Evaluate 5^2(1/40)+6^2(1/8)+7^2(3/10)+8^2(7/40)+9^2(11/40)+10^2(1/20)+11^2(1/20)

$5^{2} (\frac{1}{40}) + 6^{2} (\frac{1}{8}) + 7^{2} (\frac{3}{10}) + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Simplify each term.

Raise $5$ to the power of $2$ .

$25 (\frac{1}{40}) + 6^{2} (\frac{1}{8}) + 7^{2} (\frac{3}{10}) + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Cancel the common factor of $5$ .

Factor $5$ out of $25$ .

$5 (5) \frac{1}{40} + 6^{2} (\frac{1}{8}) + 7^{2} (\frac{3}{10}) + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Factor $5$ out of $40$ .

$5 \cdot 5 \frac{1}{5 \cdot 8} + 6^{2} (\frac{1}{8}) + 7^{2} (\frac{3}{10}) + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Cancel the common factor.

$5 \cdot 5 \frac{1}{5 \cdot 8} + 6^{2} (\frac{1}{8}) + 7^{2} (\frac{3}{10}) + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Rewrite the expression.

$5 (\frac{1}{8}) + 6^{2} (\frac{1}{8}) + 7^{2} (\frac{3}{10}) + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Combine $5$ and $\frac{1}{8}$ .

$\frac{5}{8} + 6^{2} (\frac{1}{8}) + 7^{2} (\frac{3}{10}) + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Raise $6$ to the power of $2$ .

$\frac{5}{8} + 36 (\frac{1}{8}) + 7^{2} (\frac{3}{10}) + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Cancel the common factor of $4$ .

Factor $4$ out of $36$ .

$\frac{5}{8} + 4 (9) \frac{1}{8} + 7^{2} (\frac{3}{10}) + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Factor $4$ out of $8$ .

$\frac{5}{8} + 4 \cdot 9 \frac{1}{4 \cdot 2} + 7^{2} (\frac{3}{10}) + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Cancel the common factor.

$\frac{5}{8} + 4 \cdot 9 \frac{1}{4 \cdot 2} + 7^{2} (\frac{3}{10}) + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Rewrite the expression.

$\frac{5}{8} + 9 (\frac{1}{2}) + 7^{2} (\frac{3}{10}) + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Combine $9$ and $\frac{1}{2}$ .

$\frac{5}{8} + \frac{9}{2} + 7^{2} (\frac{3}{10}) + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Raise $7$ to the power of $2$ .

$\frac{5}{8} + \frac{9}{2} + 49 (\frac{3}{10}) + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Multiply $49 (\frac{3}{10})$ .

Combine $49$ and $\frac{3}{10}$ .

$\frac{5}{8} + \frac{9}{2} + \frac{49 \cdot 3}{10} + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Multiply $49$ by $3$ .

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + 8^{2} (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Raise $8$ to the power of $2$ .

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + 64 (\frac{7}{40}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Cancel the common factor of $8$ .

Factor $8$ out of $64$ .

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + 8 (8) \frac{7}{40} + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Factor $8$ out of $40$ .

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + 8 \cdot 8 \frac{7}{8 \cdot 5} + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Cancel the common factor.

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + 8 \cdot 8 \frac{7}{8 \cdot 5} + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Rewrite the expression.

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + 8 (\frac{7}{5}) + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Combine $8$ and $\frac{7}{5}$ .

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + \frac{8 \cdot 7}{5} + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Multiply $8$ by $7$ .

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + \frac{56}{5} + 9^{2} (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Raise $9$ to the power of $2$ .

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + \frac{56}{5} + 81 (\frac{11}{40}) + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Multiply $81 (\frac{11}{40})$ .

Combine $81$ and $\frac{11}{40}$ .

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + \frac{56}{5} + \frac{81 \cdot 11}{40} + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Multiply $81$ by $11$ .

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + \frac{56}{5} + \frac{891}{40} + 10^{2} (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Raise $10$ to the power of $2$ .

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + \frac{56}{5} + \frac{891}{40} + 100 (\frac{1}{20}) + 11^{2} (\frac{1}{20})$

Cancel the common factor of $20$ .

Factor $20$ out of $100$ .

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + \frac{56}{5} + \frac{891}{40} + 20 (5) \frac{1}{20} + 11^{2} (\frac{1}{20})$

Cancel the common factor.

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + \frac{56}{5} + \frac{891}{40} + 20 \cdot 5 \frac{1}{20} + 11^{2} (\frac{1}{20})$

Rewrite the expression.

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + \frac{56}{5} + \frac{891}{40} + 5 + 11^{2} (\frac{1}{20})$

Raise $11$ to the power of $2$ .

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + \frac{56}{5} + \frac{891}{40} + 5 + 121 (\frac{1}{20})$

Combine $121$ and $\frac{1}{20}$ .

$\frac{5}{8} + \frac{9}{2} + \frac{147}{10} + \frac{56}{5} + \frac{891}{40} + 5 + \frac{121}{20}$

Find the common denominator.

