For example, if you are calculating 24+14{\displaystyle {\frac {2}{4}}+{\frac {1}{4}}}, you can note that both fractions have the same denominator: 4.
For example, the numerators of 24{\displaystyle {\frac {2}{4}}} and 14{\displaystyle {\frac {1}{4}}} are 2 and 1, so you would calculate 2+1=3{\displaystyle 2+1=3}. So, 3 is the numerator of your sum.
For example, the sum of 24+14{\displaystyle {\frac {2}{4}}+{\frac {1}{4}}} will have a denominator of 4: 24+14=34{\displaystyle {\frac {2}{4}}+{\frac {1}{4}}={\frac {3}{4}}}.
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.
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.
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.
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}.
For example, 45=1620{\displaystyle {\frac {4}{5}}={\frac {16}{20}}}.
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.
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}.
For example, 34=1520{\displaystyle {\frac {3}{4}}={\frac {15}{20}}}.
For example, 16+15=31{\displaystyle 16+15=31}.
For example, 1620+1520=3120{\displaystyle {\frac {16}{20}}+{\frac {15}{20}}={\frac {31}{20}}}.
For example, if simplifying the fraction 2490{\displaystyle {\frac {24}{90}}}, you would calculate that 24=2×2×2×3{\displaystyle 24=2\times 2\times 2\times 3}. So, rewrite the fraction as 2×2×2×390{\displaystyle {\frac {2\times 2\times 2\times 3}{90}}}
For example, if simplifying the fraction 2490{\displaystyle {\frac {24}{90}}}, you would calculate that 90=2×3×3×5{\displaystyle 90=2\times 3\times 3\times 5}. So, rewrite the fraction as 2×2×2×32×3×3×5{\displaystyle {\frac {2\times 2\times 2\times 3}{2\times 3\times 3\times 5}}}.
For example, you can cancel out a 2 and a 3 in the numerator and denominator: 2×2×2×32×3×3×5{\displaystyle {\frac {{\cancel {2\times }}2\times 2{\cancel {\times 3}}}{{\cancel {2\times }}{\cancel {3\times }}3\times 5}}}.
For example:2×2×2×32×3×3×5{\displaystyle {\frac {{\cancel {2\times }}2\times 2{\cancel {\times 3}}}{{\cancel {2\times }}{\cancel {3\times }}3\times 5}}}2×23×5{\displaystyle {\frac {2\times 2}{3\times 5}}} 415{\displaystyle {\frac {4}{15}}}So, the fraction 2490{\displaystyle {\frac {24}{90}}} simplifies to 415{\displaystyle {\frac {4}{15}}}.
