1) $$ \frac{16}{5}-\frac{13}{15}+\frac{29}{30}-\frac{16}{9} $$

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UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ 16/5-13/15+29/30-16/9 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{16}{5}-\frac{13}{15}+\frac{29}{30}-\frac{16}{9}$$
- step1: Reduce fractions to a common denominator:
  $$\frac{16	imes 3	imes 2	imes 3}{5	imes 3	imes 2	imes 3}-\frac{13	imes 2	imes 3}{15	imes 2	imes 3}+\frac{29	imes 3}{30	imes 3}-\frac{16	imes 10}{9	imes 10}$$
- step2: Multiply the terms:
  $$\frac{16	imes 3	imes 2	imes 3}{90}-\frac{13	imes 2	imes 3}{15	imes 2	imes 3}+\frac{29	imes 3}{30	imes 3}-\frac{16	imes 10}{9	imes 10}$$
- step3: Multiply the terms:
  $$\frac{16	imes 3	imes 2	imes 3}{90}-\frac{13	imes 2	imes 3}{90}+\frac{29	imes 3}{30	imes 3}-\frac{16	imes 10}{9	imes 10}$$
- step4: Multiply the numbers:
  $$\frac{16	imes 3	imes 2	imes 3}{90}-\frac{13	imes 2	imes 3}{90}+\frac{29	imes 3}{90}-\frac{16	imes 10}{9	imes 10}$$
- step5: Multiply the numbers:
  $$\frac{16	imes 3	imes 2	imes 3}{90}-\frac{13	imes 2	imes 3}{90}+\frac{29	imes 3}{90}-\frac{16	imes 10}{90}$$
- step6: Transform the expression:
  $$\frac{16	imes 3	imes 2	imes 3-13	imes 2	imes 3+29	imes 3-16	imes 10}{90}$$
- step7: Multiply the terms:
  $$\frac{288-13	imes 2	imes 3+29	imes 3-16	imes 10}{90}$$
- step8: Multiply the terms:
  $$\frac{288-78+29	imes 3-16	imes 10}{90}$$
- step9: Multiply the numbers:
  $$\frac{288-78+87-16	imes 10}{90}$$
- step10: Multiply the numbers:
  $$\frac{288-78+87-160}{90}$$
- step11: Calculate:
  $$\frac{137}{90}$$
La expresión $$ \frac{16}{5}-\frac{13}{15}+\frac{29}{30}-\frac{16}{9} $$ se simplifica a $$ \frac{137}{90} $$ o $$ 1\frac{47}{90} $$ o $$ 1.5\dot{2} $$.
La expresión simplifica a $$ \frac{137}{90} $$ o $$ 1\frac{47}{90} $$ o $$ 1.5\dot{2} $$.

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