What is 3/5 \div 2+3*1/4 ?

The solution to 3/5 \div 2+3*1/4 is 1 1/20

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Popular Pre Algebra >

3/5 \div 2+3*1/4

Solution

\frac{3}{5} \div 2 + 3 \cdot \frac{1}{4}

Solution

1 \frac{1}{20}

Decimal

1.05

Solution steps

\frac{3}{5} \div 2 + 3 \cdot \frac{1}{4}

Follow the PEMDAS order of operations

Multiply and divide (left to right)

\frac{3}{5} \div 2 : \frac{3}{10}

\frac{3}{5} \div 2

Convert element to fraction:

2 = \frac{2}{1}

= \frac{3}{5} \div \frac{2}{1}

Apply the fraction rule:

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

= \frac{3}{5} \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{3 \cdot 1}{5 \cdot 2}

Multiply the numbers:

3 \cdot 1 = 3

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

Multiply the numbers:

5 \cdot 2 = 10

= \frac{3}{10}

= \frac{3}{10} + 3 \cdot \frac{1}{4}

Multiply and divide (left to right)

3 \cdot \frac{1}{4} : \frac{3}{4}

3 \cdot \frac{1}{4}

Convert element to fraction:

3 = \frac{3}{1}

= \frac{3}{1} \cdot \frac{1}{4}

Apply the fraction rule:

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

= \frac{3 \cdot 1}{1 \cdot 4}

Multiply the numbers:

3 \cdot 1 = 3

= \frac{3}{1 \cdot 4}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{3}{4}

= \frac{3}{10} + \frac{3}{4}

Add and subtract (left to right)

\frac{3}{10} + \frac{3}{4} : \frac{21}{20}

\frac{3}{10} + \frac{3}{4}

\frac{3}{10} + \frac{3}{4} = \frac{21}{20}

\frac{3}{10} + \frac{3}{4}

Least Common Multiplier of

10, 4 : 20

10, 4

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

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

10

4

= 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{3}{10} :

multiply the denominator and numerator by

2

\frac{3}{10} = \frac{3 \cdot 2}{10 \cdot 2} = \frac{6}{20}

For

\frac{3}{4} :

multiply the denominator and numerator by

5

\frac{3}{4} = \frac{3 \cdot 5}{4 \cdot 5} = \frac{15}{20}

= \frac{6}{20} + \frac{15}{20}

Since the denominators are equal, combine the fractions:

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

= \frac{6 + 15}{20}

Add the numbers:

6 + 15 = 21

= \frac{21}{20}

= \frac{21}{20}

= \frac{21}{20}

Convert improper fractions to mixed numbers:

\frac{21}{20} = 1 \frac{1}{20}

\frac{21}{20} = 1

Remainder

1

\frac{21}{20}

Write the problem in long division format

20 \overline{∣ 21}

Divide

21

20

to get

1

Divide

21

20

to get

1

1 20 \overline{∣ 21}

Multiply the quotient digit

(1)

by the divisor

20

1 20 \overline{∣ 21} \underline{20}

Subtract

20

from

21

1 20 \overline{∣ 21} \underline{20} 1

1 20 \overline{∣ 21} \underline{20} 1

The solution for Long Division of

\frac{21}{20}

1

with remainder of

1

1 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{21}{20} = 1 \frac{1}{20}

= 1 \frac{1}{20}

= 1 \frac{1}{20}

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Frequently Asked Questions (FAQ)

What is 3/5 \div 2+3*1/4 ?
The solution to 3/5 \div 2+3*1/4 is 1 1/20

3/5 \div 2+3*1/4

Solution

Solution

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Frequently Asked Questions (FAQ)

What is 3/5 \div 2+3*1/4 ?

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