QQuestionMathematics
QuestionMathematics
Decompose 5 / 6 into three fractions, none of which has a denominator of 6. What fractions did Mark use?
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand the Problem
We need to find three fractions that, when added together, equal $$\frac{5}{6}$$, and none of these fractions can have 6 as a denominator.
Step 3:: Initial Strategy
We'll need to break $$\frac{5}{6}$$ into three fractions that satisfy the conditions.
This requires careful selection of denominators.
Step 4:: First Fraction Selection
Let's choose $$\frac{1}{2}$$ as our first fraction.
- \frac{1}{2} = 0.5
Step 5:: Remaining Value
After subtracting $$\frac{1}{2}$$ from $$\frac{5}{6}$$, we need to find the remaining value:
\frac{5}{6} - \frac{1}{2} = \frac{5}{6} - \frac{3}{6} = \frac{2}{6} = \frac{1}{3}
Step 6:: Second and Third Fractions
- $$\frac{1}{12}
- \frac{1}{4}
Step 7:: Verification
\frac{1}{2} + \frac{1}{4} + \frac{1}{12} = \frac{6}{12} + \frac{3}{12} + \frac{1}{12} = \frac{10}{12} = \frac{5}{6}
Let's verify our decomposition:
Final Answer
Mark used the fractions \frac{1}{2}, \frac{1}{4}, and \frac{1}{12}.
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