Lösung 1.2:4c
Aus Online Mathematik Brückenkurs 1
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Because <math>10=2\cdot 5</math> and <math>4=2\cdot 2</math>, we can cancel out the common factors 2 and 5 and obtain the answer | Because <math>10=2\cdot 5</math> and <math>4=2\cdot 2</math>, we can cancel out the common factors 2 and 5 and obtain the answer | ||
| - | {{Displayed math||<math>\frac{10}{3\cdot 4\cdot 5}=\frac{\rlap{/}2{}\cdot{}\rlap{/}5}{3\cdot 2\cdot{}\rlap{/}2\cdot{}\rlap{/}5}=\frac{1}{6}\,</math>.}} | + | {{Displayed math||<math>\frac{10}{3\cdot 4\cdot 5}=\frac{\rlap{/}2{}\cdot{}\rlap{/}5}{3\cdot 2\cdot{}\rlap{/}2\cdot{}\rlap{/}5}=\frac{1}{3\cdot 2}=\frac{1}{6}\,</math>.}} |
Version vom 12:26, 22. Sep. 2008
Method 1
If we calculate the numerator in the main fraction first, we get
The double fraction on the right-hand side becomes, after multiplying top and bottom by \displaystyle {10}/{3}\,,
Then, we remove the common factor 10,
Method 2
Another way to calculate the expression is to divide it up into two separate terms
We simplify both double fractions on the right-hand side by multiplying top and bottom by 10/3
Instead of multiplying, respectively, by \displaystyle 4\cdot 3 and \displaystyle 5\cdot 3, we keep the numerators factorized and observe that if we multiply the top and bottom of the first fraction by 5 and the second by 4, we obtain the common denominator
Because \displaystyle 10=2\cdot 5 and \displaystyle 4=2\cdot 2, we can cancel out the common factors 2 and 5 and obtain the answer
