Using partial quotients for division is helpful as it simplifies division into easier to manage multiplication and subtraction problems, enhances intuitive and mental math skills, and allows students to verify their answers easily.
Explanation:Using partial quotients when dividing can be helpful because this method turns a complex division problem into a series of simpler multiplication and subtraction problems. Unlike traditional long division that requires more complex, multiple-digit calculations, partial quotients approach the division process by allowing the student to subtract multiples of the divisor from the dividend in parts. This can be intuitive and less intimidating for students as they can work with smaller, more manageable numbers.
Partial quotients also allow for flexible thinking in mathematics. One can use estimates and adjust them in subsequent steps if necessary. This builds a deeper understanding of the division process instead of just rote procedure-following, and develops estimation and mental math skills over time. Moreover, it provides a clear pathway to check the work by adding the partial quotients, enhancing the student's ability to verify their own answers, and reinforcing the relationship between multiplication and division.
In practice, breaking down a division problem into smaller parts makes solving complex calculations more accessible and can be considered a shortcut that streamlines the division process. As such, this technique can be especially useful when dealing with larger numbers where traditional methods could become cumbersome. It introduces students to the concept of approximation, which is a valuable skill in both mathematics and real-life problem-solving scenarios.
A rectangle is 15 cm long. Find the area and perimeter of the rectangle if it's width is 3/5 of the length
The area of the rectangle is 135 [tex]cm^{2}[/tex], and the perimeter is 48 cm, given that the width is 3 / 5 of the rectangle's length which is 15 cm.
To find the area and perimeter of a rectangle where the width is 3/5 of the length, we apply the formulas. First, calculate the width:
Width = 3 / 5 × Length
Width = 3 / 5 × 15
Width = 9 cm
Now, calculate the area:
Area = Length × Width
Area = 15 cm × 9 cm
Area = 135 cm²
Next, calculate the perimeter:
Perimeter = 2 x (Length + Width)
Perimeter = 2 x (15 cm + 9 cm) = 2 x (24 cm)
Perimeter = 48 cm
The area of the rectangle is 135 cm2, and the perimeter is 48 cm.
a golf practice range has 245 balls. the owner bought a carton of golf ball. how many golf balls does the owner have after buying the carton? 12 balls ti a box 15 boxes to a crate 5 crates to a carton
how many 2/3 cup servings are in a 4 cup container of food
Final answer:
To find out how many 2/3 cup servings are in a 4 cup container, divide 4 by 2/3, resulting in 6 servings.
Explanation:
The question is about determining how many 2/3 cup servings are in a 4 cup container of food. To find the answer, you divide the total amount of the container by the serving size. So, you divide 4 cups by 2/3 cup.
Calculation:
1 cup / (2/3 cup) = 3/2 servings
4 cups * (3/2 servings) = 6 servings
Therefore, you can fit 6 servings of 2/3 cup each in a 4 cup container.
What is 30% of 32.95
doors for the small cabinets are 11.5 inches long. doors for the large cabinets are 2.3 times as long as the doors for the small cabinets. how many large doors can be cut from a board that is 10 1/2 feet long?
Answer:
The answer to this problem is 2.52.
A vat of orange juice was 26 pints. If you wanted to pour the vat into 3 glasses with the same amount in each glass, how many pints would be in each glass?
Last year 950 people attended a town's annual parade. This year 1,520 people attended. What was the percent increase in attendance from last year's to this year?
Two similar vases have heights which are in the ratio 3 : 2.
(a) The volume of the larger vase is 1080 cm cube. Calculate the volume of the smaller vase.
(b) The surface area of the smaller vase is 252cm square. Calculate the surface area of the larger vase.
Answer:
a). Volume of the smaller vase = 320 cm³
b). Surface area of the larger vase = 567 cm²
Step-by-step explanation:
When we calculate the volume of any figure we multiply it's three dimensions either length, width, height or we do the cube of the radius (r×r×r=r³).
In other words volume is a three dimensional figure and surface area is two dimensional.
Therefore, ratio of volumes of two similar structures will be the ratio of cube of one side given.
a). [tex]\frac{V_{1}}{V_{2} }=(\frac{Side 1}{Side2})^{3}[/tex]
[tex]\frac{V_{1}}{V_{2} }=(\frac{3}{2})^{3}[/tex]
[tex]\frac{1080}{V_{2} }=(\frac{3}{2})^{3}[/tex]
[tex]\frac{1080}{V_{2} }=(\frac{27}{8})[/tex]
[tex]27V_{2}=8\times 1080[/tex]
[tex]V_{2}=\frac{8640}{27}[/tex]
[tex]V_{2}=320[/tex] cm³
b). Similarly ratio of the surface area of two vase will be
[tex]\frac{A_{1}}{A_{2} }=(\frac{Side 1}{Side2})^{2}[/tex]
[tex]\frac{A_{1}}{252}=(\frac{3}{2})^{2}[/tex]
[tex]\frac{A_{1}}{252}=(\frac{9}{4})[/tex]
[tex]A_{1}=\frac{9\times 252}{4}[/tex]
[tex]A_{1}=567[/tex] cm²
How many times can 80 go into 467
Find two positive fractions with a quotient of 5/6. Give the equivalent multiplication sentence.
3+4(10-8)? I have to simplify
The simplified form of the expression 3 + 4(10 - 8) is 11.
Here, we have,
To simplify the expression 3 + 4(10 - 8), you can follow the order of operations, which is often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):
Step 1:
Start by evaluating the expression inside the parentheses: 10 - 8 = 2.
Now, the expression becomes 3 + 4(2).
Step 2:
Next, perform the multiplication: 4 * 2 = 8.
The expression now becomes 3 + 8.
Step 3:
Finally, perform the addition: 3 + 8 = 11.
