Solve 0.75*21/7+3/4*73/7+7.5*1/7

$$0.75 \times 2 \frac{ 1 }{ 7 } + \frac{ 3 }{ 4 } \times 7 \frac{ 3 }{ 7 } +7.5 \times \frac{ 1 }{ 7 }$$

Evaluate

$$8.25$$

Solution Steps

Multiply 2 and 7 to get 14.

$$0.75\times \frac{14+1}{7}+\frac{3}{4}\times \frac{7\times 7+3}{7}+7.5\times \frac{1}{7}$$

Add 14 and 1 to get 15.

$$0.75\times \frac{15}{7}+\frac{3}{4}\times \frac{7\times 7+3}{7}+7.5\times \frac{1}{7}$$

Convert decimal number 0.75 to fraction \frac{75}{100}. Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{3}{4}\times \frac{15}{7}+\frac{3}{4}\times \frac{7\times 7+3}{7}+7.5\times \frac{1}{7}$$

Multiply \frac{3}{4} times \frac{15}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 15}{4\times 7}+\frac{3}{4}\times \frac{7\times 7+3}{7}+7.5\times \frac{1}{7}$$

Do the multiplications in the fraction \frac{3\times 15}{4\times 7}.

$$\frac{45}{28}+\frac{3}{4}\times \frac{7\times 7+3}{7}+7.5\times \frac{1}{7}$$

Multiply 7 and 7 to get 49.

$$\frac{45}{28}+\frac{3}{4}\times \frac{49+3}{7}+7.5\times \frac{1}{7}$$

Add 49 and 3 to get 52.

$$\frac{45}{28}+\frac{3}{4}\times \frac{52}{7}+7.5\times \frac{1}{7}$$

Multiply \frac{3}{4} times \frac{52}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{45}{28}+\frac{3\times 52}{4\times 7}+7.5\times \frac{1}{7}$$

Do the multiplications in the fraction \frac{3\times 52}{4\times 7}.

$$\frac{45}{28}+\frac{156}{28}+7.5\times \frac{1}{7}$$

Since \frac{45}{28} and \frac{156}{28} have the same denominator, add them by adding their numerators.

$$\frac{45+156}{28}+7.5\times \frac{1}{7}$$

Add 45 and 156 to get 201.

$$\frac{201}{28}+7.5\times \frac{1}{7}$$

Convert decimal number 7.5 to fraction \frac{75}{10}. Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

$$\frac{201}{28}+\frac{15}{2}\times \frac{1}{7}$$

Multiply \frac{15}{2} times \frac{1}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{201}{28}+\frac{15\times 1}{2\times 7}$$

Do the multiplications in the fraction \frac{15\times 1}{2\times 7}.

$$\frac{201}{28}+\frac{15}{14}$$

Least common multiple of 28 and 14 is 28. Convert \frac{201}{28} and \frac{15}{14} to fractions with denominator 28.

$$\frac{201}{28}+\frac{30}{28}$$

Since \frac{201}{28} and \frac{30}{28} have the same denominator, add them by adding their numerators.

$$\frac{201+30}{28}$$

Add 201 and 30 to get 231.

$$\frac{231}{28}$$

Reduce the fraction \frac{231}{28} to lowest terms by extracting and canceling out 7.

$$\frac{33}{4}$$

Factor

$$\frac{3 \cdot 11}{2 ^ {2}} = 8\frac{1}{4} = 8.25$$