For this case we must simplify the following expression:
[tex]1 \frac {1} {3}[/tex]÷ [tex]\frac {1} {4}[/tex]+ [tex]\frac {2} {5}[/tex]÷[tex]\frac {1} {4}[/tex]+ [tex]\frac {4} {15}[/tex]÷[tex]\frac {1 }{4}[/tex]
We convert mixed numbers to improper fractions:
[tex]\frac {3 * 1 + 1} {3}[/tex] ÷ [tex]\frac {1} {4}[/tex] + [tex]\frac {2} {5}[/tex]÷[tex]\frac {1} {4}[/tex] + [tex]\frac {4} {15}[/tex] ÷ [tex]\frac {1} {4}[/tex]=
[tex]\frac {4} {3}[/tex] ÷[tex]\frac {1} {4}[/tex]+ [tex]\frac {2} {5}[/tex]÷ [tex]\frac {1} {4}[/tex]+[tex]\frac {4} {15}[/tex]÷[tex]\frac {1} {4}[/tex] =
We first solve the divisions:
[tex]\frac {\frac {4} {3}} {\frac {1} {4}} + \frac {\frac {2} {5}} {\frac {1} {4}} + \frac {\frac {4} {15}} {\frac {1} {4}} =\\\frac {4 * 4} {3 * 1} + \frac {4 * 2} {5 * 1} + \frac {4 * 4} {15 * 1} =\\\frac {16} {3} + \frac {8} {5} + \frac {16} {15} =[/tex]
We rewrite the fractions:
[tex]\frac {16 * 5} {3 * 5} + \frac {8 * 3} {5 * 3} + \frac {16} {15} =\\\frac {80} {15} + \frac {24} {15} + \frac {16} {15} =\\\frac {80 + 24 + 16} {15} =\\\frac {120} {15} =\\\frac {24} {3} =\\8[/tex]
Answer:
8
