Ratios

Quantities with same units can be expressed as a ratio in three diff ways:
a or a : b or a to b
b

To write the ratios in simplest form, divide the numerator & the denominator by their GCF

To write fractions in simplest form, multiply the ratio by the LCD (Lowest Common Denominator)

In case of mixed numbers first convert them to improper fractions.
E.g. 4 3 = 31
         7     7

To express the quantities with different units as a ratio, first express them in same units

Now, quantities with same units can be expressed as a ratio in three different ways:
a or a : b or a to b
b

To write the ratio in simplest form, divide the numerator & the denominator by their GCF

To compare quantities with the same units do the following steps:

1) Express the quantities as ratios

Then express the ratios with the same denominators

To do so, multiply the numerators and the denominators of the ratios with an appropriate number such that the denominators become equal to their LCM

Now compare only the numerators of the ratios since the denominators are same