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

The solution to (5 1/2)\div (3 2/5)+1 is 2 21/34

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

Solution

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

Solution

2 \frac{21}{34}

Solution steps

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

Convert mixed numbers to improper fractions:

5 \frac{1}{2} = \frac{11}{2}

5 \frac{1}{2}

Convert mixed numbers to improper fraction:

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

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

= \frac{11}{2}

= (\frac{11}{2}) \div (3 \frac{2}{5}) + 1

Convert mixed numbers to improper fractions:

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

3 \frac{2}{5}

Convert mixed numbers to improper fraction:

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

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

= \frac{17}{5}

= (\frac{11}{2}) \div (\frac{17}{5}) + 1

Follow the PEMDAS order of operations

Multiply and divide (left to right)

(\frac{11}{2}) \div (\frac{17}{5}) : \frac{( \frac{11}{2} )}{( \frac{17}{5} )}

(\frac{11}{2}) \div (\frac{17}{5})

(\frac{11}{2}) \div (\frac{17}{5}) = \frac{( \frac{11}{2} )}{( \frac{17}{5} )}

= \frac{( \frac{11}{2} )}{( \frac{17}{5} )}

= \frac{( \frac{11}{2} )}{( \frac{17}{5} )} + 1

Add and subtract (left to right)

\frac{( \frac{11}{2} )}{( \frac{17}{5} )} + 1 : \frac{89}{34}

\frac{( \frac{11}{2} )}{( \frac{17}{5} )} + 1

\frac{( \frac{11}{2} )}{( \frac{17}{5} )} + 1 = \frac{89}{34}

\frac{\frac{11}{2}}{\frac{17}{5}} + 1

\frac{\frac{11}{2}}{\frac{17}{5}} = \frac{55}{34}

\frac{\frac{11}{2}}{\frac{17}{5}}

Divide fractions:

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

= \frac{11 \cdot 5}{2 \cdot 17}

Multiply the numbers:

2 \cdot 17 = 34

= \frac{11 \cdot 5}{34}

Multiply the numbers:

11 \cdot 5 = 55

= \frac{55}{34}

= \frac{55}{34} + 1

Convert element to fraction:

1 = \frac{1 \cdot 34}{34}

= \frac{1 \cdot 34}{34} + \frac{55}{34}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 34 + 55}{34}

1 \cdot 34 + 55 = 89

1 \cdot 34 + 55

Multiply the numbers:

1 \cdot 34 = 34

= 34 + 55

Add the numbers:

34 + 55 = 89

= 89

= \frac{89}{34}

= \frac{89}{34}

= \frac{89}{34}

Convert improper fractions to mixed numbers:

\frac{89}{34} = 2 \frac{21}{34}

\frac{89}{34} = 2

Remainder

21

\frac{89}{34}

Write the problem in long division format

34 \overline{∣ 89}

Divide

89

34

to get

2

Divide

89

34

to get

2

2 34 \overline{∣ 89}

Multiply the quotient digit

(2)

by the divisor

34

2 34 \overline{∣ 89} \underline{68}

Subtract

68

from

89

2 34 \overline{∣ 89} \underline{68} 21

2 34 \overline{∣ 89} \underline{68} 21

The solution for Long Division of

\frac{89}{34}

2

with remainder of

21

2 Remainder 21

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{89}{34} = 2 \frac{21}{34}

= 2 \frac{21}{34}

= 2 \frac{21}{34}

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Frequently Asked Questions (FAQ)

What is (5 1/2)\div (3 2/5)+1 ?
The solution to (5 1/2)\div (3 2/5)+1 is 2 21/34