What is (1/2+2 3/5)+1 1/2 ?

The solution to (1/2+2 3/5)+1 1/2 is 4 3/5

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Popular >

(1/2+2 3/5)+1 1/2

Solution

(\frac{1}{2} + 2 \frac{3}{5}) + 1 \frac{1}{2}

Solution

4 \frac{3}{5}

Solution steps

(\frac{1}{2} + 2 \frac{3}{5}) + 1 \frac{1}{2}

Convert mixed numbers to improper fractions:

1 \frac{1}{2} = \frac{3}{2}

1 \frac{1}{2}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

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

= \frac{3}{2}

= (\frac{1}{2} + 2 \frac{3}{5}) + \frac{3}{2}

Convert mixed numbers to improper fractions:

2 \frac{3}{5} = \frac{13}{5}

2 \frac{3}{5}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

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

= \frac{13}{5}

= (\frac{1}{2} + \frac{13}{5}) + \frac{3}{2}

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{2} + \frac{13}{5}) : \frac{31}{10}

\frac{1}{2} + \frac{13}{5}

\frac{1}{2} + \frac{13}{5} = \frac{31}{10}

\frac{1}{2} + \frac{13}{5}

Least Common Multiplier of

2, 5 : 10

2, 5

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

2

5

= 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 10

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

10

For

\frac{1}{2} :

multiply the denominator and numerator by

5

\frac{1}{2} = \frac{1 \cdot 5}{2 \cdot 5} = \frac{5}{10}

For

\frac{13}{5} :

multiply the denominator and numerator by

2

\frac{13}{5} = \frac{13 \cdot 2}{5 \cdot 2} = \frac{26}{10}

= \frac{5}{10} + \frac{26}{10}

Since the denominators are equal, combine the fractions:

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

= \frac{5 + 26}{10}

Add the numbers:

5 + 26 = 31

= \frac{31}{10}

= \frac{31}{10}

= \frac{31}{10} + \frac{3}{2}

Add and subtract (left to right)

\frac{31}{10} + \frac{3}{2} : \frac{23}{5}

\frac{31}{10} + \frac{3}{2}

\frac{31}{10} + \frac{3}{2} = \frac{23}{5}

\frac{31}{10} + \frac{3}{2}

Least Common Multiplier of

10, 2 : 10

10, 2

Least Common Multiplier (LCM)

Prime factorization of

10 : 2 \cdot 5

10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 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

10

2

= 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 10

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

10

For

\frac{3}{2} :

multiply the denominator and numerator by

5

\frac{3}{2} = \frac{3 \cdot 5}{2 \cdot 5} = \frac{15}{10}

= \frac{31}{10} + \frac{15}{10}

Since the denominators are equal, combine the fractions:

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

= \frac{31 + 15}{10}

Add the numbers:

31 + 15 = 46

= \frac{46}{10}

Cancel the common factor:

2

= \frac{23}{5}

= \frac{23}{5}

= \frac{23}{5}

Convert improper fractions to mixed numbers:

\frac{23}{5} = 4 \frac{3}{5}

\frac{23}{5} = 4

Remainder

3

\frac{23}{5}

Write the problem in long division format

5 \overline{∣ 23}

Divide

23

5

to get

4

Divide

23

5

to get

4

4 5 \overline{∣ 23}

Multiply the quotient digit

(4)

by the divisor

5

4 5 \overline{∣ 23} \underline{20}

Subtract

20

from

23

4 5 \overline{∣ 23} \underline{20} 3

4 5 \overline{∣ 23} \underline{20} 3

The solution for Long Division of

\frac{23}{5}

4

with remainder of

3

4 Remainder 3

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{23}{5} = 4 \frac{3}{5}

= 4 \frac{3}{5}

= 4 \frac{3}{5}

Popular Examples

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4^{3} - 2^{3}

2(1-3)^2+2/3

2 (1 - 3)^{2} + \frac{2}{3}

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3^{7} - 2^{7}

(3/6-1/2)^2

(\frac{3}{6} - \frac{1}{2})^{2}

Frequently Asked Questions (FAQ)

What is (1/2+2 3/5)+1 1/2 ?
The solution to (1/2+2 3/5)+1 1/2 is 4 3/5