1.5.2 Switching Numbers and Negating on Subtraction

Far too common, students make a mistake when subtracting two fractions whose result is a negative answer. An example of this is 456−1011124 \frac{5}{6} - 10 \frac{11}{12}. Most of the time, it is incredibly easier switching the order of the subtraction then negating the answer. Taking the above problem as an example:

456−101112=−(101112−456)4 \frac{5}{6} - 10 \frac{11}{12} = -(10 \frac{11}{12} - 4 \frac{5}{6}) =−(101112−41012)= -(10 \frac{11}{12} - 4 \frac{10}{12}) =−(6112)= -(6 \frac{1}{12})

Here is another example to illustrate the same point:

256−423=−(423−256)2 \frac{5}{6} - 4 \frac{2}{3} = -(4 \frac{2}{3} - 2 \frac{5}{6}) =−(446−256)= -(4 \frac{4}{6} - 2 \frac{5}{6}) =−(156)= -(1 \frac{5}{6})

Problem Set 1.5.2

223−3562 \frac{2}{3} - 3 \frac{5}{6}
423−6354 \frac{2}{3} - 6 \frac{3}{5}
159−3591 \frac{5}{9} - 3 \frac{5}{9}
234−4352 \frac{3}{4} - 4 \frac{3}{5}
137−31 \frac{3}{7} - 3
238−3142 \frac{3}{8} - 3 \frac{1}{4}
234−6782 \frac{3}{4} - 6 \frac{7}{8}
345−89103 \frac{4}{5} - 8 \frac{9}{10}
349−5133 \frac{4}{9} - 5 \frac{1}{3}
567−1213145 \frac{6}{7} - 12 \frac{13}{14}
316−6133 \frac{1}{6} - 6 \frac{1}{3}
256−4232 \frac{5}{6} - 4 \frac{2}{3}
478−1223244 \frac{7}{8} - 12 \frac{23}{24}
456−1011124 \frac{5}{6} - 10 \frac{11}{12}
235−71102 \frac{3}{5} - 7 \frac{1}{10}
145−3251 \frac{4}{5} - 3 \frac{2}{5}