Solve 100.5/36+121*6/36+144*5/36/36+169*4/36

$$100.5 / 36 + 121 \cdot 6 / 36 + 144 \cdot \frac { 5 / 36 } { 36 } + 169 \cdot \frac { 4 } { 36 }$$

Evaluate

$$\frac{1015}{24}\approx 42.291666667$$

Solution Steps

Expand \frac{100.5}{36} by multiplying both numerator and the denominator by 10.

$$\frac{1005}{360}+121\times \frac{6}{36}+144\times \frac{\frac{5}{36}}{36}+169\times \frac{4}{36}$$

Reduce the fraction \frac{1005}{360} to lowest terms by extracting and canceling out 15.

$$\frac{67}{24}+121\times \frac{6}{36}+144\times \frac{\frac{5}{36}}{36}+169\times \frac{4}{36}$$

Reduce the fraction \frac{6}{36} to lowest terms by extracting and canceling out 6.

$$\frac{67}{24}+121\times \frac{1}{6}+144\times \frac{\frac{5}{36}}{36}+169\times \frac{4}{36}$$

Multiply 121 and \frac{1}{6} to get \frac{121}{6}.

$$\frac{67}{24}+\frac{121}{6}+144\times \frac{\frac{5}{36}}{36}+169\times \frac{4}{36}$$

Least common multiple of 24 and 6 is 24. Convert \frac{67}{24} and \frac{121}{6} to fractions with denominator 24.

$$\frac{67}{24}+\frac{484}{24}+144\times \frac{\frac{5}{36}}{36}+169\times \frac{4}{36}$$

Since \frac{67}{24} and \frac{484}{24} have the same denominator, add them by adding their numerators.

$$\frac{67+484}{24}+144\times \frac{\frac{5}{36}}{36}+169\times \frac{4}{36}$$

Add 67 and 484 to get 551.

$$\frac{551}{24}+144\times \frac{\frac{5}{36}}{36}+169\times \frac{4}{36}$$

Express \frac{\frac{5}{36}}{36} as a single fraction.

$$\frac{551}{24}+144\times \frac{5}{36\times 36}+169\times \frac{4}{36}$$

Multiply 36 and 36 to get 1296.

$$\frac{551}{24}+144\times \frac{5}{1296}+169\times \frac{4}{36}$$

Express 144\times \frac{5}{1296} as a single fraction.

$$\frac{551}{24}+\frac{144\times 5}{1296}+169\times \frac{4}{36}$$

Multiply 144 and 5 to get 720.

$$\frac{551}{24}+\frac{720}{1296}+169\times \frac{4}{36}$$

Reduce the fraction \frac{720}{1296} to lowest terms by extracting and canceling out 144.

$$\frac{551}{24}+\frac{5}{9}+169\times \frac{4}{36}$$

Least common multiple of 24 and 9 is 72. Convert \frac{551}{24} and \frac{5}{9} to fractions with denominator 72.

$$\frac{1653}{72}+\frac{40}{72}+169\times \frac{4}{36}$$

Since \frac{1653}{72} and \frac{40}{72} have the same denominator, add them by adding their numerators.

$$\frac{1653+40}{72}+169\times \frac{4}{36}$$

Add 1653 and 40 to get 1693.

$$\frac{1693}{72}+169\times \frac{4}{36}$$

Reduce the fraction \frac{4}{36} to lowest terms by extracting and canceling out 4.

$$\frac{1693}{72}+169\times \frac{1}{9}$$

Multiply 169 and \frac{1}{9} to get \frac{169}{9}.

$$\frac{1693}{72}+\frac{169}{9}$$

Least common multiple of 72 and 9 is 72. Convert \frac{1693}{72} and \frac{169}{9} to fractions with denominator 72.

$$\frac{1693}{72}+\frac{1352}{72}$$

Since \frac{1693}{72} and \frac{1352}{72} have the same denominator, add them by adding their numerators.

$$\frac{1693+1352}{72}$$

Add 1693 and 1352 to get 3045.

$$\frac{3045}{72}$$

Reduce the fraction \frac{3045}{72} to lowest terms by extracting and canceling out 3.

$$\frac{1015}{24}$$

Factor

$$\frac{5 \cdot 7 \cdot 29}{3 \cdot 2 ^ {3}} = 42\frac{7}{24} = 42.291666666666664$$