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Sandy finished 3/8 of her homework before supper and 4/8 after supper. What fraction of her homework did she finish in total?

Mathematics

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a) What fraction of her homework did Sandy finish in total?

  1. Add the fractions of homework finished before and after supper.

    38+48\frac{3}{8} + \frac{4}{8}
  2. Add the numerators since the denominators are the same.

    3+48=78\frac{3+4}{8} = \frac{7}{8}

    Sandy finished 78\boxed{\frac{7}{8}} of her homework in total.

    b) What fraction of her homework will Sandy still have to do before school the next day?

  3. The total homework is represented by 1 (or 88\frac{8}{8}).

    Subtract the fraction finished from the total.

    1−781 - \frac{7}{8}
  4. Convert 1 to a fraction with a denominator of 8.

    88−78=8−78=18\frac{8}{8} - \frac{7}{8} = \frac{8-7}{8} = \frac{1}{8}

    Sandy will still have 18\boxed{\frac{1}{8}} of her homework to do.


    Hlengiwe has 2582\frac{5}{8} bags of sweets and Craig has 3783\frac{7}{8} bags of sweets. If they combine their sweets, how many bags of sweets will they have together?

  5. Add the mixed numbers.

    Add the whole numbers and the fractions separately.

    258+378=(2+3)+(58+78)2\frac{5}{8} + 3\frac{7}{8} = (2+3) + \left(\frac{5}{8} + \frac{7}{8}\right)
  6. Perform the addition.

    5+5+78=5+1285 + \frac{5+7}{8} = 5 + \frac{12}{8}
  7. Simplify the improper fraction 128\frac{12}{8} to a mixed number.

    128=88+48=1+48=148\frac{12}{8} = \frac{8}{8} + \frac{4}{8} = 1 + \frac{4}{8} = 1\frac{4}{8}
  8. Add this back to the whole number and simplify the fraction part.

    5+148=648=6125 + 1\frac{4}{8} = 6\frac{4}{8} = 6\frac{1}{2}

    They will have 612\boxed{6\frac{1}{2}} bags of sweets together.


    Lucas spent 512\frac{5}{12} of his salary on rent and another 612\frac{6}{12} of his salary on food.

    a) What fraction of his salary did he use for rent and food combined?

  9. Add the fractions of salary spent on rent and food.

    512+612\frac{5}{12} + \frac{6}{12}
  10. Add the numerators since the denominators are the same.

    5+612=1112\frac{5+6}{12} = \frac{11}{12}

    Lucas used 1112\boxed{\frac{11}{12}} of his salary for rent and food combined.

    b) What fraction of his salary was left over after these expenses?

  11. The total salary is represented by 1 (or 1212\frac{12}{12}).

    Subtract the fraction spent from the total.

    1−11121 - \frac{11}{12}
  12. Convert 1 to a fraction with a denominator of 12.

    1212−1112=12−1112=112\frac{12}{12} - \frac{11}{12} = \frac{12-11}{12} = \frac{1}{12}

    Lucas had 112\boxed{\frac{1}{12}} of his salary left over.

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