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Practice
Adding and Subtracting Mixed Numbers
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Adding and Subtracting Mixed Numbers: Very Difficult Problems with Solutions
Problem 1
[tex]2\frac{1}{9} + 1\frac{1}{6} + 3\frac{3}{5} - 2\frac{2}{3} = ? [/tex]
$4\frac{21}{90}$
$4\frac{19}{90}$
$5\frac{19}{90}$
$5\frac{19}{30}$
Solution:
[tex]2\frac{1}{9} + 1\frac{1}{6} + 3\frac{3}{5} - 2\frac{2}{3} = (2 + 1 + 3 - 2) + (\frac{1}{9} + \frac{1}{6} + \frac{3}{5} - \frac{2}{3}) = 4 + \frac{10 + 15 + 54 - 60}{90} = 4 + \frac{19}{90} = 4\frac{19}{90}[/tex]
Problem 2
If you spend [tex]\frac{1}{4}[/tex] of your salary during the first week of the month and 20% of it during each of the coming 3 weeks, what part(fraction) of your salary will leave unspent at the end of the month?
Solution:
[tex]\frac{1}{4} + 3(\frac{20}{100}) = \frac{1}{4} + \frac{3}{5} = \frac{5+12}{20} = \frac{17}{20}[/tex]
The sallary that will be spent = [tex]\frac{17}{20}[/tex]
Unspend will be = [tex]1 - \frac{17}{20} = \frac{20 - 17}{20} = \frac{3}{20}[/tex]
Problem 3
A father bought fruits for the whole week. The family ate [tex]\frac{1}{8}[/tex] of the fruits per day during the first 4 days, and [tex]\frac{1}{6}[/tex] of the fruits every day till the end of the week. What part of the fruits did they leave for the next week?
Solution:
[tex]4(\frac{1}{8}) + 3(\frac{1}{6}) = \frac{1}{2} + \frac{1}{2} = \frac{1 + 1}{2} = 1 [/tex]
They ate all fruits and nothing left for the next week.
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