A denominator is the number below the fraction bar.For example, if you are calculating 45+34{\displaystyle {\frac {4}{5}}+{\frac {3}{4}}}, you can note that the fractions have different denominators: 5 and 4.
 A multiple is a number that another number equally divides into. You can also think of a multiple as the result of multiplying a number by a whole number. You are looking for the smallest multiple that the two denominators have in common.For example, the smallest denominator in 45+34{\displaystyle {\frac {4}{5}}+{\frac {3}{4}}} is 4. The first several multiples of 4 are 4, 8, 12, 16, and 20. The smallest of these multiples that 5 shares with 4 is 20. So, 20 is the least common multiple of the two denominators.
 The result will give you a factor of change. This factor tells you how much bigger the common multiple is than the denominator.

For example, if the least common multiple is 20, and the first fraction’s denominator is 5, you would calculate 205=4{\displaystyle {\frac {20}{5}}=4}. That means 4 is the factor of change. The least common multiple is 4 times larger than the denominator.
 Doing this will keep the numerator and denominator of the equivalent fraction in proportion.For example, if the factor of change is 4, and the first fraction’s numerator is 4, you would calculate 4×4=16{\displaystyle 4\times 4=16}.
 The numerator will be the product of the factor of change and the original fraction’s numerator. The denominator will be the least common multiple.

For example, 45=1620{\displaystyle {\frac {4}{5}}={\frac {16}{20}}}.
 The result will give you a factor of change for the second fraction. This factor tells you how much bigger the common multiple is than the denominator.

For example, if the least common multiple is 20, and the second fraction’s denominator is 4, you would calculate 204=5{\displaystyle {\frac {20}{4}}=5}. That means 5 is the factor of change for the second fraction.
 This will give you the numerator of your equivalent fraction.

For example, if the factor of change is 5, and the second fraction’s numerator is 3, you would calculate 5×3=15{\displaystyle 5\times 3=15}.
 The numerator will be the product of the factor of change and the original fraction’s numerator. The denominator will be the least common multiple.

For example, 34=1520{\displaystyle {\frac {3}{4}}={\frac {15}{20}}}.
 Since the equivalent fractions have the same denominator, you can add the numerators as you normally would. For example, 16+15=31{\displaystyle 16+15=31}.
 Make sure you use the common denominator of the equivalent fractions. For example, 1620+1520=3120{\displaystyle {\frac {16}{20}}+{\frac {15}{20}}={\frac {31}{20}}}.
Verify the fractions have different denominators.
List the first several multiples of the smaller denominator.
Divide the first fraction’s denominator into the least common multiple.
Multiply the numerator of the first fraction by the factor of change.
Write the first fraction’s equivalent fraction.
Divide the second fraction’s denominator into the least common multiple.
Multiply the numerator of the second fraction by the factor of change.
Write the second fraction’s equivalent fraction.
Add the numerators of the equivalent fractions.
Place the sum of the numerators over the new denominator.
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