Solve (2-1/2)(3-2/3)+4(1^2)

$$(2- \frac{ 1 }{ 2 } )(3- \frac{ 2 }{ 3 } )+4( { 1 }^{ 2 } )$$

Evaluate

$$\frac{15}{2}=7.5$$

Solution Steps

Convert 2 to fraction \frac{4}{2}.

$$\left(\frac{4}{2}-\frac{1}{2}\right)\left(3-\frac{2}{3}\right)+4\times 1^{2}$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-1}{2}\left(3-\frac{2}{3}\right)+4\times 1^{2}$$

Subtract 1 from 4 to get 3.

$$\frac{3}{2}\left(3-\frac{2}{3}\right)+4\times 1^{2}$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{3}{2}\left(\frac{9}{3}-\frac{2}{3}\right)+4\times 1^{2}$$

Since \frac{9}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}\times \frac{9-2}{3}+4\times 1^{2}$$

Subtract 2 from 9 to get 7.

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

Multiply \frac{3}{2} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

$$\frac{7}{2}+4\times 1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{7}{2}+4\times 1$$

Multiply 4 and 1 to get 4.

$$\frac{7}{2}+4$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{7}{2}+\frac{8}{2}$$

Since \frac{7}{2} and \frac{8}{2} have the same denominator, add them by adding their numerators.

$$\frac{7+8}{2}$$

Add 7 and 8 to get 15.

$$\frac{15}{2}$$

Factor

$$\frac{3 \cdot 5}{2} = 7\frac{1}{2} = 7.5$$