What is (8-3/5)\div 3 1/2 ?

The solution to (8-3/5)\div 3 1/2 is 2 4/35

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(8-3/5)\div 3 1/2

Solution

(8 - \frac{3}{5}) \div 3 \frac{1}{2}

Solution

2 \frac{4}{35}

Solution steps

(8 - \frac{3}{5}) \div 3 \frac{1}{2}

Convert mixed numbers to improper fractions:

3 \frac{1}{2} = \frac{7}{2}

3 \frac{1}{2}

Convert mixed numbers to improper fraction:

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

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

= \frac{7}{2}

= (8 - \frac{3}{5}) \div \frac{7}{2}

Follow the PEMDAS order of operations

Calculate within parentheses

(8 - \frac{3}{5}) : \frac{37}{5}

8 - \frac{3}{5}

8 - \frac{3}{5} = \frac{37}{5}

8 - \frac{3}{5}

Convert element to fraction:

8 = \frac{8 \cdot 5}{5}

= \frac{8 \cdot 5}{5} - \frac{3}{5}

Since the denominators are equal, combine the fractions:

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

= \frac{8 \cdot 5 - 3}{5}

8 \cdot 5 - 3 = 37

8 \cdot 5 - 3

Multiply the numbers:

8 \cdot 5 = 40

= 40 - 3

Subtract the numbers:

40 - 3 = 37

= 37

= \frac{37}{5}

= \frac{37}{5}

= \frac{37}{5} \div \frac{7}{2}

Multiply and divide (left to right)

\frac{37}{5} \div \frac{7}{2} : \frac{74}{35}

\frac{37}{5} \div \frac{7}{2}

Apply the fraction rule:

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

= \frac{37}{5} \cdot \frac{2}{7}

Multiply fractions:

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

= \frac{37 \cdot 2}{5 \cdot 7}

Multiply the numbers:

37 \cdot 2 = 74

= \frac{74}{5 \cdot 7}

Multiply the numbers:

5 \cdot 7 = 35

= \frac{74}{35}

= \frac{74}{35}

Convert improper fractions to mixed numbers:

\frac{74}{35} = 2 \frac{4}{35}

\frac{74}{35} = 2

Remainder

4

\frac{74}{35}

Write the problem in long division format

35 \overline{∣ 74}

Divide

74

35

to get

2

Divide

74

35

to get

2

2 35 \overline{∣ 74}

Multiply the quotient digit

(2)

by the divisor

35

2 35 \overline{∣ 74} \underline{70}

Subtract

70

from

74

2 35 \overline{∣ 74} \underline{70} 4

2 35 \overline{∣ 74} \underline{70} 4

The solution for Long Division of

\frac{74}{35}

2

with remainder of

4

2 Remainder 4

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{74}{35} = 2 \frac{4}{35}

= 2 \frac{4}{35}

= 2 \frac{4}{35}

Popular Examples

1^2+8^2

1^{2} + 8^{2}

8(2)^2-11

8 (2)^{2} - 11

1*10^0

1 \cdot 1 0^{0}

4(4)+5

4 (4) + 5

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

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

Frequently Asked Questions (FAQ)

What is (8-3/5)\div 3 1/2 ?
The solution to (8-3/5)\div 3 1/2 is 2 4/35