Mathematical expressions with their pronounciations

1.        The mathematical expression is :

The sum of two even numbers is even

Suppose M and N are even numbers. Then, by the definition of even number, each of these is twice some integer. Thus M = 2k and N = 2l for some integers k and l. We need to show that the sum of these numbers is even, and that means that the sum must also be shown to be twice some integer. We do that as follows:

M + N       = 2k + 2l

= 2(k + l)

The pronounciation is :

The sum of two even numbers is even

Suppose M and N are even numbers. Then, by the definition of even number, each of these is twice some integer. Thus M = twice k and N = twice l for some integers k and l. We need to show that the sum of these numbers is even, and that means that the sum must also be shown to be twice some integer. We do that as follows:

M plus N equals twice k plus twice l also equals twice (k plus l)

2.        The mathematical expression is :

The product of two odd numbers is odd

Suppose M and N are odd integers. Then by the definition of odd number, each of these is one more than an even number. That is, M = 2k + 1 and N = 2l + 1 for some integers k and l. We need to show that MN is odd. That is, it is of the form 2m+ 1 for some integer m. But

M         = (2k + 1) (2l + 1)

 = 4kl + 2l + 2k + 1

 = 2(2kl + l + k) + 1

 = 2m+ 1

where m= 2kl + l + k. Thus the product of two odd numbers is odd.

The pronounciation is :

Suppose M and N are odd integers. Then by the definition of odd number, each of these is one more than an even number. That is, M equals twice k plus 1 and N equals twice l pus 1 for some integers k and l. We need to show that MN is odd. That is, it is of the form twice m plus 1 for some integer m. But

M equals (twice k plus 1) times ( twice l plus 1) equals four times kl plus twice l plus twice k plus 1 equals twice (twice kl plus l plus k) plus 1 equals twice m plus 1

where m is twice kl plus l plus k. Thus the product of two odd numbers is odd.

3.        The mathematical expression is

(u + v)³ + p(u + v)

= (u³ + v³) + 3uv(u + v) + p(u + v), which by factoring out u + v yields

= (u³ + v³) + (u + v)(3uv + p).

The pronounciation is :

(u plus v) cubic plus p times (u plus v)

equals (u cubic plus v cubic) plus three times uv times (u plus v) plus p times (u plus v), which by factoring out u plus v yields

equal to (u cubic plus v plus) plus (u plus v) times (three times uv plus p).

4.        The mathematical expression is :

So the pronounciation is :

Area of the quarter circle per area of the square equals a quarter pi

5.        The mathematical expresssion is

So the pronounciation will be :

C square equals a square plus twice ab cos c

6.        The mathematical expression is :

The pronounciation is :

Cos c equals a square plus b square minus c square per twice ab

7.        The mathematical expression is :

The pronounciation is :

Sin (alpha plus beta) equals sin alpha cos beta plus cos alpha sin beta

8.        The mathematical expression is :

The area, A, of a triangle with sides a, b, and c is given by

where s is half the perimeter of the triangle; that is, where

So the pronounciation is :

The area, A, of a triangle with sides a, b, and c is given by

A is square root of s times (s minus a) times (s minus b) times (s minus c)

where s is half the perimeter of the triangle; that is, where s is a half of the sum of a, b, c

9.        The mathematical expression is :

The pronounciation is :

Six times five minus ( a half of three times three plus a half of three times five plus a half of two times six ) equals twelve

10.    The mathematical expression is :

The pronounciation is :

Three plus four is less than five plus six