Example Question - subtracting mixed numbers
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Subtracting Mixed Numbers
The image displays a fraction subtraction problem, which is part (iii) of a larger set of problems. Here's how to solve it: \( 1\frac{1}{5} - 1\frac{2}{3} \) First, convert the mixed numbers into improper fractions to make subtraction easier. For the first number: \( 1\frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5} \) For the second number: \( 1\frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \) Now, subtract the second improper fraction from the first: \( \frac{6}{5} - \frac{5}{3} \) To subtract fractions, they must have a common denominator. The least common multiple (LCM) of the denominators 5 and 3 is 15, so convert each fraction to have the same denominator: \( \frac{6}{5} \times \frac{3}{3} = \frac{18}{15} \) \( \frac{5}{3} \times \frac{5}{5} = \frac{25}{15} \) Now perform the subtraction: \( \frac{18}{15} - \frac{25}{15} = \frac{18 - 25}{15} = \frac{-7}{15} \) The answer is a negative fraction because the second number was larger than the first one. Therefore, \( 1\frac{1}{5} - 1\frac{2}{3} = -\frac{7}{15} \).
Solution to Subtracting Mixed Numbers
To solve the equation given in the image, we must subtract the two mixed numbers. The first mixed number is \(6 \frac{11}{12}\) and the second one is \(4 \frac{1}{3}\). Before we subtract, we should convert these mixed numbers into improper fractions: For \(6 \frac{11}{12}\): \(6 \times 12 = 72\), then add \(11\) for the numerator: \(72 + 11 = 83\). This gives us \( \frac{83}{12} \). For \(4 \frac{1}{3}\): \(4 \times 3 = 12\), then add \(1\) for the numerator: \(12 + 1 = 13\). This gives us \( \frac{13}{3} \). Now let's subtract \( \frac{83}{12} - \frac{13}{3}\). First, we need to find a common denominator. The lowest common denominator for \(12\) and \(3\) is \(12\). Convert \( \frac{13}{3} \) to have a denominator of \(12\): \( \frac{13}{3} \) can be changed by multiplying both the numerator and denominator by \(4\), because \(12\) is \(4\) times \(3\). So, \( \frac{13}{3} \) becomes \( \frac{13 \times 4}{3 \times 4} \), which is \( \frac{52}{12} \). Now we have: \( \frac{83}{12} - \frac{52}{12} = \frac{83 - 52}{12} = \frac{31}{12} \). This improper fraction can be converted back to a mixed number. \(31\) divided by \(12\) gives \(2\) with a remainder of \(7\), hence the mixed number is \(2 \frac{7}{12}\). So the answer to the subtraction is \(2 \frac{7}{12}\), which is the whole number 2 plus the fraction \( \frac{7}{12} \). Since the question seems to ask for a whole number, the answer is \(2\).
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