13. Higher Order Thinking Mark decomposed $$ \frac{5}{6} $$ into three fractions. None of the fractions had a denominator of 6 . What fractions might Mark have used? Remember, you can use equivalent fractions.

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To decompose $$ \frac{5}{6} $$ into three fractions without using a denominator of 6, we can explore various combinations of fractions with different denominators. Here are a few possible ways Mark might have done this:

### **1. Using Denominators 2, 4, and 12**
$$
\frac{1}{2} + \frac{1}{4} + \frac{1}{12} = \frac{6}{12} + \frac{3}{12} + \frac{1}{12} = \frac{10}{12} = \frac{5}{6}
$$
**Fractions Used:** $$ \frac{1}{2} $$, $$ \frac{1}{4} $$, $$ \frac{1}{12} $$

### **2. Using Denominators 3 and 4**
$$
\frac{1}{3} + \frac{1}{4} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} + \frac{3}{12} = \frac{10}{12} = \frac{5}{6}
$$
**Fractions Used:** $$ \frac{1}{3} $$, $$ \frac{1}{4} $$, $$ \frac{1}{4} $$

### **3. Using Denominators 3, 5, and 10**
$$
\frac{1}{3} + \frac{1}{5} + \frac{3}{10} = \frac{10}{30} + \frac{6}{30} + \frac{9}{30} = \frac{25}{30} = \frac{5}{6}
$$
**Fractions Used:** $$ \frac{1}{3} $$, $$ \frac{1}{5} $$, $$ \frac{3}{10} $$

These are just a few examples of how $$ \frac{5}{6} $$ can be broken down into three fractions without any of them having a denominator of 6. You can create other valid combinations by selecting different fractions that add up to $$ \frac{5}{6} $$ while ensuring none have a denominator of 6.
Mark might have used fractions like $$ \frac{1}{2} $$, $$ \frac{1}{4} $$, and $$ \frac{1}{12} $$ to decompose $$ \frac{5}{6} $$ without any denominator being 6.

13. Higher Order Thinking Mark decomposed \( \frac{5}{6} \) into three fractions. None of the fractions had a denominator of 6 . What fractions might Mark have used? Remember, you can use equivalent fractions.

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