Multiply $\frac{5}{8}$ by $\frac{5}{5}$ .

$\frac{5}{8} \cdot \frac{5}{5} + \frac{9}{2} + \frac{147}{10} + \frac{56}{5} + \frac{891}{40} + 5 + \frac{121}{20}$

Multiply $\frac{5}{8}$ by $\frac{5}{5}$ .

$\frac{5 \cdot 5}{8 \cdot 5} + \frac{9}{2} + \frac{147}{10} + \frac{56}{5} + \frac{891}{40} + 5 + \frac{121}{20}$

Multiply $\frac{9}{2}$ by $\frac{20}{20}$ .

$\frac{5 \cdot 5}{8 \cdot 5} + \frac{9}{2} \cdot \frac{20}{20} + \frac{147}{10} + \frac{56}{5} + \frac{891}{40} + 5 + \frac{121}{20}$

Multiply $\frac{9}{2}$ by $\frac{20}{20}$ .

$\frac{5 \cdot 5}{8 \cdot 5} + \frac{9 \cdot 20}{2 \cdot 20} + \frac{147}{10} + \frac{56}{5} + \frac{891}{40} + 5 + \frac{121}{20}$

Multiply $\frac{147}{10}$ by $\frac{4}{4}$ .

$\frac{5 \cdot 5}{8 \cdot 5} + \frac{9 \cdot 20}{2 \cdot 20} + \frac{147}{10} \cdot \frac{4}{4} + \frac{56}{5} + \frac{891}{40} + 5 + \frac{121}{20}$

Multiply $\frac{147}{10}$ by $\frac{4}{4}$ .

$\frac{5 \cdot 5}{8 \cdot 5} + \frac{9 \cdot 20}{2 \cdot 20} + \frac{147 \cdot 4}{10 \cdot 4} + \frac{56}{5} + \frac{891}{40} + 5 + \frac{121}{20}$

Multiply $\frac{56}{5}$ by $\frac{8}{8}$ .

$\frac{5 \cdot 5}{8 \cdot 5} + \frac{9 \cdot 20}{2 \cdot 20} + \frac{147 \cdot 4}{10 \cdot 4} + \frac{56}{5} \cdot \frac{8}{8} + \frac{891}{40} + 5 + \frac{121}{20}$

Multiply $\frac{56}{5}$ by $\frac{8}{8}$ .

$\frac{5 \cdot 5}{8 \cdot 5} + \frac{9 \cdot 20}{2 \cdot 20} + \frac{147 \cdot 4}{10 \cdot 4} + \frac{56 \cdot 8}{5 \cdot 8} + \frac{891}{40} + 5 + \frac{121}{20}$

Write $5$ as a fraction with denominator $1$ .

$\frac{5 \cdot 5}{8 \cdot 5} + \frac{9 \cdot 20}{2 \cdot 20} + \frac{147 \cdot 4}{10 \cdot 4} + \frac{56 \cdot 8}{5 \cdot 8} + \frac{891}{40} + \frac{5}{1} + \frac{121}{20}$

Multiply $\frac{5}{1}$ by $\frac{40}{40}$ .

$\frac{5 \cdot 5}{8 \cdot 5} + \frac{9 \cdot 20}{2 \cdot 20} + \frac{147 \cdot 4}{10 \cdot 4} + \frac{56 \cdot 8}{5 \cdot 8} + \frac{891}{40} + \frac{5}{1} \cdot \frac{40}{40} + \frac{121}{20}$

Multiply $\frac{5}{1}$ by $\frac{40}{40}$ .

$\frac{5 \cdot 5}{8 \cdot 5} + \frac{9 \cdot 20}{2 \cdot 20} + \frac{147 \cdot 4}{10 \cdot 4} + \frac{56 \cdot 8}{5 \cdot 8} + \frac{891}{40} + \frac{5 \cdot 40}{40} + \frac{121}{20}$

Multiply $\frac{121}{20}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 5}{8 \cdot 5} + \frac{9 \cdot 20}{2 \cdot 20} + \frac{147 \cdot 4}{10 \cdot 4} + \frac{56 \cdot 8}{5 \cdot 8} + \frac{891}{40} + \frac{5 \cdot 40}{40} + \frac{121}{20} \cdot \frac{2}{2}$

Multiply $\frac{121}{20}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 5}{8 \cdot 5} + \frac{9 \cdot 20}{2 \cdot 20} + \frac{147 \cdot 4}{10 \cdot 4} + \frac{56 \cdot 8}{5 \cdot 8} + \frac{891}{40} + \frac{5 \cdot 40}{40} + \frac{121 \cdot 2}{20 \cdot 2}$

Reorder the factors of $8 \cdot 5$ .

$\frac{5 \cdot 5}{5 \cdot 8} + \frac{9 \cdot 20}{2 \cdot 20} + \frac{147 \cdot 4}{10 \cdot 4} + \frac{56 \cdot 8}{5 \cdot 8} + \frac{891}{40} + \frac{5 \cdot 40}{40} + \frac{121 \cdot 2}{20 \cdot 2}$

Multiply $5$ by $8$ .

