why the sum of two sides of triangle is greater than the third side and their difference less than the third side

in the triangle ABC
AB + BC > AC
because the straight line is the shortest distance between two points
and by taking away BC from both sides then
AB + BC - BC > AC - BC
AB > AC - BC

imagine math: multiplying mixed numbers

imagine math: multiplying mixed numbers: "when multiplying mixed numbers we first convert them to improper fractions before multiplying , for example"

prime number

a prime number has exactly two positive divisors itself and one .
1)now  is the number zero is a prime number ?
no because the zero divisible by any nonzero number so it has an infinite numbers of divisors
2) is the number one is a prime number ?
no because the number one has one positive divisor is itself
3) is the number two a prime number ?
yes because the number two divisible by one and it self so it has two divisors one and it self and the number two is the only even prime number
so we can define the prime number as it greater than one and has no divisors other than one and itself

multiplying mixed numbers

when multiplying mixed numbers we first convert them to improper fractions before multiplying , for example

mixed number arithmetic

we can add or subtract two mixed numbers in one of two ways
1) first strategy is to add the whole numbers and then to add fractions , for example

2) second strategy is to convert the mixed numbers into improper fractions before adding them , for example

to convert an improper fraction into a mixed number

first we will review the parts of division problem  and the rule is

in an improper fraction the numerator is the dividend and the denominator is the divisor . but in the mixed number the quotient is the whole number and the remainder is the new numerator and the denominator is the divisor
to convert an improper fraction to a mixed number divide the numerator into the denominator and the remainder will be a new numerator and the quotient will be a whole number , for example

mixed numbers and improper fractions

1) what is the improper fraction ?
is a fractions whose numerator is larger than its denominator for example

2) what is the mixed number ?
a mixed number consist of the sum of whole number and a fraction. for example

now we will writing the mixed number as an improper fraction
1)to convert a mixed number  into an improper fraction, we multiply the
whole number by the fraction’s denominator and then add this to the numerator.
The sum is the new numerator.

the rule is
 
2) by another method