What is 3+2/5-1/4+7/2 ?

The solution to 3+2/5-1/4+7/2 is 6 13/20

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3+2/5-1/4+7/2

Solution

3 + \frac{2}{5} - \frac{1}{4} + \frac{7}{2}

Solution

6 \frac{13}{20}

Solution steps

3 + \frac{2}{5} - \frac{1}{4} + \frac{7}{2}

Follow the PEMDAS order of operations

Add and subtract (left to right)

3 + \frac{2}{5} = \frac{17}{5}

3 + \frac{2}{5}

Convert element to fraction:

3 = \frac{3 \cdot 5}{5}

= \frac{3 \cdot 5}{5} + \frac{2}{5}

Since the denominators are equal, combine the fractions:

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

= \frac{3 \cdot 5 + 2}{5}

3 \cdot 5 + 2 = 17

3 \cdot 5 + 2

Multiply the numbers:

3 \cdot 5 = 15

= 15 + 2

Add the numbers:

15 + 2 = 17

= 17

= \frac{17}{5}

= \frac{17}{5} - \frac{1}{4} + \frac{7}{2}

\frac{17}{5} - \frac{1}{4} = \frac{63}{20}

\frac{17}{5} - \frac{1}{4}

Least Common Multiplier of

5, 4 : 20

5, 4

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

5

4

= 5 \cdot 2 \cdot 2

Multiply the numbers:

5 \cdot 2 \cdot 2 = 20

= 20

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

20

For

\frac{17}{5} :

multiply the denominator and numerator by

4

\frac{17}{5} = \frac{17 \cdot 4}{5 \cdot 4} = \frac{68}{20}

For

\frac{1}{4} :

multiply the denominator and numerator by

5

\frac{1}{4} = \frac{1 \cdot 5}{4 \cdot 5} = \frac{5}{20}

= \frac{68}{20} - \frac{5}{20}

Since the denominators are equal, combine the fractions:

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

= \frac{68 - 5}{20}

Subtract the numbers:

68 - 5 = 63

= \frac{63}{20}

= \frac{63}{20} + \frac{7}{2}

\frac{63}{20} + \frac{7}{2} = \frac{133}{20}

\frac{63}{20} + \frac{7}{2}

Least Common Multiplier of

20, 2 : 20

20, 2

Least Common Multiplier (LCM)

Prime factorization of

20 : 2 \cdot 2 \cdot 5

20

20

divides by

220 = 10 \cdot 2

= 2 \cdot 10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 5

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

20

2

= 2 \cdot 2 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 5 = 20

= 20

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

20

For

\frac{7}{2} :

multiply the denominator and numerator by

10

\frac{7}{2} = \frac{7 \cdot 10}{2 \cdot 10} = \frac{70}{20}

= \frac{63}{20} + \frac{70}{20}

Since the denominators are equal, combine the fractions:

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

= \frac{63 + 70}{20}

Add the numbers:

63 + 70 = 133

= \frac{133}{20}

= \frac{133}{20}

Convert improper fractions to mixed numbers:

\frac{133}{20} = 6 \frac{13}{20}

\frac{133}{20} = 6

Remainder

13

\frac{133}{20}

Write the problem in long division format

20 \overline{∣ 133}

Divide

133

20

to get

6

Divide

133

20

to get

6

6 20 \overline{∣ 133}

Multiply the quotient digit

(6)

by the divisor

20

6 20 \overline{∣ 133} \underline{120}

Subtract

120

from

133

6 20 \overline{∣ 133} \underline{120} 13

6 20 \overline{∣ 133} \underline{120} 13

The solution for Long Division of

\frac{133}{20}

6

with remainder of

13

6 Remainder 13

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{133}{20} = 6 \frac{13}{20}

= 6 \frac{13}{20}

= 6 \frac{13}{20}

Popular Examples

3^3+3

3^{3} + 3

(1-1/5)\div (1+1/5)

(1 - \frac{1}{5}) \div (1 + \frac{1}{5})

9^2+4^2

9^{2} + 4^{2}

9^2+3^2

9^{2} + 3^{2}

9/4-2+1/2

\frac{9}{4} - 2 + \frac{1}{2}

Frequently Asked Questions (FAQ)

What is 3+2/5-1/4+7/2 ?
The solution to 3+2/5-1/4+7/2 is 6 13/20