What is 2+3\div 6/7 ?

The solution to 2+3\div 6/7 is 5 1/2

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Popular Pre Algebra >

2+3\div 6/7

Solution

2 + 3 \div \frac{6}{7}

Solution

5 \frac{1}{2}

Decimal

5.5

Solution steps

2 + 3 \div \frac{6}{7}

Follow the PEMDAS order of operations

Multiply and divide (left to right)

3 \div \frac{6}{7} : \frac{7}{2}

3 \div \frac{6}{7}

Convert element to fraction:

3 = \frac{3}{1}

= \frac{3}{1} \div \frac{6}{7}

Apply the fraction rule:

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

= \frac{3}{1} \cdot \frac{7}{6}

Cross-cancel common factor:

3

3, 6

Greatest Common Divisor (GCD)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

The prime factors common to

3, 6

are

= 3

= \frac{7}{2}

= 2 + \frac{7}{2}

Add and subtract (left to right)

2 + \frac{7}{2} : \frac{11}{2}

2 + \frac{7}{2}

2 + \frac{7}{2} = \frac{11}{2}

2 + \frac{7}{2}

Convert element to fraction:

2 = \frac{2 \cdot 2}{2}

= \frac{2 \cdot 2}{2} + \frac{7}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{2 \cdot 2 + 7}{2}

2 \cdot 2 + 7 = 11

2 \cdot 2 + 7

Multiply the numbers:

2 \cdot 2 = 4

= 4 + 7

Add the numbers:

4 + 7 = 11

= 11

= \frac{11}{2}

= \frac{11}{2}

= \frac{11}{2}

Convert improper fractions to mixed numbers:

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

\frac{11}{2} = 5

Remainder

1

\frac{11}{2}

Write the problem in long division format

2 \overline{∣ 11}

Divide

11

2

to get

5

Divide

11

2

to get

5

5 2 \overline{∣ 11}

Multiply the quotient digit

(5)

by the divisor

2

5 2 \overline{∣ 11} \underline{10}

Subtract

10

from

11

5 2 \overline{∣ 11} \underline{10} 1

5 2 \overline{∣ 11} \underline{10} 1

The solution for Long Division of

\frac{11}{2}

5

with remainder of

1

5 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

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

= 5 \frac{1}{2}

= 5 \frac{1}{2}

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Frequently Asked Questions (FAQ)

What is 2+3\div 6/7 ?
The solution to 2+3\div 6/7 is 5 1/2

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