t. $$ 6 \frac{2}{5} imes \frac{3}{35} \div \frac{1}{7}+4 \frac{5}{6} \div \frac{1}{6} $$

Question

t. $$ 6 \frac{2}{5} 	imes \frac{3}{35} \div \frac{1}{7}+4 \frac{5}{6} \div \frac{1}{6} $$

UpStudy AI · Accepted Answer

Convert the mixed numbers to improper fractions:

$$
6\frac{2}{5} = \frac{6 \times 5 + 2}{5} = \frac{30+2}{5} = \frac{32}{5},
$$
$$
4\frac{5}{6} = \frac{4 \times 6 + 5}{6} = \frac{24+5}{6} = \frac{29}{6}.
$$

Rewrite the expression:

$$
\frac{32}{5} \times \frac{3}{35} \div \frac{1}{7} + \frac{29}{6} \div \frac{1}{6}.
$$

Handle the first part:

1. Multiply first, then divide:

$$
\frac{32}{5} \times \frac{3}{35} = \frac{32 \times 3}{5 \times 35} = \frac{96}{175}.
$$

2. Divide by $$\frac{1}{7}$$ (which is equivalent to multiplying by the reciprocal):

$$
\frac{96}{175} \div \frac{1}{7} = \frac{96}{175} \times \frac{7}{1} = \frac{96 \times 7}{175} = \frac{672}{175}.
$$

Reduce the fraction $$\frac{672}{175}$$:

Notice that both numerator and denominator are divisible by 7:

$$
\frac{672 \div 7}{175 \div 7} = \frac{96}{25}.
$$

Now, handle the second part:

$$
\frac{29}{6} \div \frac{1}{6} = \frac{29}{6} \times \frac{6}{1} = \frac{29 \times 6}{6} = 29.
$$

Combine both parts:

$$
\frac{96}{25} + 29.
$$

Express $$29$$ with denominator $$25$$:

$$
29 = \frac{29 \times 25}{25} = \frac{725}{25}.
$$

Now add the fractions:

$$
\frac{96}{25} + \frac{725}{25} = \frac{96+725}{25} = \frac{821}{25}.
$$

Convert $$\frac{821}{25}$$ to a mixed number:

Divide $$821$$ by $$25$$:

$$
25 \times 32 = 800,\quad 821-800 = 21.
$$

Thus,

$$
\frac{821}{25} = 32\frac{21}{25}.
$$

The final answer is:

$$
32\frac{21}{25}.
$$
The final answer is $$32\frac{21}{25}$$.

t. \( 6 \frac{2}{5} \times \frac{3}{35} \div \frac{1}{7}+4 \frac{5}{6} \div \frac{1}{6} \)

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