Solve 22/7*1.4^2*5+4/3*22/7*1.4^3

$$\frac{ 22 }{ 7 } \times { 1.4 }^{ 2 } \times 5+ \frac{ 4 }{ 3 } \times \frac{ 22 }{ 7 } \times { 1.4 }^{ 3 }$$

Evaluate

$$\frac{15862}{375}\approx 42.298666667$$

Solution Steps

Calculate 1.4 to the power of 2 and get 1.96.

$$\frac{22}{7}\times 1.96\times 5+\frac{4}{3}\times \frac{22}{7}\times 1.4^{3}$$

Convert decimal number 1.96 to fraction \frac{196}{100}. Reduce the fraction \frac{196}{100} to lowest terms by extracting and canceling out 4.

$$\frac{22}{7}\times \frac{49}{25}\times 5+\frac{4}{3}\times \frac{22}{7}\times 1.4^{3}$$

Multiply \frac{22}{7} times \frac{49}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22\times 49}{7\times 25}\times 5+\frac{4}{3}\times \frac{22}{7}\times 1.4^{3}$$

Do the multiplications in the fraction \frac{22\times 49}{7\times 25}.

$$\frac{1078}{175}\times 5+\frac{4}{3}\times \frac{22}{7}\times 1.4^{3}$$

Reduce the fraction \frac{1078}{175} to lowest terms by extracting and canceling out 7.

$$\frac{154}{25}\times 5+\frac{4}{3}\times \frac{22}{7}\times 1.4^{3}$$

Express \frac{154}{25}\times 5 as a single fraction.

$$\frac{154\times 5}{25}+\frac{4}{3}\times \frac{22}{7}\times 1.4^{3}$$

Multiply 154 and 5 to get 770.

$$\frac{770}{25}+\frac{4}{3}\times \frac{22}{7}\times 1.4^{3}$$

Reduce the fraction \frac{770}{25} to lowest terms by extracting and canceling out 5.

$$\frac{154}{5}+\frac{4}{3}\times \frac{22}{7}\times 1.4^{3}$$

Multiply \frac{4}{3} times \frac{22}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{154}{5}+\frac{4\times 22}{3\times 7}\times 1.4^{3}$$

Do the multiplications in the fraction \frac{4\times 22}{3\times 7}.

$$\frac{154}{5}+\frac{88}{21}\times 1.4^{3}$$

Calculate 1.4 to the power of 3 and get 2.744.

$$\frac{154}{5}+\frac{88}{21}\times 2.744$$

Convert decimal number 2.744 to fraction \frac{2744}{1000}. Reduce the fraction \frac{2744}{1000} to lowest terms by extracting and canceling out 8.

$$\frac{154}{5}+\frac{88}{21}\times \frac{343}{125}$$

Multiply \frac{88}{21} times \frac{343}{125} by multiplying numerator times numerator and denominator times denominator.

$$\frac{154}{5}+\frac{88\times 343}{21\times 125}$$

Do the multiplications in the fraction \frac{88\times 343}{21\times 125}.

$$\frac{154}{5}+\frac{30184}{2625}$$

Reduce the fraction \frac{30184}{2625} to lowest terms by extracting and canceling out 7.

$$\frac{154}{5}+\frac{4312}{375}$$

Least common multiple of 5 and 375 is 375. Convert \frac{154}{5} and \frac{4312}{375} to fractions with denominator 375.

$$\frac{11550}{375}+\frac{4312}{375}$$

Since \frac{11550}{375} and \frac{4312}{375} have the same denominator, add them by adding their numerators.

$$\frac{11550+4312}{375}$$

Add 11550 and 4312 to get 15862.

$$\frac{15862}{375}$$

Factor

$$\frac{2 \cdot 7 \cdot 11 \cdot 103}{3 \cdot 5 ^ {3}} = 42\frac{112}{375} = 42.29866666666667$$