dividing

Examples of dividing in the following topics:

• A Divided Korea

• Racial Divides in South Africa

• Dividing the lifespan

  • Human life is often divided into various age spans, like the following:

• The Remainder Theorem and Synthetic Division

  • Synthetic division is a technique for dividing a polynomial and finding the quotient and remainder.
  • It states that the remainder of a polynomial $f(x)$ divided by a linear divisor $(x-a)$ is equal to $f(a)$.
  • Synthetic division only works for polynomials divided by linear expressions with a leading coefficient equal to $1.$
  • Let's use synthetic division to solve the example above $f(x)=x^3−12x^2−42 $ divided by $x-3$:
  • When we divide by $ax-b$ and $a \not = 1$, we can divide by $(x-b/a)$ and then divide the result by $a$.

• Meter

  • In other words, it is a question of division: does each beat divide into two equal parts, or three equal parts.
  • Meters that divide the beat into two equal parts are simple meters; meters that divide the beat into three equal parts are compound meters.
  • Note that because the beat is divided into three in a compound meter, the beat is always three times as long as the division note, and the beat is always dotted.

• The Party in Government

  • Despite the perceived problems of divided government, the President and Congress are often able, out of necessity, to establish an effective working relationship.
  • Divided government is suggested by some to be an undesirable product of the separation of powers in the United States' political system.
  • Earlier in the 20th century, divided government was rare, but since the 1970s it has become increasingly common.
  • Mainly in part due to the Watergate scandal which has popularized the idea that a divided government is a beneficial for the country.
  • Despite the perceived problems of divided government, the President and Congress are often able, out of necessity, to establish an effective working relationship.

• Animal Body Planes and Cavities

  • Vertebrates can be divided along different planes in order to reference the locations of defined cavities.
  • A sagittal plane divides the body into right and left portions.
  • A transverse plane (or, horizontal plane) divides the animal into upper and lower portions.
  • The midsagittal plane divides the body exactly in half into right and left portions.
  • The frontal plane divides the front and back, while the transverse plane divides the body into upper and lower portions.

• Dividing Polynomials

  • Polynomial long division is a method for dividing a polynomial by another polynomial of the same or lower degree.
  • The quotient and remainder can then be determined as follows: Divide the first term of the dividend by the highest term of the divisor (meaning the one with the highest power of $x$, which in this case is $x$): $x^3 \div x = x^2$.
  • Polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree.This method is a generalized version of the familiar arithmetic technique called long division.It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones.
  • Divide the first term of the dividend by the highest term of the divisor (meaning the one with the highest power of $x$, which in this case is $x$): $x^3 \div x = x^2$.

• Division of Complex Numbers

  • We have seen how to add, subtract, and multiply complex numbers, but it remains to learn how to divide them.
  • You are probably already familiar with this concept for ordinary real numbers: dividing by $2$ is the same as multiplying by $\frac12$, dividing by 3 is the same as multiplying by $\frac13$, and so on.
  • So the multiplicative inverse of $z$ must be the complex conjugate of $z$ divided by its modulus squared.
  • Suppose you wanted to divide the complex number $z=2+3i$ by the number $1+2i$.
  • Since dividing by $1+2i$ is the same as multiplying by the multiplicative inverse (which we have seen above is $(1/5)-(2/5)i$), we have:

• Calculating Perpetuities

  • The present value of a perpetuity is simply the payment size divided by the interest rate and there is no future value.
  • The PV is simply the payment size (A) divided by the interest rate (r).
  • Another way to think about it is that for a normal perpetuity, the growth rate is just 0, so the formula boils down to the payment size divided by r.