$\frac{5 \cdot 5}{40} + \frac{9 \cdot 20}{2 \cdot 20} + \frac{147 \cdot 4}{10 \cdot 4} + \frac{56 \cdot 8}{5 \cdot 8} + \frac{891}{40} + \frac{5 \cdot 40}{40} + \frac{121 \cdot 2}{20 \cdot 2}$

Multiply $2$ by $20$ .

$\frac{5 \cdot 5}{40} + \frac{9 \cdot 20}{40} + \frac{147 \cdot 4}{10 \cdot 4} + \frac{56 \cdot 8}{5 \cdot 8} + \frac{891}{40} + \frac{5 \cdot 40}{40} + \frac{121 \cdot 2}{20 \cdot 2}$

Reorder the factors of $10 \cdot 4$ .

$\frac{5 \cdot 5}{40} + \frac{9 \cdot 20}{40} + \frac{147 \cdot 4}{4 \cdot 10} + \frac{56 \cdot 8}{5 \cdot 8} + \frac{891}{40} + \frac{5 \cdot 40}{40} + \frac{121 \cdot 2}{20 \cdot 2}$

Multiply $4$ by $10$ .

$\frac{5 \cdot 5}{40} + \frac{9 \cdot 20}{40} + \frac{147 \cdot 4}{40} + \frac{56 \cdot 8}{5 \cdot 8} + \frac{891}{40} + \frac{5 \cdot 40}{40} + \frac{121 \cdot 2}{20 \cdot 2}$

Multiply $5$ by $8$ .

$\frac{5 \cdot 5}{40} + \frac{9 \cdot 20}{40} + \frac{147 \cdot 4}{40} + \frac{56 \cdot 8}{40} + \frac{891}{40} + \frac{5 \cdot 40}{40} + \frac{121 \cdot 2}{20 \cdot 2}$

Reorder the factors of $20 \cdot 2$ .

$\frac{5 \cdot 5}{40} + \frac{9 \cdot 20}{40} + \frac{147 \cdot 4}{40} + \frac{56 \cdot 8}{40} + \frac{891}{40} + \frac{5 \cdot 40}{40} + \frac{121 \cdot 2}{2 \cdot 20}$

Multiply $2$ by $20$ .

$\frac{5 \cdot 5}{40} + \frac{9 \cdot 20}{40} + \frac{147 \cdot 4}{40} + \frac{56 \cdot 8}{40} + \frac{891}{40} + \frac{5 \cdot 40}{40} + \frac{121 \cdot 2}{40}$

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 + 9 \cdot 20 + 147 \cdot 4 + 56 \cdot 8 + 891 + 5 \cdot 40 + 121 \cdot 2}{40}$

Simplify each term.

Multiply $5$ by $5$ .

$\frac{25 + 9 \cdot 20 + 147 \cdot 4 + 56 \cdot 8 + 891 + 5 \cdot 40 + 121 \cdot 2}{40}$

Multiply $9$ by $20$ .

$\frac{25 + 180 + 147 \cdot 4 + 56 \cdot 8 + 891 + 5 \cdot 40 + 121 \cdot 2}{40}$

Multiply $147$ by $4$ .

$\frac{25 + 180 + 588 + 56 \cdot 8 + 891 + 5 \cdot 40 + 121 \cdot 2}{40}$

Multiply $56$ by $8$ .

$\frac{25 + 180 + 588 + 448 + 891 + 5 \cdot 40 + 121 \cdot 2}{40}$

Multiply $5$ by $40$ .

$\frac{25 + 180 + 588 + 448 + 891 + 200 + 121 \cdot 2}{40}$

Multiply $121$ by $2$ .

$\frac{25 + 180 + 588 + 448 + 891 + 200 + 242}{40}$

Reduce the expression by cancelling the common factors.

Add $25$ and $180$ .

$\frac{205 + 588 + 448 + 891 + 200 + 242}{40}$

Simplify by adding numbers.

Add $205$ and $588$ .

$\frac{793 + 448 + 891 + 200 + 242}{40}$

Add $793$ and $448$ .

$\frac{1241 + 891 + 200 + 242}{40}$

Add $1241$ and $891$ .

$\frac{2132 + 200 + 242}{40}$

Add $2132$ and $200$ .

$\frac{2332 + 242}{40}$

Add $2332$ and $242$ .

$\frac{2574}{40}$

Cancel the common factor of $2574$ and $40$ .

Factor $2$ out of $2574$ .

$\frac{2 (1287)}{40}$

Cancel the common factors.

Factor $2$ out of $40$ .

$\frac{2 \cdot 1287}{2 \cdot 20}$

Cancel the common factor.

$\frac{2 \cdot 1287}{2 \cdot 20}$

Rewrite the expression.

$\frac{1287}{20}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1287}{20}$

Decimal Form:

$64.35$

Mixed Number Form:

$64 \frac{7}{20}$

Evaluate 5^2(1/40)+6^2(1/8)+7^2(3/10)+8^2(7/40)+9^2(11/40)+10^2(1/20)+11^2(1/20)

Related Questions

Support LCMGCF.com by disabling your adblocker.