Lesson 26 Hormework 5. Sean's mother bought \( \frac{3}{4} \mathrm{lb} \) of Gouda cheese and \( \frac{1}{3} \mathrm{lb} \) less of cheddar cheese. How many pounds of cheese did she buy altogether?
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To find the total pounds of cheese Sean's mother bought, first, we need to calculate the weight of the cheddar cheese. Since she bought \( \frac{1}{3} \) lb less than Gouda, we subtract \( \frac{1}{3} \) lb from \( \frac{3}{4} \) lb. We can convert \( \frac{3}{4} \) to have a common denominator with \( \frac{1}{3} \) which is 12: \[ \frac{3}{4} = \frac{9}{12} \quad \text{and} \quad \frac{1}{3} = \frac{4}{12} \] Now subtract the two: \[ \frac{9}{12} - \frac{4}{12} = \frac{5}{12} \text{ lb of cheddar cheese} \] Now, add the weights of both cheeses together: \[ \frac{3}{4} + \frac{5}{12} \] Converting \( \frac{3}{4} \) to twelfths gives: \[ \frac{3}{4} = \frac{9}{12} \] Now add: \[ \frac{9}{12} + \frac{5}{12} = \frac{14}{12} = \frac{7}{6} \text{ lb} \] So, Sean's mother bought \( \frac{7}{6} \) pounds of cheese altogether. That's 1 and \( \frac{1}{6} \) pounds of cheesy goodness!