Question

Which steps should be used to compare the tions

[ {22}/{3} ]
and
[ {5}/{6} ]?

a) Find a common numerator.
b) Add the numerators and denominators to determine which sum is larger.
c) Use the greater than" symbol to show which denominator is larger.
d) Multiply the first tion by 2 and the second tion by 3.

Answer 1

To compare the fractions 22/3 and 5/6, find the least common multiple of the denominators and express both fractions with this common denominator. Then, compare the numerators directly to determine which fraction is larger.

Step-by-step explanation:

To compare the fractions <22/3> and <5/6>, we need to use steps that involve finding a common denominator rather than a common numerator or simply adding numerators and denominators. The correct approach is to make the denominators the same to compare the sizes of the two fractions easily. This is usually done by finding the least common multiple (LCM) of the denominators. In our case,

• First, identify the LCM of 3 and 6, which is 6.
• Then, convert each fraction to an equivalent fraction with the LCM as the denominator. For <22/3>, you multiply both the numerator and denominator by 2 to get <44/6>. For <5/6>, no change is needed because it already has the denominator 6.
• Now, you can compare the fractions directly: <44/6> and <5/6>. It's clear that <44/6> is larger because it has a larger numerator.

Another method for comparing fractions, especially if you are comfortable with decimals, is to convert both fractions to their decimal form and then compare the decimals. Whichever method you use, it's important not to add denominators or to try using a common numerator which is not a proper method for comparing fractions.