Solve 4/5 + 3/7 + 5/9 + 1/5 + 4/7 + 4/9 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{4}{5}+\frac{3}{7}+\frac{5}{9}+\frac{1}{5}+\frac{4}{7}+\frac{4}{9}$$

Evaluate

$3$

Solution Steps

Least common multiple of $5$ and $7$ is $35$. Convert $\frac{4}{5}$ and $\frac{3}{7}$ to fractions with denominator $35$.

$$\frac{28}{35}+\frac{15}{35}+\frac{5}{9}+\frac{1}{5}+\frac{4}{7}+\frac{4}{9}$$

Since $\frac{28}{35}$ and $\frac{15}{35}$ have the same denominator, add them by adding their numerators.

$$\frac{28+15}{35}+\frac{5}{9}+\frac{1}{5}+\frac{4}{7}+\frac{4}{9}$$

Add $28$ and $15$ to get $43$.

$$\frac{43}{35}+\frac{5}{9}+\frac{1}{5}+\frac{4}{7}+\frac{4}{9}$$

Least common multiple of $35$ and $9$ is $315$. Convert $\frac{43}{35}$ and $\frac{5}{9}$ to fractions with denominator $315$.

$$\frac{387}{315}+\frac{175}{315}+\frac{1}{5}+\frac{4}{7}+\frac{4}{9}$$

Since $\frac{387}{315}$ and $\frac{175}{315}$ have the same denominator, add them by adding their numerators.

$$\frac{387+175}{315}+\frac{1}{5}+\frac{4}{7}+\frac{4}{9}$$

Add $387$ and $175$ to get $562$.

$$\frac{562}{315}+\frac{1}{5}+\frac{4}{7}+\frac{4}{9}$$

Least common multiple of $315$ and $5$ is $315$. Convert $\frac{562}{315}$ and $\frac{1}{5}$ to fractions with denominator $315$.

$$\frac{562}{315}+\frac{63}{315}+\frac{4}{7}+\frac{4}{9}$$

Since $\frac{562}{315}$ and $\frac{63}{315}$ have the same denominator, add them by adding their numerators.

$$\frac{562+63}{315}+\frac{4}{7}+\frac{4}{9}$$

Add $562$ and $63$ to get $625$.

$$\frac{625}{315}+\frac{4}{7}+\frac{4}{9}$$

Reduce the fraction $\frac{625}{315}$ to lowest terms by extracting and canceling out $5$.

$$\frac{125}{63}+\frac{4}{7}+\frac{4}{9}$$

Least common multiple of $63$ and $7$ is $63$. Convert $\frac{125}{63}$ and $\frac{4}{7}$ to fractions with denominator $63$.

$$\frac{125}{63}+\frac{36}{63}+\frac{4}{9}$$

Since $\frac{125}{63}$ and $\frac{36}{63}$ have the same denominator, add them by adding their numerators.

$$\frac{125+36}{63}+\frac{4}{9}$$

Add $125$ and $36$ to get $161$.

$$\frac{161}{63}+\frac{4}{9}$$

Reduce the fraction $\frac{161}{63}$ to lowest terms by extracting and canceling out $7$.

$$\frac{23}{9}+\frac{4}{9}$$

Since $\frac{23}{9}$ and $\frac{4}{9}$ have the same denominator, add them by adding their numerators.

$$\frac{23+4}{9}$$

Add $23$ and $4$ to get $27$.

$$\frac{27}{9}$$

Divide $27$ by $9$ to get $3$.

$$3$$

Factor

$3$