What is an equation that represents 4 1/4 as a sum of whole numbers and unit fractions
The equation that represents 4 1/4 as a sum of whole numbers and unit fractions is simply 4 + 1/4. This approach demonstrates the decomposition of a mixed number into its integral and fractional components.
Explanation:To represent 4 1/4 as a sum of whole numbers and unit fractions, we can break it down into its components. This fraction essentially means 4 plus 1/4. The whole number part is straightforward, and the fraction part can be represented as a unit fraction. Thus, 4 1/4 can be expressed as the sum 4 + 1/4.
In mathematics, when decomposing mixed numbers into a sum of whole numbers and fractions, it’s essential to clearly distinguish between the integral and fractional parts. For example, similar numbers like 5 1/3 would decompose into 5 + 1/3. This helps illustrate how mixed numbers can be broken into more straightforward components, making them easier to work with in various mathematical operations and providing a bridge to understanding fractional expressions and addition.
Answer:
4 1/4 = 1 + 3 + 1/6 + 1/12
Step-by-step explanation:
You want an equation that represents 4 1/4 as the sum of whole numbers and unit fractions.
Whole numbersThe whole number portion of 4 1/4 is 4. The number 4 can be represented as a sum of whole numbers (plural) several ways:
4 = 0 + 4
4 = 1 + 3
4 = 2 + 2
4 = 0 + 1 + 3
4 = 1 + 1 + 2
4 = 1 + 1 + 1 + 1
Of course, any quantity of the whole number 0 can be added to any of these sums. We have shown a couple of instances of that.
In our answer here, we choose the representation to be 4 = 1 +3.
Unit fractionsA unit fraction is a fraction with a numerator of 1. In the mixed number 4 1/4, the fraction portion, 1/4, is already a unit fraction. The problem statement here asks for a representation involving "unit fractions" (plural). We can divide 1/4 into any number of equal unit fractions:
1/4 = 1/8 + 1/8 . . . . 2 equal unit fractions
1/4 = 1/12 + 1/12 + 1/12 . . . . 3 equal unit fractions
This latter representation suggests a way to use unequal unit fractions to represent 1/4:
1/4 = (1/12 + 1/12) +1/12 = 2/12 +1/12 = 1/6 +1/12
Using these two unit fractions, our equation can be written ...
4 1/4 = 1 + 3 + 1/6 + 1/12
What is the area of 14km and 12km and 8km and 5km and 4km and 9km
Final answer:
Calculate the sum of areas of squares with given side lengths to find the total area.
Explanation:
Area of a Square:
Calculate the area of each square:
14 km x 14 km = (14)² = 196 km²
12 km x 12 km = (12)² = 144 km²
8 km x 8 km = (8)² = 64 km²
5 km x 5 km = (5)² = 25 km²
4 km x 4 km = (4)² = 16 km²
9 km x 9 km = (9)² = 81 km²
Sum of Areas:
Add the areas of all squares together:
196 km² + 144 km² + 64 km² + 25 km² + 16 km² + 81 km² = 526 km²
Therefore, the total area is 526 km².
Which of the following is the inverse of the statement "if I like carrots, then I like vegetables
Answer:
f I don't like carrots, then I don't like vegetables
Step-by-step explanation:
A bag contains 8 blue marbles, 6 green marbles, 12 yellow marbles, and 10 orange marbles. A marble is drawn at random from the bag.
What is the probability that the marble drawn will not be blue?
A.) 29
B.) 34
C.) 79
D.) 78
Answer:
C
Step-by-step explanation:
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write the next number in this pattern. 10, 11, 20, 21, 30, 31
How do u solve 63=-9d?
Use pictures or words to explain what shapes can be put together to make a hexagon shape.
compare the amount of sand in the top cone of the hourglass to the amount there will be when the height of the sand in the top cone is only one inch.
To compare the amount of sand in the top cone of an hourglass when the height is one inch, calculate the volume using the formula volume = length × width × height. Compare the original volume to the new volume with a height of one inch to determine the difference in the amount of sand.
