What is 1/10+2-2/35 ?

The solution to 1/10+2-2/35 is 2 3/70

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1/10+2-2/35

Solution

\frac{1}{10} + 2 - \frac{2}{35}

Solution

2 \frac{3}{70}

Solution steps

\frac{1}{10} + 2 - \frac{2}{35}

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{1}{10} + 2 = \frac{21}{10}

\frac{1}{10} + 2

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

2 \cdot 10 + 1 = 21

2 \cdot 10 + 1

Multiply the numbers:

2 \cdot 10 = 20

= 20 + 1

Add the numbers:

20 + 1 = 21

= 21

= \frac{21}{10}

= \frac{21}{10} - \frac{2}{35}

\frac{21}{10} - \frac{2}{35} = \frac{143}{70}

\frac{21}{10} - \frac{2}{35}

Least Common Multiplier of

10, 35 : 70

10, 35

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

35 : 5 \cdot 7

35

35

divides by

535 = 7 \cdot 5

= 5 \cdot 7

5, 7

are all prime numbers, therefore no further factorization is possible

= 5 \cdot 7

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

10

35

= 2 \cdot 5 \cdot 7

Multiply the numbers:

2 \cdot 5 \cdot 7 = 70

= 70

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

70

For

\frac{21}{10} :

multiply the denominator and numerator by

7

\frac{21}{10} = \frac{21 \cdot 7}{10 \cdot 7} = \frac{147}{70}

For

\frac{2}{35} :

multiply the denominator and numerator by

2

\frac{2}{35} = \frac{2 \cdot 2}{35 \cdot 2} = \frac{4}{70}

= \frac{147}{70} - \frac{4}{70}

Since the denominators are equal, combine the fractions:

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

= \frac{147 - 4}{70}

Subtract the numbers:

147 - 4 = 143

= \frac{143}{70}

= \frac{143}{70}

Convert improper fractions to mixed numbers:

\frac{143}{70} = 2 \frac{3}{70}

\frac{143}{70} = 2

Remainder

3

\frac{143}{70}

Write the problem in long division format

70 \overline{∣ 143}

Divide

143

70

to get

2

Divide

143

70

to get

2

2 70 \overline{∣ 143}

Multiply the quotient digit

(2)

by the divisor

70

2 70 \overline{∣ 143} \underline{140}

Subtract

140

from

143

2 70 \overline{∣ 143} \underline{140} 3

2 70 \overline{∣ 143} \underline{140} 3

The solution for Long Division of

\frac{143}{70}

2

with remainder of

3

2 Remainder 3

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{143}{70} = 2 \frac{3}{70}

= 2 \frac{3}{70}

= 2 \frac{3}{70}

Popular Examples

(7\div 10-1\div 5)\div 10\div 7

(7 \div 10 - 1 \div 5) \div 10 \div 7

-3(4)^2+6(4)+24

- 3 (4)^{2} + 6 (4) + 24

(1-41)^3

(1 - 41)^{3}

6-6\times 1/3

6 - 6 \times \frac{1}{3}

(30+7)^2

(30 + 7)^{2}

Frequently Asked Questions (FAQ)

What is 1/10+2-2/35 ?
The solution to 1/10+2-2/35 is 2 3/70