To subtract -3.5 from 10 9/10, first convert the mixed number and the decimal to a common form.
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Convert the mixed number 10 9/10 to an improper fraction:
- The whole number part (10) can be converted to a fraction: \( 10 = \frac{10 \times 10}{10} = \frac{100}{10} \).
- Add the fractional part: \[ 10 9/10 = \frac{100}{10} + \frac{9}{10} = \frac{109}{10} \]
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Convert -3.5 to a fraction:
- The decimal -3.5 can be expressed as: \[ -3.5 = -\frac{35}{10} \]
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Subtract the fractions:
- We need to subtract -3.5 (which is -35/10) from 10 9/10 (which is 109/10). Since subtracting a negative is the same as adding: \[ 10 9/10 - (-3.5) = \frac{109}{10} + \frac{35}{10} \]
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Combine the fractions: \[ \frac{109 + 35}{10} = \frac{144}{10} \]
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Convert the improper fraction back to a mixed number:
- Divide 144 by 10, which equals 14 with a remainder of 4. Therefore: \[ \frac{144}{10} = 14 \frac{4}{10} = 14 \frac{2}{5} \text{ (simplifying } \frac{4}{10}\text{)} \]
Thus, \( 10 9/10 - (-3.5) = 14 \frac{2}{5} \).