Explanation:The question asks to compare the amount of sand in the top cone of an hourglass to the amount when the height of the sand in the top cone is only one inch. In an idealized model of the hourglass, the volume of the stack of sand in the top cone can be calculated using the formula volume = length × width × height. From the given information, the volume of the stack is 9 in³. To find the amount of sand when the height is one inch, we can calculate the new volume using the same formula with the new height.
Original volume of stack = length × width × height = 9 in³New volume of stack with a height of one inch = length × width × 1 in.By comparing the original volume of 9 in³ to the new volume with a height of one inch, you can determine the difference in the amount of sand in the top cone of the hourglass.
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The amount of sand in the top cone when the height of the sand is h is h times the amount of sand there will be when the height of the sand is only one inch.
The volume of a cone is given by the formula:
V = (1/3)πr²h
where r is the radius of the base of the cone and h is the height of the cone.
If the height of the sand in the top cone is currently h, then the volume of the sand in the top cone is:
V₁ = (1/3)πr²h
When the height of the sand in the top cone is only one inch, the volume of the sand in the top cone will be:
V₂ = (1/3)πr²(1 inch)
To compare the two volumes, we can divide V₁ by V₂
V₁ / V₂ = (1/3)πr²h / (1/3)πr²(1 inch)
V₁ / V₂ = h / 1 inch
Therefore, the amount of sand in the top cone when the height of the sand is h is h times the amount of sand there will be when the height of the sand is only one inch.
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write the expression 7b - 3(b - 1) in simplest form
If s = 1 over 2 unit and A = 12s2, what is the value of A, in square units? ____ square unit(s). (Input whole number only.)
Answer:
The value of A is 3 square units.
Step-by-step explanation:
Given: [tex]s=\frac{1}[2}[/tex] unit and A is given by [tex]A=12s^2[/tex]
We have to find the value of A.
Consider the given formula [tex]A=12s^2[/tex]
Put [tex]s=\frac{1}[2}[/tex]
We get,
[tex]A=12(\frac{1}{2})^2[/tex]
Simplify, we have,
[tex]A=12\cdot\frac{1}{4}[/tex]
Further simplify, we have,
[tex]A=3[/tex]
Thus, The value of A is 3 square units.
Prove that the triangles shown below are similar and provide a similarity statement
Natalie picked 135 berries in 15 minutes. If she continues picking at that rate, how many total minutes will it take her to pick 486 berries?
Can you please give a step by step explanation? Thank you.
Help me on this question
NEED HELP ASAP
Which of the following expressions is equivalent to (-7)(-7)(-7)?
3 · -7
-7 · 3
(-7)3
3-7
According to the order of operations, which of the following operations should be completed first in the following expression?
2(5 - 3)^2 + 6^2
multiply (5 - 3) by 2
square (5 - 3)
simplify (5 - 3)
add (5 - 3) to 6^2
Select all that apply.
Which expressions are equal to "five to the third power"?
5^3
3 · 3 · 3 · 3 · 3
5 · 5 · 5
125
15
243
3^5
The expression -8 · -8 · -8 · -8 can be expressed as _____.
-8^4
(-8)^4
-(8^4)
What is the value of -6^2?
-36
36
-12
12
Find the value of |5| - 4(3^2 - 2).
-11
-33
7
-23
Evaluate 8 ÷ -2 · 4^2 + 9.
-100
-55
73
-23
Simplify -5^2 + 8|-1| + (-3).
30
14
-20
-36
Answer:
The answers are solved below.
Step-by-step explanation:
we have to solve the given expressions
Part A: The expression (-7)(-7)(-7)
[tex] (-7)(-7)(-7)=(-1)^37^3[/tex]
Option 3 is correct
Part B: [tex]2(5 - 3)^2 + 6^2[/tex]
First step to solve the above expression is to simplify (5-3) by BODMAS rule then to square the simplification.
Option 3 is correct.
Part C: To choose the expression "five to the third power"
"five to the third power" is
[tex]5^3=5.5.5=125[/tex]
All 3 represents the expression "five to the third power"
Option 1,3,4 are correct.
