Rekenen met variabelen *: Optellen en aftrekken van breuken *
Addition and subtraction of fractions
Both the sum and the difference of two rational numbers is a rational number.
Addition of fractions
Let #a#, #b#, #m#, and #n# be integers with #m\ne0# and #n\ne0#.
A general formula for addition of the fractions #\frac{a}{b}# and #\frac{c}{d}# is\[\frac{a}{b}+\frac{c}{d} = \frac{a\cdot d+b\cdot c}{b\cdot d} \tiny.\]
In the case of common denominators, we have\[ \frac{a}{n}+\frac{b}{n}=\frac{a+b}{n}\tiny.\]
A common mistake is adding numerators without common denominators. For example: \[\frac{1}{2}+\frac{1}{3}\ne\frac{2}{5}\tiny.\]
A formula for the subtraction of fractions is obtained from the given formulas by replacing #c# by #-c# in the formula for addition of fractions:
\[\frac{a}{b}-\frac{c}{d} = \frac{a\cdot d-b\cdot c}{b\cdot d} \tiny.\]
The fastest method does this by
- first determining the least common multiple of the two denominators: \(\mathrm{lcm}(11,7)=\frac{11\times 7}{\mathrm{gcd}(11,7)}=\frac{77}{1}=77\),
- next adjusting the numerators accordingly: \(\frac{1}{11}=\frac{1\times 7}{11\times 7}=\frac{7}{77}\) and \(\frac{5}{7}=\frac{5\times 11}{7\times 11}=\frac{55}{77}\).
Or visit omptest.org if jou are taking an OMPT exam.
