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2 years ago

Multiply 58x7. Enter your answers in the boxes to complete the area model, 7 58 x 7 =

Mathematics

2 answers:

zubka84 [21]2 years ago

8 0

Answer:

$7 \times 58 = 406$

Nina [5.8K]2 years ago

3 0

In mathematics, an area model is a rectangular diagram or model used for multiplication and division problems, in which the factors or the quotient and divisor define the length and width of the rectangle.

We can break one large area of the rectangle into several smaller boxes, using number bonds, to make the calculation easier. Then we add to get the area of the whole, which is the product or quotient.

To multiply two 2-digit numbers, using the area model, follow the given steps:

Write the multiplicands in expanded form as tens and ones.

For example, 27 as 20 and 7, and 35 as 30 and 5.

Draw a 2 × 2 grid, that is, a box with 2 rows and 2 columns.

Write the terms of one of the multiplicands on the top of the grid (box). One on the top of each cell.

On the left of the grid, write the terms of the other multiplicand. One on the side of each cell.

Write the product of the number on the tens in the first cell. Then write the product of the tens and ones in the second and third cell. Write the product of the ones in the fourth cell.

write the product in the cell

Finally, add all the partial products to get the final product.
Here, for example, the area model has been used to multiply 27 and 35.

area model multiplication

Let us see how to find the product of 3-digit number by a 2-digit number using the area model.

Find the Product using Area Model

Let us now use the area model for the division. Here, we divide 825 by 5.

Area Model Division 1

Area Model Division 2

Fun Facts

The area model is also known as the box model.

The area model of solving multiplication and division problems is derived from the concept of finding the area of a rectangle. Area of a rectangle = Length × Width.

So I think the answer would be 406?

Goodluck!!!

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In isosceles right triangle ABC, point is on hypotenuse \overline{BC} such that \overline{AD} is an altitude of \triangle ABC an

Dmitriy789 [7]

Answer:

Area of triangle is 25.

Step-by-step explanation:

We have been given an isosceles right triangle

Isosceles triangle is the triangle having two sides equal.

Figure is shown in attachment

By Pythagoras theorem

$BC^2=AC^2+AB^2$

AD is altitude which divides the triangle into two parts

DC=5 implies BC =10 since D equally divides BC

Let AC=a implies AB=a being Isosceles

On substituting the values in the Pythagoras theorem:

$10^2=a^2+a^2$

$100=2a^2$

$\Rightarrow a^2=50$

$\Rightarrow a=\pm5\sqrt{2}$

WE can find area of right triangle by considering height AB and AD

Area of triangle ABC is:

$\frac{1}{2}\cdot BC\cdot AD$ (1)

$\Rightarrow \frac{1}{2}\cdot 10\cdot AD$

And other method of area of triangle is:

$\frac{1}{2}\cdot AB\cdot BC$ (2)

Equating (1) and (2) we get:

$\frac{1}{2}\cdot 10\cdot AD=\frac{1}{2}\cdot a\cdot a$

$\Rightarrow AD=\frac{a^2}{10}$

$\Rightarrow AD=\frac{50}{10}=5$

Using area of triangle is: $\frac{1}{2}\cdot BC\cdot AD$

Now, the area of triangle ABC= $\frac{1}{2}\cdot 5\cdot 10$

$\Rightarrow 25$

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3 years ago

Midpoint is the center point on the line segment <br> True or false?

Mariana [72]

Your Answer should be True

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3 years ago

F(x)= 25 + 4x How would you solve this please show your work. ASAP

kvv77 [185]

Ok so f(x) really just means y so ur equation is
y=4x+25

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3 years ago

Select all the expressions which have 3 as the greatest common factor of the terms.

Natalija [7]

Answer:

b+3+6c, 27n+66p ,12x + 75y + 21

Step-by-step explanation:

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3 years ago

Read 2 more answers

Let’s pretend that we want to give our employees in total a28% raise in the next two years, but we want to spread out aconsisten

Roman55 [17]

Solution

- The solution steps are given below:

$\begin{gathered} \text{ Let the original amount be X} \\ \\ \text{ If we want a 28\% raise over the next two years, then it means that the amount will be:} \\ X+\frac{28}{100}X=1.28X \\ \\ \text{ If we want to give them a consistent raise each year, we can compute the scenario as follows:} \\ \text{ Let the percentage be }y \\ \\ X+y\%\text{ of }X=\text{ Salary after first year} \\ \\ (X+y\%\text{ of }X)+y\%\text{ of }(X+y\%\text{ of }X)\text{ = Salary after second year.} \\ \\ \text{ But we already know that the salary after second year is }1.28X \\ \text{ Thus, we can say:} \\ (X+y\%\text{ of }X)+y\%\text{ of }(X+y\%\text{ of }X)=1.28X \\ \\ \text{ Simplifying, we have:} \\ X+\frac{yX}{100}+\frac{y}{100}(X+\frac{yX}{100})=1.28X \\ \\ \text{ Divide through by }X \\ 1+\frac{y}{100}+\frac{y}{100}(1+\frac{y}{100})=1.28 \\ \\ \text{ Subtract 1 from both sides and expand the brackets} \\ \frac{y}{100}+\frac{y}{100}+(\frac{y}{100})^2=1.28-1=0.28 \\ \\ \frac{2y}{100}+(\frac{y}{100})^2=0.28 \\ \\ \text{ Multiply both sides by }100^2 \\ 200y+y^2=2800 \\ \\ \text{ Rewrite, we have:} \\ y^2+200y-2800=0 \\ \\ Solving\text{ the equation using the Quadratic formula, we have that:} \\ y=\frac{-200\pm\sqrt{200^2-4(-2800)}(1)}{2(1)} \\ \\ y=-213.137\text{ or }13.137 \\ \\ \text{ Since the change in salary is an increase, thus, the rate }y\text{ has to be positive.} \\ \text{ Thus, } \\ y=13.137\approx13.14\% \\ \\ \end{gathered}$

Final Answer

y = 13.14%

The screenshots of the solution are:

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10 months ago