Compare the relationships of these numbers.

0.045 is ______________ 0.054

 

First convert the mixed fractions into improper fractions as follows:

1 3/5 =\(\frac{\left(5\ast1\right)+3}{5}=\frac{5+3}{5}=\frac{8}{5}\)

2 7/9 =\(\frac{\left(9\ast2\right)+7}{9}=\frac{18+7}{9}=\frac{25}{9}\)

Then, multiply the fractions:

1/2 x 1 3/5 x 2 7/9 =\(\frac{1}{2}\ast\frac{8}{5}\ast\frac{25}{9}=\frac{20}{9}\)

As a mixed fraction\( \frac{20}{9}\) becomes\(2\frac{2}{9}\)

Use 1 pint =16 ounces to convert between pints and ounces

\(34 pints\ast\frac{16 ounces}{1 pint}\ =\ 12 ounces\)

\(\frac{x}{4}=\frac{9}{x}\)

Cross-multiply the above proportion equation

\(x^2=9\ast4\)

\(x^2=36\)

Take square root on both sides

\(\sqrt{x^2}=\sqrt{36}\)

\(x=\pm6 \ (6\ or\ -6)\)

Taking the positive square root, x=6

A ration of the form a:b = c:d is converted to a proportion as \(\frac{a}{b}=\frac{c}{d}\) where b and d are not equal to zero. Now applying the same concept to 3:10=12:X yields,

\(\frac{3}{10}=\frac{12}{X}\)

Find the value of X by cross-product

\(3X=12\ast10\)

Divide both sides by 3

\(\frac{3X}{3}=\frac{120}{3}\)

\(X=40\)

Thus, the value of X is 40.