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