Therefore, the simplified form of the expression 3 + 4(10 - 8) is 11.
To learn more on Expression click:
brainly.com/question/14083225
#SPJ6
20 to 25 percent change
Reid ate 1/4 of the pumpkin pie. Vince ate 1/3 of the same pie. how much of the pie was left after Reid and Vince ate their pieces?
write a numerator that makes the statement true..
two-fifths of a number is decreased by three.find the value of the expression if the number is twenty five
larry can buy 2 1/2 pounds of chicken for 10.00 how meany pounds of chicken can he but for 1.00 btw the 2 is on the side of the 1/2
Which of the following rational numbers is equivalent to a terminating decimal
A sail on a sailboat is a triangle with two sides perpendicular and each side is a different length. What are the two terms that could be used to describe the sail?
Base of the Sail is 12 feet and Height of the Sail is 5 feet
What is Right Angle Triangle?A right triangle or right-angled triangle, or more technically an orthogonal triangle, historically known as a rectangled triangle, is a triangle with one right angle (that is, a 90-degree angle) and two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.
here, we have,
Solution:
According to the Question,
Let, Base = x and Height = y
x = 7 + y
Using the Pythagorous Theorem
a^2 + b^2 = c^2
Using the above mentioned relation
49 + y^2 + 14y + y^2 = 169
2y^2 + 14y - 120 = 0
Discriminant = 34
y = 5, -12
The length of a sail can not be negative, therefore y = 5
From the equation 1, x = 12
To learn more about Right Angle Triangle from the given link
brainly.com/question/64787
#SPJ3
PLZ HELP ME!!!!!!!!!!
Which equation represents this situation?
José worked 2.5 hours more than William. Together, they worked a total of 22 hours. William worked h hours.
h+2.4=22h+2.4=22
h+5=22h+5=22
h+(h+2.5)=22h+(h+2.5)=22
h+(h−2.5)=22
The equation represents the given situation is h+h+2.5=22. Therefore, option C is the correct answer.
Given that, José worked 2.5 hours more than William. Together, they worked a total of 22 hours.
We need to find which equation represents this situation.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
William worked h hours.
Now, number of hours Jose worked = h+2.5
h+h+2.5=22
⇒2h+2.5=22
⇒2h=22-2.5
⇒2h=19.5
⇒h=9.75 hours
The equation represents the given situation is h+h+2.5=22. Therefore, option C is the correct answer.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
More the 50 but less than 70 with multiples of 4 and 7
the chess club has 50 members. they want to raise $680 for a trip to a competition. The school will give $130. how much must each member pay?
Find 5/6 of 15. Express your answer in simplest form.
To find 5/6 of 15, you convert the whole number 15 into a fraction (15/1) and then multiply the numerators and denominators. This results in the fraction 75/6 which simplifies to 12.5.
Explanation:The subject of this question is finding 5/6 of 15. This is a simple multiplication problem that involves fractions.
To solve this, you must multiply the fraction with the whole number. The calculation is as follows:
Write the whole number 15 as a fraction, which would be 15/1.Multiply the numerator (top) of each fraction with each other and do the same with the denominators (bottom). This will give you a new fraction.So, (5 * 15) / (6 * 1) equals 75/6.Simplify the result by dividing 75 by 6. The result is 12.5.Learn more about Fractions here:https://brainly.com/question/10354322
#SPJ12
Final answer:
To find 5/6 of 15, multiply 5/6 by 15/1 to get 75/6, which simplifies to 25/2 or 12.5 in decimal form.
Explanation:
To find 5/6 of 15, we can approach the problem in a straightforward manner by multiplying 5/6 by 15. Here are the steps to do this:
First, express the number 15 as a fraction by putting it over 1, so it becomes 15/1.Next, multiply the numerators (top numbers) of the fractions together: 5 times 15 equals 75.Then, multiply the denominators (bottom numbers) of the fractions together: 6 times 1 equals 6.The result of multiplication gives you 75/6.Now, to simplify the fraction, divide both the numerator and the denominator by their greatest common divisor, which in this case is 3.75 divided by 3 equals 25, and 6 divided by 3 equals 2.Therefore, the simplified result is 25/2, which is the same as 12.5 when expressed as a decimal.The answer in simplest form is 25/2 or 12.5.
I don't understand slope intercept or how to calculate it. Can you simplify it for me being as specific as possible? What do I do?
What is a division problem that has a quotient of 8 with a remainder of 11
how many fossil kits with 10 samples each have the same number of fossils as 30 fossi; kits with 8 samples each?
Answer:
24 fossil kits
Step-by-step explanation:
30 fossil kits with 8 samples in each of them would have a total of :
[tex]30*8=240[/tex] samples
The other one has 10 samples per kit, so to have 240 samples, the number of fossil kits needed would be:
[tex]\frac{240}{10}=24[/tex] kits
What is 11x15=? I do not know what it is can you help me
How many thirds are in - 4 2/3
The number of thirds in ( -4 2/3 ) is given by the equation A = -14
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number be represented as n
And , the value of n = - 4 2/3
On simplifying the equation , we get
n = ( -12 -2 ) / 3
n = -14/3
Now , the number of thirds in the number n is A = n / ( 1/3 )
Substituting the values in the equation , we get
A = ( -14/3 ) / ( 1/3 )
On simplifying the equation , we get
A = -14
Hence , the equation is A = -14
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
solve and SHOW WORK
A fax machine can transmit 48 pages in 6 minutes.
a.) How many pages can the fax machine transmit per minute?
b.) How many pages can the fax machine transmit in 10 minutes?
three diferent fractions that are all equivalent to 2/3 and that have an odd denominator list three fractions that the students might have given
PV = nRT
Solve the formula for the BOLD variable. Bold variable is T