times x and 2 times 3
2x + 6
B) you do 5 times 2x and 5 times 4
10x - 20
C) you do 4 times 2x and 4 times 1
8x + 4
D) you do 6 times x and 6 times 4y
6x - 24y
what is the most effluence first step to isolate the variable term on one side of this equation -9x=-4x+5
Answers
pls help, thank you!!
Answers
Answer: 1, 3
For a cubic polynomial, there are either 3 real roots or 1 real root nad 2 complex roots in a conjugate pair.
A circus show started at 6:15 p.m and ended at 9:30 p.m. What was the duration of the show?
Answers
Triangle ABC is dilated about the origin to create triangle A′B′C′. Triangle ABC with vertices at A negative 6 comma negative 4, B negative 2 comma negative 4, and C negative 2 comma 2 and triangle A prime B prime C prime with vertices at A prime negative 9 comma negative 6, B prime negative 3 comma negative 6, and C prime negative 3 comma 3. Determine the scale factor used to create the image. two fifths 1.5 one half 2.5
Answers
Answer:
1.5
Step-by-step explanation:
To determine the scale factor used to create the image, we can compare the distances between corresponding vertices of the two triangles.
Let's start by finding the distance between A and B in triangle ABC:
distance AB = sqrt[(x_B - x_A)^2 + (y_B - y_A)^2]
= sqrt[(-2 - (-6))^2 + (-4 - (-4))^2]
= sqrt[16 + 0]
= 4
Now let's find the distance between A' and B' in triangle A'B'C':
distance A'B' = sqrt[(x_B' - x_A')^2 + (y_B' - y_A')^2]
= sqrt[(-3 - (-9))^2 + (-6 - (-6))^2]
= sqrt[36 + 0]
= 6
To find the scale factor, we can divide the distance between corresponding vertices in the image triangle by the distance between the corresponding vertices in the original triangle:
scale factor = distance A'B' / distance AB
= 6 / 4
= 1.5
Therefore, the scale factor used to create the image is 1.5.
To find the scale factor of a dilation, one can divide a side length of the enlarged shape by the corresponding side length of the original shape. In this case, the scale factor from triangle ABC to A'B'C' is 6/4 = 1.5.
Explanation:In Mathematics, we can find the scale factor of a dilation by comparing corresponding distances in the original shape and its image. The scale factor can be found by dividing a side length of the enlarged shape (triangle A′B′C′) by the corresponding side length of the original shape (triangle ABC).
For example, the distance between points A and B in the original triangle ABC is 4 units (-2 - (-6) = 4), and the distance between points A′ and B′ in the enlarged triangle A′B′C′ is 6 units (-3 - (-9) = 6). So, the scale factor from ABC to A'B'C' is 6/4 = 1.5.
Therefore, the scale factor used to create the image of triangle A'B'C' from triangle ABC is 1.5.
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Fifteen percent of 168
Answers
Answer:
25.2
Step-by-step explanation:
168 x .15 = 25.2
\(\large\text{Hey there!}\)
\(\rm{15\%\ of\ 168}\\\\\rm{= 15\% \times 168} \\\\\rm{= \dfrac{15}{100}\times 168}\\\\\rm{= \dfrac{15}{100}\times \dfrac{168}{1}}\\\\\rm{=\dfrac{15\times168}{100\times1}}\\\\\rm{= \dfrac{2,520}{100}}\\\\\rm{= 25.2}\)
\(\huge\text{Therefore, your answer should be: }\)
\(\huge\boxed{\frak{25.2}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)
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Hoang has worked as a nurse at Springfield General Hospital for 5 years longer than her friend Bill. Two years ago, she had been at the hospital for twice as long. How long has each been at the hospital?
Answers
5 years longer then Bill, 2x5=10.
10+2=12.
12-5=7
Hoang has be there for 12 years. Bill has for 7 years.
