Question

use the distributive property of multiplication of rational numbers over their addition and subtraction and simplify the following

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Answer 1

Answer:

1) $\frac{12}{75}$

2) $-24$

3) $\frac{-248}{105}$

Step-by-step explanation:

1)

$\frac{4}{5} (\frac{-6}{5}+\frac{21}{15} )\\\\=>(\frac{4}{5} )(\frac{-6}{5})+(\frac{4}{5} )(\frac{21}{15})\\\\=>\frac{-24}{25}+\frac{84}{75}\\\\=> \frac{-72+84}{75} \\\\=>\frac{12}{75}$

2)

$\\\frac{5}{7} (-10+\frac{2}{5} )\\\\=>(\frac{5}{7})(-10)+(\frac{5}{7})(\frac{2}{5})\\\\=>\frac{-50}{7}+\frac{2}{7}\\\\=>\frac{-48}{2}\\\\=>-24$

3)

$2 {\frac{2}{3} } (\frac{-2}{5}-\frac{4}{7} )\\\\=>{\frac{8}{3} } (\frac{-2}{5}-\frac{4}{7} )\\\\=>({\frac{8}{3} })(\frac{-2}{5})-({\frac{8}{3} })(\frac{4}{7} )\\\\=>\frac{-16}{15}-\frac{24}{21} \\\\=>\frac{-80-168}{105} \\\\=>-\frac{248}{105}$