The solution to 3-2/21-5/9 is 2 22/63

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Popular Pre Algebra >

3-2/21-5/9

Solution

3 - \frac{2}{21} - \frac{5}{9}

Solution

2 \frac{22}{63}

Decimal

2.34920 \dots

Solution steps

3 - \frac{2}{21} - \frac{5}{9}

Follow the PEMDAS order of operations

Add and subtract (left to right)

3 - \frac{2}{21} = \frac{61}{21}

3 - \frac{2}{21}

Convert element to fraction:

3 = \frac{3 \cdot 21}{21}

= \frac{3 \cdot 21}{21} - \frac{2}{21}

Since the denominators are equal, combine the fractions:

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

= \frac{3 \cdot 21 - 2}{21}

3 \cdot 21 - 2 = 61

3 \cdot 21 - 2

Multiply the numbers:

3 \cdot 21 = 63

= 63 - 2

Subtract the numbers:

63 - 2 = 61

= 61

= \frac{61}{21}

= \frac{61}{21} - \frac{5}{9}

\frac{61}{21} - \frac{5}{9} = \frac{148}{63}

\frac{61}{21} - \frac{5}{9}

Least Common Multiplier of

21, 9 : 63

21, 9

Least Common Multiplier (LCM)

Prime factorization of

21 : 3 \cdot 7

21

21

divides by

321 = 7 \cdot 3

= 3 \cdot 7

3, 7

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 7

Prime factorization of

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

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

21

9

= 3 \cdot 3 \cdot 7

Multiply the numbers:

3 \cdot 3 \cdot 7 = 63

= 63

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

63

For

\frac{61}{21} :

multiply the denominator and numerator by

3

\frac{61}{21} = \frac{61 \cdot 3}{21 \cdot 3} = \frac{183}{63}

For

\frac{5}{9} :

multiply the denominator and numerator by

7

\frac{5}{9} = \frac{5 \cdot 7}{9 \cdot 7} = \frac{35}{63}

= \frac{183}{63} - \frac{35}{63}

Since the denominators are equal, combine the fractions:

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

= \frac{183 - 35}{63}

Subtract the numbers:

183 - 35 = 148

= \frac{148}{63}

= \frac{148}{63}

Convert improper fractions to mixed numbers:

\frac{148}{63} = 2 \frac{22}{63}

\frac{148}{63} = 2

Remainder

22

\frac{148}{63}

Write the problem in long division format

63 \overline{∣ 148}

Divide

148

63

to get

2

Divide

148

63

to get

2

2 63 \overline{∣ 148}

Multiply the quotient digit

(2)

by the divisor

63

2 63 \overline{∣ 148} \underline{126}

Subtract

126

from

148

2 63 \overline{∣ 148} \underline{126} 22

2 63 \overline{∣ 148} \underline{126} 22

The solution for Long Division of

\frac{148}{63}

2

with remainder of

22

2 Remainder 22

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{148}{63} = 2 \frac{22}{63}

= 2 \frac{22}{63}

= 2 \frac{22}{63}

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What is 3-2/21-5/9 ?
The solution to 3-2/21-5/9 is 2 22/63

3-2/21-5/9

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