Find the volume of the tank with a radius of 2 m and height of 5 m
Answers
Answer:
20.943951023932 m^3
Step-by-step explanation:
v=1/3pi(r)^2h
v=1/3pi(2)^2(5)
v=20.943951023932 m^3
Answer:
62.8
Step-by-step explanation:
2 × 2 × 3.14 × 5 = 62.8
the national association of home builders ranks the most and least affordable housing markets based on the proportion of homes that a family earning the median income in that market could afford to buy. data containing the median income($1000s) and the median sale price($1000s) for a sample of 12 housing markets appearing on the list of most affordable markets were subjected to a simple linear regression analysis. the following results were obtained
Answers
The results based on the information provided in the question will be as follows:
a) By using the analysis of variance (ANOVA) table,
MSE= 440.1/10 = 44.01
F = 2717.9/44.01 =61.756
b) To interpret the slope of regression model,
the slope represents that for each $1000 increase in the income of a family on an average sale price increase by 2184.3
c) To calculate the value of coefficient of determination and its interpretation,
0.712 and the lowest that coefficient of determination is 0 and highest is 1. Thus, here the coefficient is high.
d) By using regression equation,
Price = 11.8+2.18×income
Predicted value = (-11.8+2.18×20)×1000 = 31800
e) To compute, 95% confidence slope
= 2.1843/2.228×0.278 = 1.565;2.804
f) The linear relationship between income and price,
All the intervals above have a value of more than 0 therefore we can conclude that the slope is significant. Thus, we have sufficient evidence that at 0.05 level of significance the linear relationship between income and price is inter related.
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Note that the full question is:
The National Association of Home Builders ranks the most and least affordable housing markets based on the proportion of homes that a family earning the median income in that market could afford to buy. Data containing the median income $1000s) and the median sale price($1000s) for a sample of 12 honsing markets appearing on the list of most affordable markets were subjected to a simple linear regression analysis. The following results were obtained. The regression equation is price-11.8 +2.18 income Predictor Coef StDev Constant11.80 12.84 income 2.1843 0.2780 S 6.634 Analysis of Variance Source Regression 1 2717.9 2717 DF SS MS F P Residuni Eror 10 440. Total 1 3158.0 a. Using the snalysis of variance table, find MSE b. Interpret the slope of the regression model. the valus ul and interpret it d. Using the estimated regression equation, the value ofy ifx-$20,000 e. Compute 95% confidence al for the slope 43-1+2.2280T g. At the 0.05 level of significunce, is there evidence of a linear relationship between income and price
8th grade math, please help.
I’ll give you brainliest if you want.
-Find the volume-
*links are reported*
Answers
Chandra needs to make 3 gallons of punch. How many cups of frozen strawberries are needed? Use the drown-down menus to complete the answer.
Answers
The number of cups of frozen strawberries that are needed to make 3 gallons of punch is equal to 48 cups.
How to calculate the cups of frozen strawberries needed?In this exercise, you're required to determine the number of cups of frozen strawberries that are needed to make 3 gallons of punch. Thus, we would apply direct proportion.
Note: There are 16 cups of frozen strawberries in a gallon.
By direct proportion:
16 cups = 1 gallon
X cups = 3 gallons
Cross-multiplying, we have:
X = 16 × 3
X = 48 cups of frozen strawberries.
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Show the solution and answer
(3x + 5)(x - 9)
Answers
Answer : 3x^2 -22x -45
You basically cross multiply each term by the opposing one, so 3x times x would be 3x^2 , 3x times 9 would be -27x, 5 times x would be 5x, and 5 times -9 would be -45 :)
ILL GIVE BRAINLIEST IF CORRECT!! The average of x+6, 6x+2, and 2x+7 is 4x-7. What is x?
Answers
Answer:
35/3
Step-by-step explanation:
\(\frac{x+6 + 6x+2+x+6}{3} =4x-7\)
Simplify to get
9x+14=3(4x-7)
35=3x
x=35/3 or 11.66
Please help me with this math problem
1. Josiah is making a candle by pouring melted wax into a mold in the shape of a square pyramid. Each side of the base of the pyramid is 12 in and the height of the pyramid is 14in. To get the wax for the candle, Josiah melts cubes of wax that are each 6 in by 6 in by 6 in. How many of the wax cubes will Josiah need in order to make the candle? Show your work.