Part D: The expression -8 · -8 · -8 · -8
The above expression can be written as
[tex](-8)^4[/tex]
Option 2 is correct
Part E: [tex]\text{The value of } -6^2[/tex]
[tex]-6^2=-(6\times 6)=-36[/tex]
Option 1 is correct
Part F: [tex]\text{The value of } |5| - 4(3^2 - 2)[/tex]
[tex]|5| - 4(3^2 - 2)=5-4(9-2)=5-4(7)=5-28=-23[/tex]
Option 4 is correct.
Part G: Evaluate [tex]\frac{8}{ -2}\times 4^2 + 9[/tex]
[tex]\frac{8}{ -2}\times 4^2 + 9=-4\times 16+9=-64+9=-55{ [/tex]
Option 2 is correct.
Part H: Simplify [tex]-5^2 + 8|-1| + (-3)[/tex]
[tex]-5^2 + 8|-1| + (-3)=-25+8-3=-17-3=-20[/tex]
Option 3 is correct.
m/18=24/15
how do I do this problem?
A baseball has a diameter of 5.1 inches. Find the volume of the baseball. Round your answer to the nearest tenth. Use 3.14 for pi
Which expression represents the product of 3 and (5/4 n + 1.8)
The correct expression is:
[tex]\[ \text{C) } 3.75n + 5.4 \][/tex]
To find the product of 3 and [tex]\( \left(\frac{5}{4}n + 1.8\right) \)[/tex] , we multiply 3 by each term inside the parentheses:
[tex]\[ 3 \times \frac{5}{4}n = \frac{15}{4}n \][/tex]
[tex]\[ 3 \times 1.8 = 5.4 \][/tex]
Now, combine the two results:
[tex]\[ \frac{15}{4}n + 5.4 \][/tex]
To express this in a more common form, we can rewrite [tex]\( \frac{15}{4} \)[/tex] as 3.75:
[tex]\[ 3.75n + 5.4 \][/tex]
So, the correct expression is:
[tex]\[ \text{C) } 3.75n + 5.4 \][/tex]
Complete correct question:
Which expression represents the product of 3 and (5/4n + 1.8)?
A) 5.55n
B) 9.15n
C) 3.75n + 1.8
D) 3.75n + 5.4.
how long will it take for the pool to completely full with water? (explain why so i understand)
the number of club members is at least 25
i think your answer is
x(number of club members) is equal(=) or larger(>) to 25
im not sure its right though
What is 56% written as a ratio?
Val’s go cart has a gas tank with the dimensions shown below. He uses a gas can that holds 1 gallon of gas, to fill the go cart tank. 1 gallon = 231 inched cubed
what value is most affected by an outlier, the median or the ranhe? explain. can you see these effects in a dot plot
What is the area of sector GPH? the angle inside the circle measures 80º and the radius from p to h is 15
Answer:
The area of sector GPH is equal to [tex]50\pi\ units^{2}[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=15\ units[/tex]
substitute
[tex]A=\pi(15)^{2}=225 \pi\ units^{2}[/tex]
[tex]360\°[/tex] subtends the complete circle of area [tex]225 \pi\ units^{2}[/tex]
so
By proportion
Find the area of sector GPH
[tex]\frac{225 \pi}{360}\frac{\ units^{2} }{degrees} =\frac{x}{80}\frac{\ units^{2} }{degrees}\\ \\x=80*225\pi /360\\ \\x=50\pi\ units^{2}[/tex]
Could anyone help me with these?
Evan and Sam were playing basketball. Evan made 2/3 of his shots. Sam made 2/4 of his shots. Who made more shots? Explain
harry can water 2 1/4 acres of cornfields in 1 day. How many acres of cornfields can he water in 3 2/3 days
The stem-and-leaf plot represents the distances, in miles, people in an office drive to work each morning.
How many people drive 20 miles or fewer to work?
Enter your answer in the box.
Answer: it is 7.7
Step-by-step explanation:
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Determine if the side lengths 2.1in,4in,7.9in form a triangle
if LuxRide's revenues in London grow by 20% next year, what will their market share be?
Help me asap please !!