Number of fractions
Calculation
How to Make the Denominators the Same
How to make the denominators of two fractions the same:
1. If one of the fractions is mixed (has an integer part), it is necessary to convert such a fraction into an improper one (represent the numerator as the product of the integer part and the denominator plus the numerator, leave the denominator the same).
2. Calculate the LCM of the denominators of fractions.
3. Calculate additional factors for each fraction by dividing the LCM by the denominator of each fraction.
4. Multiply the numerator and denominator of each fraction by its additional factor.
Let's give an example, let's make the denominators of two fractions the same:
Convert the mixed fraction $5\u2064\frac{6}{7}$ to an improper fraction:
$5\u2064\frac{6}{7}$$=$$\mathrm{}\u2064\frac{\mathrm{(5\; \xb7\; 7)\; +\; 6}}{7}$$=$$\mathrm{}\u2064\frac{41}{7}$
Convert the mixed fraction $2\u2064\frac{1}{9}$ to an improper fraction:
$2\u2064\frac{1}{9}$$=$$\mathrm{}\u2064\frac{\mathrm{(2\; \xb7\; 9)\; +\; 1}}{9}$$=$$\mathrm{}\u2064\frac{19}{9}$
Calculate the least common multiple LCM(7, 9)
LCM(7, 9) = 63
We calculate additional factors for each fraction, for this we divide LCM by the denominators of each of the fractions:
63 : 7 = 9 (factor of fraction 1)
63 : 9 = 7 (factor of fraction 2)
We multiply the numerator and denominator of each fraction by an additional factor of this fraction:
$\mathrm{}\u2064\frac{41}{7}$$=$$\mathrm{}\u2064\frac{\mathrm{41\; \xb7\; 9}}{\mathrm{7\; \xb7\; 9}}$$=$$\mathrm{}\u2064\frac{369}{63}$$\mathrm{}\u2064\frac{19}{9}$$=$$\mathrm{}\u2064\frac{\mathrm{19\; \xb7\; 7}}{\mathrm{7\; \xb7\; 7}}$$=$$\mathrm{}\u2064\frac{133}{63}$Result$5\u2064\frac{6}{7}$$=$$\mathrm{}\u2064\frac{41}{7}$$=$$\mathrm{}\u2064\frac{369}{63}$$2\u2064\frac{1}{9}$$=$$\mathrm{}\u2064\frac{19}{9}$$=$$\mathrm{}\u2064\frac{133}{63}$