What is 2/5 \div 2+7/30 ?

The solution to 2/5 \div 2+7/30 is 13/30

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Popular >

2/5 \div 2+7/30

Solution

\frac{2}{5} \div 2 + \frac{7}{30}

Solution

\frac{13}{30}

Solution steps

\frac{2}{5} \div 2 + \frac{7}{30}

Follow the PEMDAS order of operations

Multiply and divide (left to right)

\frac{2}{5} \div 2 : \frac{1}{5}

\frac{2}{5} \div 2

Convert element to fraction:

2 = \frac{2}{1}

= \frac{2}{5} \div \frac{2}{1}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{2}{5} \cdot \frac{1}{2}

Cross-cancel:

2

= \frac{1}{5}

= \frac{1}{5} + \frac{7}{30}

Add and subtract (left to right)

\frac{1}{5} + \frac{7}{30} : \frac{13}{30}

\frac{1}{5} + \frac{7}{30}

\frac{1}{5} + \frac{7}{30} = \frac{13}{30}

\frac{1}{5} + \frac{7}{30}

Least Common Multiplier of

5, 30 : 30

5, 30

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Prime factorization of

30 : 2 \cdot 3 \cdot 5

30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 5

Multiply each factor the greatest number of times it occurs in either

5

30

= 5 \cdot 2 \cdot 3

Multiply the numbers:

5 \cdot 2 \cdot 3 = 30

= 30

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

30

For

\frac{1}{5} :

multiply the denominator and numerator by

6

\frac{1}{5} = \frac{1 \cdot 6}{5 \cdot 6} = \frac{6}{30}

= \frac{6}{30} + \frac{7}{30}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{6 + 7}{30}

Add the numbers:

6 + 7 = 13

= \frac{13}{30}

= \frac{13}{30}

= \frac{13}{30}

Popular Examples

-7/2 (-4)^2+4

- \frac{7}{2} (- 4)^{2} + 4

4^3\times 4

4^{3} \times 4

-6+8(11-4)+3^2

- 6 + 8 (11 - 4) + 3^{2}

7*3-2*5

7 \cdot 3 - 2 \cdot 5

3(-4)^2-18(-4)+15

3 (- 4)^{2} - 18 (- 4) + 15

Frequently Asked Questions (FAQ)

What is 2/5 \div 2+7/30 ?
The solution to 2/5 \div 2+7/30 is 13/30