Answers
Answer:
10 wax cubes
Step-by-step explanation:
the volume of the square pyramid can be found by using the following formula:
\(V = \frac{1}{3} * B * h\)
where b is the base of the pyramid and h is the height of the pyramid
The area of the base of the pyramid is given as 12 in * 12 in = 144 in^2
So, the volume of the pyramid is:
V = (1/3) * 144 in^2 * 14 in = 2,016 in^3
Each wax cube has a volume of 6 in * 6 in * 6 in = 216 in^3.
To find the number of wax cubes needed, we can divide the volume of the pyramid by the volume of each wax cube:
Number of wax cubes = Volume of pyramid / Volume of each wax cube
Number of wax cubes = 2,016 in^3 / 216 in^3
Number of wax cubes = 9.33 (rounded to two decimal places)
Since we can't have a fraction of a wax cube, Josiah will need to use 10 wax cubes to make the candle.
The black triangles are similar. Find the value of x
Answers
Answer:
if triangles are similar then
ratio of sides are equal,
x/12=28/21
x=16
the value of x is 16 unit
What is similar triangle?Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion
According to the question,
if triangles are similar then
ratio of sides are equal,
28/21 = x/12
x = 28 ×12/21
x = 4 × 4
x=16
Hence , the value of x is 16 unit
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Please solve this. I need help on it
Answers
Answer:
look at the photo............
9514 1404 393
Answer:
∠PTQ = 40°
∠PTR = 140°
Step-by-step explanation:
The two marked angles are "vertical" angles, so are congruent.
∠PTQ = ∠STR
(x +28)° = (2x +16)°
12 = x . . . . . . . . . . . . . . . divide by °, subtract x+16
Then the measure of angle PTQ is ...
∠PTQ = (x +28)° = (12 +28)° = 40°
That and angle PTR form a linear pair, so are supplementary.
∠PTR = 180° -∠PTQ = 180° -40° = 140°
Select all the expressions that are equivalent to (12 + x)10.5.
It’s multiple choice and these are the answers
10.5(12x)
(10.5 + 12 + x)
10.5(12 + x)
126x
126 + 10.5x
22.5 + x
Answers
126+10.5x
Step-By-Step:
Find the sum of 7/13 and 11/26. 25/26 25/39 18/39 3/26
Answers
Step-by-step explanation:
\( = \frac{7}{13} + \frac{11}{26} \)
\( = \frac{14 + 11}{26} \)
\( = \frac{25}{26} \)
Naji is trying to draw an isosceles triangle. He is
given point A at (-4,-2) and point B at (2,-2).
Plot these two points, then help Naji make the
isosceles triangle ABC by ploting point C. Give
your coordinates for point C. It must be on the
grid provided.
Answers
Answ
Step-by-step explanation:wirugf4
Julian belongs to a club that is marching in a parade. Each member of the club needs to wear one of the hats listed in the table below.
PARADE HATS
Straw Hat
25 red
20 white
40 blue
Cowboy Hat
30 red
25 white
10 blue
Julian chooses the first hat at random from all the hats. What is the probability the hat Julian chooses is blue? Show your work or explain your answer.
Answers
The probability Julian chooses a blue hat is 1/3.
What is the probability Julian chooses a blue hat?Probability refers to the branch of math which deals with finding out the likelihood of the occurrence of an event.
Total hat is:
= 25+20+40+30+25+1
= 150.
There are a total of 150 hats to choose from.
The number of blue hats to choose from is:
= 40 + 10
= 50.
The probability that Julian chooses a blue hat is:
= 50/150
= 1/3
= 0.33 or 33.33%.
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how to convert 4.5 into a percentage
Answers
Answer:
450%
Step-by-step explanation:
(4.5 × 100) × 1100 = 450100
Hope this helps! :)