Question

are these expression in the correct order. from least to greater

Answer 1

In order to answer this question, we must compute the products.

From left to right, we have

$\frac{3}{4}\times\frac{4}{9}=\frac{3\times4}{4\times9}=\frac{3}{9}=\frac{1}{3}$

the second expression is

$\frac{7}{7}\times\frac{4}{9}=1\times\frac{4}{9}=\frac{4}{9}$

In the third expression, we must convert the mixed fraction form into a simple fraction form

$1\frac{2}{3}=\frac{3\cdot1+2}{3}=\frac{5}{3}$

then, the product is given by

$1\frac{2}{3}\times\frac{4}{9}\Rightarrow\frac{5}{3}\times\frac{4}{9}=\frac{5\times4}{3\times9}=\frac{20}{27}$

And the last expression is

$2\times\frac{4}{9}=\frac{2}{1}\times\frac{4}{9}=\frac{8}{9}$

Then we have the following table:

now, we can use cross-multiplication to compare fractions and find out which is greater.

they both are in order. Now, lets compute the cross multiplication for the others:

Therefore, they are in the correct order.