What is 5/7+9-5/3-9/4 ?

The solution to 5/7+9-5/3-9/4 is 5 67/84

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Popular Pre Algebra >

5/7+9-5/3-9/4

Solution

\frac{5}{7} + 9 - \frac{5}{3} - \frac{9}{4}

Solution

5 \frac{67}{84}

Decimal

5.79761 \dots

Solution steps

\frac{5}{7} + 9 - \frac{5}{3} - \frac{9}{4}

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{5}{7} + 9 = \frac{68}{7}

\frac{5}{7} + 9

Convert element to fraction:

9 = \frac{9 \cdot 7}{7}

= \frac{9 \cdot 7}{7} + \frac{5}{7}

Since the denominators are equal, combine the fractions:

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

= \frac{9 \cdot 7 + 5}{7}

9 \cdot 7 + 5 = 68

9 \cdot 7 + 5

Multiply the numbers:

9 \cdot 7 = 63

= 63 + 5

Add the numbers:

63 + 5 = 68

= 68

= \frac{68}{7}

= \frac{68}{7} - \frac{5}{3} - \frac{9}{4}

\frac{68}{7} - \frac{5}{3} = \frac{169}{21}

\frac{68}{7} - \frac{5}{3}

Least Common Multiplier of

7, 3 : 21

7, 3

Least Common Multiplier (LCM)

Prime factorization of

7 : 7

7

7

is a prime number, therefore no factorization is possible

= 7

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

7

3

= 7 \cdot 3

Multiply the numbers:

7 \cdot 3 = 21

= 21

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

21

For

\frac{68}{7} :

multiply the denominator and numerator by

3

\frac{68}{7} = \frac{68 \cdot 3}{7 \cdot 3} = \frac{204}{21}

For

\frac{5}{3} :

multiply the denominator and numerator by

7

\frac{5}{3} = \frac{5 \cdot 7}{3 \cdot 7} = \frac{35}{21}

= \frac{204}{21} - \frac{35}{21}

Since the denominators are equal, combine the fractions:

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

= \frac{204 - 35}{21}

Subtract the numbers:

204 - 35 = 169

= \frac{169}{21}

= \frac{169}{21} - \frac{9}{4}

\frac{169}{21} - \frac{9}{4} = \frac{487}{84}

\frac{169}{21} - \frac{9}{4}

Least Common Multiplier of

21, 4 : 84

21, 4

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

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

21

4

= 3 \cdot 7 \cdot 2 \cdot 2

Multiply the numbers:

3 \cdot 7 \cdot 2 \cdot 2 = 84

= 84

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

84

For

\frac{169}{21} :

multiply the denominator and numerator by

4

\frac{169}{21} = \frac{169 \cdot 4}{21 \cdot 4} = \frac{676}{84}

For

\frac{9}{4} :

multiply the denominator and numerator by

21

\frac{9}{4} = \frac{9 \cdot 21}{4 \cdot 21} = \frac{189}{84}

= \frac{676}{84} - \frac{189}{84}

Since the denominators are equal, combine the fractions:

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

= \frac{676 - 189}{84}

Subtract the numbers:

676 - 189 = 487

= \frac{487}{84}

= \frac{487}{84}

Convert improper fractions to mixed numbers:

\frac{487}{84} = 5 \frac{67}{84}

\frac{487}{84} = 5

Remainder

67

\frac{487}{84}

Write the problem in long division format

84 \overline{∣ 487}

Divide

487

84

to get

5

Divide

487

84

to get

5

5 84 \overline{∣ 487}

Multiply the quotient digit

(5)

by the divisor

84

5 84 \overline{∣ 487} \underline{420}

Subtract

420

from

487

5 84 \overline{∣ 487} \underline{420} 67

5 84 \overline{∣ 487} \underline{420} 67

The solution for Long Division of

\frac{487}{84}

5

with remainder of

67

5 Remainder 67

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{487}{84} = 5 \frac{67}{84}

= 5 \frac{67}{84}

= 5 \frac{67}{84}

Popular Examples

500-(2^5-20+15\div 4)\div 2

Frequently Asked Questions (FAQ)

What is 5/7+9-5/3-9/4 ?
The solution to 5/7+9-5/3-9/4 is 5 67/84

5/7+9-5/3-9/4

Solution

Solution

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Frequently Asked Questions (FAQ)

What is 5/7+9-5/3-9/4 ?

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