Solve 71/8+11/16+41/32+51/4

$$7 \frac { 1 } { 8 } + 1 \frac { 1 } { 16 } + 4 \frac { 1 } { 32 } + 5 \frac { 1 } { 4 }$$

Evaluate

$$\frac{559}{32}=17.46875$$

Solution Steps

Multiply 7 and 8 to get 56.

$$\frac{56+1}{8}+\frac{1\times 16+1}{16}+\frac{4\times 32+1}{32}+\frac{5\times 4+1}{4}$$

Add 56 and 1 to get 57.

$$\frac{57}{8}+\frac{1\times 16+1}{16}+\frac{4\times 32+1}{32}+\frac{5\times 4+1}{4}$$

Multiply 1 and 16 to get 16.

$$\frac{57}{8}+\frac{16+1}{16}+\frac{4\times 32+1}{32}+\frac{5\times 4+1}{4}$$

Add 16 and 1 to get 17.

$$\frac{57}{8}+\frac{17}{16}+\frac{4\times 32+1}{32}+\frac{5\times 4+1}{4}$$

Least common multiple of 8 and 16 is 16. Convert \frac{57}{8} and \frac{17}{16} to fractions with denominator 16.

$$\frac{114}{16}+\frac{17}{16}+\frac{4\times 32+1}{32}+\frac{5\times 4+1}{4}$$

Since \frac{114}{16} and \frac{17}{16} have the same denominator, add them by adding their numerators.

$$\frac{114+17}{16}+\frac{4\times 32+1}{32}+\frac{5\times 4+1}{4}$$

Add 114 and 17 to get 131.

$$\frac{131}{16}+\frac{4\times 32+1}{32}+\frac{5\times 4+1}{4}$$

Multiply 4 and 32 to get 128.

$$\frac{131}{16}+\frac{128+1}{32}+\frac{5\times 4+1}{4}$$

Add 128 and 1 to get 129.

$$\frac{131}{16}+\frac{129}{32}+\frac{5\times 4+1}{4}$$

Least common multiple of 16 and 32 is 32. Convert \frac{131}{16} and \frac{129}{32} to fractions with denominator 32.

$$\frac{262}{32}+\frac{129}{32}+\frac{5\times 4+1}{4}$$

Since \frac{262}{32} and \frac{129}{32} have the same denominator, add them by adding their numerators.

$$\frac{262+129}{32}+\frac{5\times 4+1}{4}$$

Add 262 and 129 to get 391.

$$\frac{391}{32}+\frac{5\times 4+1}{4}$$

Multiply 5 and 4 to get 20.

$$\frac{391}{32}+\frac{20+1}{4}$$

Add 20 and 1 to get 21.

$$\frac{391}{32}+\frac{21}{4}$$

Least common multiple of 32 and 4 is 32. Convert \frac{391}{32} and \frac{21}{4} to fractions with denominator 32.

$$\frac{391}{32}+\frac{168}{32}$$

Since \frac{391}{32} and \frac{168}{32} have the same denominator, add them by adding their numerators.

$$\frac{391+168}{32}$$

Add 391 and 168 to get 559.

$$\frac{559}{32}$$

Factor

$$\frac{13 \cdot 43}{2 ^ {5}} = 17\frac{15}{32} = 17.46875$$