What is (4 2/5+7 8/9)-6 2/4 ?

The solution to (4 2/5+7 8/9)-6 2/4 is 5 71/90

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Popular >

(4 2/5+7 8/9)-6 2/4

Solution

(4 \frac{2}{5} + 7 \frac{8}{9}) - 6 \frac{2}{4}

Solution

5 \frac{71}{90}

Solution steps

(4 \frac{2}{5} + 7 \frac{8}{9}) - 6 \frac{2}{4}

Convert mixed numbers to improper fractions:

6 \frac{2}{4} = \frac{26}{4}

6 \frac{2}{4}

Convert mixed numbers to improper fraction:

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

6 \frac{2}{4} = \frac{6 \cdot 4 + 2}{4}

= \frac{26}{4}

= (4 \frac{2}{5} + 7 \frac{8}{9}) - \frac{26}{4}

Convert mixed numbers to improper fractions:

4 \frac{2}{5} = \frac{22}{5}

4 \frac{2}{5}

Convert mixed numbers to improper fraction:

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

4 \frac{2}{5} = \frac{4 \cdot 5 + 2}{5}

= \frac{22}{5}

= (\frac{22}{5} + 7 \frac{8}{9}) - \frac{26}{4}

Convert mixed numbers to improper fractions:

7 \frac{8}{9} = \frac{71}{9}

7 \frac{8}{9}

Convert mixed numbers to improper fraction:

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

7 \frac{8}{9} = \frac{7 \cdot 9 + 8}{9}

= \frac{71}{9}

= (\frac{22}{5} + \frac{71}{9}) - \frac{26}{4}

\frac{26}{4} = \frac{13}{2}

Cancel the common factor:

2

\frac{13}{2}

= \frac{22}{5} + \frac{71}{9} - \frac{13}{2}

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{22}{5} + \frac{71}{9} - \frac{13}{2} : \frac{521}{90}

\frac{22}{5} + \frac{71}{9} - \frac{13}{2}

\frac{22}{5} + \frac{71}{9} = \frac{553}{45}

\frac{22}{5} + \frac{71}{9}

Least Common Multiplier of

5, 9 : 45

5, 9

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

5

9

= 5 \cdot 3 \cdot 3

Multiply the numbers:

5 \cdot 3 \cdot 3 = 45

= 45

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

45

For

\frac{22}{5} :

multiply the denominator and numerator by

9

\frac{22}{5} = \frac{22 \cdot 9}{5 \cdot 9} = \frac{198}{45}

For

\frac{71}{9} :

multiply the denominator and numerator by

5

\frac{71}{9} = \frac{71 \cdot 5}{9 \cdot 5} = \frac{355}{45}

= \frac{198}{45} + \frac{355}{45}

Since the denominators are equal, combine the fractions:

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

= \frac{198 + 355}{45}

Add the numbers:

198 + 355 = 553

= \frac{553}{45}

= \frac{553}{45} - \frac{13}{2}

\frac{553}{45} - \frac{13}{2} = \frac{521}{90}

\frac{553}{45} - \frac{13}{2}

Least Common Multiplier of

45, 2 : 90

45, 2

Least Common Multiplier (LCM)

Prime factorization of

45 : 3 \cdot 3 \cdot 5

45

45

divides by

345 = 15 \cdot 3

= 3 \cdot 15

15

divides by

315 = 5 \cdot 3

= 3 \cdot 3 \cdot 5

3, 5

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 3 \cdot 5

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

45

2

= 3 \cdot 3 \cdot 5 \cdot 2

Multiply the numbers:

3 \cdot 3 \cdot 5 \cdot 2 = 90

= 90

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

90

For

\frac{553}{45} :

multiply the denominator and numerator by

2

\frac{553}{45} = \frac{553 \cdot 2}{45 \cdot 2} = \frac{1106}{90}

For

\frac{13}{2} :

multiply the denominator and numerator by

45

\frac{13}{2} = \frac{13 \cdot 45}{2 \cdot 45} = \frac{585}{90}

= \frac{1106}{90} - \frac{585}{90}

Since the denominators are equal, combine the fractions:

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

= \frac{1106 - 585}{90}

Subtract the numbers:

1106 - 585 = 521

= \frac{521}{90}

= \frac{521}{90}

= \frac{521}{90}

Convert improper fractions to mixed numbers:

\frac{521}{90} = 5 \frac{71}{90}

\frac{521}{90} = 5

Remainder

71

\frac{521}{90}

Write the problem in long division format

90 \overline{∣ 521}

Divide

521

90

to get

5

Divide

521

90

to get

5

5 90 \overline{∣ 521}

Multiply the quotient digit

(5)

by the divisor

90

5 90 \overline{∣ 521} \underline{450}

Subtract

450

from

521

5 90 \overline{∣ 521} \underline{450} 71

5 90 \overline{∣ 521} \underline{450} 71

The solution for Long Division of

\frac{521}{90}

5

with remainder of

71

5 Remainder 71

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{521}{90} = 5 \frac{71}{90}

= 5 \frac{71}{90}

= 5 \frac{71}{90}

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2 \times 1 + 4

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2 \times 1 - 5

Frequently Asked Questions (FAQ)

What is (4 2/5+7 8/9)-6 2/4 ?
The solution to (4 2/5+7 8/9)-6 2/4 is 5 71/90