Solve (45div6)-4^3+5^2*4

$$(45 \div 6)- { 4 }^{ 3 } + { 5 }^{ 2 } \times 4$$

Evaluate

$$\frac{87}{2}=43.5$$

Solution Steps

Reduce the fraction \frac{45}{6} to lowest terms by extracting and canceling out 3.

$$\frac{15}{2}-4^{3}+5^{2}\times 4$$

Calculate 4 to the power of 3 and get 64.

$$\frac{15}{2}-64+5^{2}\times 4$$

Convert 64 to fraction \frac{128}{2}.

$$\frac{15}{2}-\frac{128}{2}+5^{2}\times 4$$

Since \frac{15}{2} and \frac{128}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-128}{2}+5^{2}\times 4$$

Subtract 128 from 15 to get -113.

$$-\frac{113}{2}+5^{2}\times 4$$

Calculate 5 to the power of 2 and get 25.

$$-\frac{113}{2}+25\times 4$$

Multiply 25 and 4 to get 100.

$$-\frac{113}{2}+100$$

Convert 100 to fraction \frac{200}{2}.

$$-\frac{113}{2}+\frac{200}{2}$$

Since -\frac{113}{2} and \frac{200}{2} have the same denominator, add them by adding their numerators.

$$\frac{-113+200}{2}$$

Add -113 and 200 to get 87.

$$\frac{87}{2}$$

Factor

$$\frac{3 \cdot 29}{2} = 43\frac{1}{2} = 43.5$$