geno3141

When you start with a ratio like  14:4,

you can write it as a common fraction:  14/4,

and as a common fraction in reduced form:  7/2.

Sometimes, it is valuable to have one of the terms 1, such as 3.5/1.

This ratio would be difficult to write with a numerator of 1, but if the ratio were  4:14,

it could be reduced to 1:3.5.

You would like to have two numbers in your answer, so for 4:14, you probably wouldn't want to write it as a decimal:  0.285714285714...

And, you wouldn't want to write 14:4 as a mixed fraction  3 1/2/ 

You can set up a proportion:  30 girls / n boys  =  3 girls / 7 boys

Cross-multiply:  3 x n  =  30 x 7

                           3n  =  210

                             n  =  70

700 ÷ 20  =  35

5 ^ (1/2)  =  √5

Whole numbers are:  0, 1, 2, 3, 4, ...  (none of these, when squared will give you 5)

Integers:  ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...  (again, none of these, when squared will give you 5)

Rational numbers are common fractions; √5 cannot be written as a common fraction; it can be written as a decimal fraction but the decimal never ends and never repeats; thus, it is an irrational number.

Use '^'.      5^4  =  5 x 5 x 5 x 5  =  625

Distance  =  Rate x Time

6.8 miles  =  (2.72 miles per hour ) x t

    6.8  =  2.72 x t

Divide both sides by 2.72

  6.8 / 2.72  =  t

t  =  2.5 hours

Area of a triangle  =  ½·base·height

                       A  =  ½·(5 2/3)·(3)

                       A  =  8.5 square inches

d^(1/2) = √d

2.5 = (1/4) √d

Multiply both sides times 4:

4 x 2.5  =  4 x (1/4)√d

10  =  √d

To remove a square root, square both sides:

100  =  d

Do you have a particular question?

Let c = weight of cat.

Let d = weight of dog.

      d = 8c                  (the dog weights 8 times as much as the cat)

d + c = 54                  (together, they weigh 54 pounds)

Substitute  8c  for  d  from the first equation into the second equation:

8c + c = 54

      9c = 54

        c = 6

if c = 6, the d= 8c = 8(6) = 48.