5) $$ \frac{2}{7}+\frac{1}{5}+\frac{2}{3}+\frac{1}{6} $$

Question

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ 2/7+1/5+2/3+1/6 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{2}{7}+\frac{1}{5}+\frac{2}{3}+\frac{1}{6}$$
- step1: Reduce fractions to a common denominator:
  $$\frac{2	imes 5	imes 2	imes 3}{7	imes 5	imes 2	imes 3}+\frac{7	imes 2	imes 3}{5	imes 7	imes 2	imes 3}+\frac{2	imes 2	imes 7	imes 5}{3	imes 2	imes 7	imes 5}+\frac{35}{6	imes 35}$$
- step2: Multiply the terms:
  $$\frac{2	imes 5	imes 2	imes 3}{210}+\frac{7	imes 2	imes 3}{5	imes 7	imes 2	imes 3}+\frac{2	imes 2	imes 7	imes 5}{3	imes 2	imes 7	imes 5}+\frac{35}{6	imes 35}$$
- step3: Multiply the terms:
  $$\frac{2	imes 5	imes 2	imes 3}{210}+\frac{7	imes 2	imes 3}{210}+\frac{2	imes 2	imes 7	imes 5}{3	imes 2	imes 7	imes 5}+\frac{35}{6	imes 35}$$
- step4: Multiply the terms:
  $$\frac{2	imes 5	imes 2	imes 3}{210}+\frac{7	imes 2	imes 3}{210}+\frac{2	imes 2	imes 7	imes 5}{210}+\frac{35}{6	imes 35}$$
- step5: Multiply the numbers:
  $$\frac{2	imes 5	imes 2	imes 3}{210}+\frac{7	imes 2	imes 3}{210}+\frac{2	imes 2	imes 7	imes 5}{210}+\frac{35}{210}$$
- step6: Transform the expression:
  $$\frac{2	imes 5	imes 2	imes 3+7	imes 2	imes 3+2	imes 2	imes 7	imes 5+35}{210}$$
- step7: Multiply the terms:
  $$\frac{60+7	imes 2	imes 3+2	imes 2	imes 7	imes 5+35}{210}$$
- step8: Multiply the terms:
  $$\frac{60+42+2	imes 2	imes 7	imes 5+35}{210}$$
- step9: Multiply the terms:
  $$\frac{60+42+140+35}{210}$$
- step10: Add the numbers:
  $$\frac{277}{210}$$
La suma de las fracciones dadas es $$ \frac{277}{210} $$ o $$ 1\frac{67}{210} $$ o aproximadamente $$ 1.3\dot{1}9047\dot{6} $$.
La suma de las fracciones es $$ \frac{277}{210} $$ o aproximadamente $$ 1.3190476 $$.

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