Solve 7/35*1/3+8/35*1/2+frac{20}{35}*frac{5}{24}

$$\frac { 7 } { 35 } \cdot \frac { 1 } { 3 } + \frac { 8 } { 35 } \cdot \frac { 1 } { 2 } + \frac { 20 } { 35 } \cdot \frac { 5 } { 24 }$$

Evaluate

$$\frac{3}{10}=0.3$$

Solution Steps

Reduce the fraction \frac{7}{35} to lowest terms by extracting and canceling out 7.

$$\frac{1}{5}\times \frac{1}{3}+\frac{8}{35}\times \frac{1}{2}+\frac{20}{35}\times \frac{5}{24}$$

Multiply \frac{1}{5} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{5\times 3}+\frac{8}{35}\times \frac{1}{2}+\frac{20}{35}\times \frac{5}{24}$$

Do the multiplications in the fraction \frac{1\times 1}{5\times 3}.

$$\frac{1}{15}+\frac{8}{35}\times \frac{1}{2}+\frac{20}{35}\times \frac{5}{24}$$

Multiply \frac{8}{35} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{15}+\frac{8\times 1}{35\times 2}+\frac{20}{35}\times \frac{5}{24}$$

Do the multiplications in the fraction \frac{8\times 1}{35\times 2}.

$$\frac{1}{15}+\frac{8}{70}+\frac{20}{35}\times \frac{5}{24}$$

Reduce the fraction \frac{8}{70} to lowest terms by extracting and canceling out 2.

$$\frac{1}{15}+\frac{4}{35}+\frac{20}{35}\times \frac{5}{24}$$

Least common multiple of 15 and 35 is 105. Convert \frac{1}{15} and \frac{4}{35} to fractions with denominator 105.

$$\frac{7}{105}+\frac{12}{105}+\frac{20}{35}\times \frac{5}{24}$$

Since \frac{7}{105} and \frac{12}{105} have the same denominator, add them by adding their numerators.

$$\frac{7+12}{105}+\frac{20}{35}\times \frac{5}{24}$$

Add 7 and 12 to get 19.

$$\frac{19}{105}+\frac{20}{35}\times \frac{5}{24}$$

Reduce the fraction \frac{20}{35} to lowest terms by extracting and canceling out 5.

$$\frac{19}{105}+\frac{4}{7}\times \frac{5}{24}$$

Multiply \frac{4}{7} times \frac{5}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19}{105}+\frac{4\times 5}{7\times 24}$$

Do the multiplications in the fraction \frac{4\times 5}{7\times 24}.

$$\frac{19}{105}+\frac{20}{168}$$

Reduce the fraction \frac{20}{168} to lowest terms by extracting and canceling out 4.

$$\frac{19}{105}+\frac{5}{42}$$

Least common multiple of 105 and 42 is 210. Convert \frac{19}{105} and \frac{5}{42} to fractions with denominator 210.

$$\frac{38}{210}+\frac{25}{210}$$

Since \frac{38}{210} and \frac{25}{210} have the same denominator, add them by adding their numerators.

$$\frac{38+25}{210}$$

Add 38 and 25 to get 63.

$$\frac{63}{210}$$

Reduce the fraction \frac{63}{210} to lowest terms by extracting and canceling out 21.

$$\frac{3}{10}$$

Factor

$$\frac{3}{2 \cdot 5} = 0.3$$