Solve 43/32-41/6497/16

$$4 \frac{ 3 }{ 32 } -4 \frac{ 1 }{ 64 } 9 \frac{ 7 }{ 16 }$$

Evaluate

$$-\frac{34615}{1024}\approx -33.803710938$$

Solution Steps

Multiply 4 and 32 to get 128.

$$\frac{128+3}{32}-\frac{4\times 64+1}{64}\times \frac{9\times 16+7}{16}$$

Add 128 and 3 to get 131.

$$\frac{131}{32}-\frac{4\times 64+1}{64}\times \frac{9\times 16+7}{16}$$

Multiply 4 and 64 to get 256.

$$\frac{131}{32}-\frac{256+1}{64}\times \frac{9\times 16+7}{16}$$

Add 256 and 1 to get 257.

$$\frac{131}{32}-\frac{257}{64}\times \frac{9\times 16+7}{16}$$

Multiply 9 and 16 to get 144.

$$\frac{131}{32}-\frac{257}{64}\times \frac{144+7}{16}$$

Add 144 and 7 to get 151.

$$\frac{131}{32}-\frac{257}{64}\times \frac{151}{16}$$

Multiply \frac{257}{64} times \frac{151}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{131}{32}-\frac{257\times 151}{64\times 16}$$

Do the multiplications in the fraction \frac{257\times 151}{64\times 16}.

$$\frac{131}{32}-\frac{38807}{1024}$$

Least common multiple of 32 and 1024 is 1024. Convert \frac{131}{32} and \frac{38807}{1024} to fractions with denominator 1024.

$$\frac{4192}{1024}-\frac{38807}{1024}$$

Since \frac{4192}{1024} and \frac{38807}{1024} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4192-38807}{1024}$$

Subtract 38807 from 4192 to get -34615.

$$-\frac{34615}{1024}$$

Factor

$$-\frac{34615}{1024} = -33\frac{823}{1024} = -33.8037109375$$