What is 24(6)^2+29/24 (6)-62/3 ?

The solution to 24(6)^2+29/24 (6)-62/3 is 850 7/12

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Popular Pre Algebra >

24(6)^2+29/24 (6)-62/3

Solution

24 (6)^{2} + \frac{29}{24} (6) - \frac{62}{3}

Solution

850 \frac{7}{12}

Decimal

850.58333 \dots

Solution steps

24 (6)^{2} + \frac{29}{24} (6) - \frac{62}{3}

Follow the PEMDAS order of operations

Calculate exponents

(6)^{2} : 36

(6)^{2}

(6)^{2} = 36

= 36

= 24 \cdot 36 + \frac{29}{24} (6) - \frac{62}{3}

Multiply and divide (left to right)

24 \cdot 36 : 864

24 \cdot 36

24 \cdot 36 = 864

= 864

= 864 + \frac{29}{24} (6) - \frac{62}{3}

Multiply and divide (left to right)

\frac{29}{24} (6) : \frac{29}{4}

\frac{29}{24} (6)

Apply rule:

(a) = a

(6) = 6

= \frac{29}{24} \cdot 6

\frac{29}{24} \cdot 6 = \frac{29}{4}

\frac{29}{24} \cdot 6

Convert element to fraction:

6 = \frac{6}{1}

= \frac{29}{24} \cdot \frac{6}{1}

Apply the fraction rule:

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

= \frac{29 \cdot 6}{24 \cdot 1}

\frac{29 \cdot 6}{24 \cdot 1} = \frac{29}{4}

\frac{29 \cdot 6}{24 \cdot 1}

Multiply the numbers:

24 \cdot 1 = 24

= \frac{29 \cdot 6}{24}

Factor the number:

24 = 6 \cdot 4

= \frac{29 \cdot 6}{6 \cdot 4}

Cancel the common factor:

6

= \frac{29}{4}

= \frac{29}{4}

= \frac{29}{4}

= 864 + \frac{29}{4} - \frac{62}{3}

Add and subtract (left to right)

864 + \frac{29}{4} - \frac{62}{3} : \frac{10207}{12}

864 + \frac{29}{4} - \frac{62}{3}

864 + \frac{29}{4} = \frac{3485}{4}

864 + \frac{29}{4}

Convert element to fraction:

864 = \frac{864 \cdot 4}{4}

= \frac{864 \cdot 4}{4} + \frac{29}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{864 \cdot 4 + 29}{4}

864 \cdot 4 + 29 = 3485

864 \cdot 4 + 29

Multiply the numbers:

864 \cdot 4 = 3456

= 3456 + 29

Add the numbers:

3456 + 29 = 3485

= 3485

= \frac{3485}{4}

= \frac{3485}{4} - \frac{62}{3}

\frac{3485}{4} - \frac{62}{3} = \frac{10207}{12}

\frac{3485}{4} - \frac{62}{3}

Least Common Multiplier of

4, 3 : 12

4, 3

Least Common Multiplier (LCM)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

4

3

= 2 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 3 = 12

= 12

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

12

For

\frac{3485}{4} :

multiply the denominator and numerator by

3

\frac{3485}{4} = \frac{3485 \cdot 3}{4 \cdot 3} = \frac{10455}{12}

For

\frac{62}{3} :

multiply the denominator and numerator by

4

\frac{62}{3} = \frac{62 \cdot 4}{3 \cdot 4} = \frac{248}{12}

= \frac{10455}{12} - \frac{248}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{10455 - 248}{12}

Subtract the numbers:

10455 - 248 = 10207

= \frac{10207}{12}

= \frac{10207}{12}

= \frac{10207}{12}

Convert improper fractions to mixed numbers:

\frac{10207}{12} = 850 \frac{7}{12}

\frac{10207}{12} = 850

Remainder

7

\frac{10207}{12}

Write the problem in long division format

12 \overline{∣ 10207}

Divide

102

12

to get

8

Divide

102

12

to get

8

8 12 \overline{∣ 10207}

Multiply the quotient digit

(8)

by the divisor

12

8 12 \overline{∣ 10207} \underline{96}

Subtract

96

from

102

8 12 \overline{∣ 10207} \underline{96} 6

Bring down the next number of the dividend

8 12 \overline{∣ 10207} \underline{96} 60

8 12 \overline{∣ 10207} \underline{96} 60

Divide

60

12

to get

5

Divide

60

12

to get

5

85 12 \overline{∣ 10207} \underline{96} 60

Multiply the quotient digit

(5)

by the divisor

12

85 12 \overline{∣ 10207} \underline{96} 60 \underline{60}

Subtract

60

from

60

85 12 \overline{∣ 10207} \underline{96} 60 \underline{60} 0

Bring down the next number of the dividend

85 12 \overline{∣ 10207} \underline{96} 60 \underline{60} 07

85 12 \overline{∣ 10207} \underline{96} 60 \underline{60} 07

Divide

7

12

to get

0

Divide

7

12

to get

0

850 12 \overline{∣ 10207} \underline{96} 60 \underline{60} 07

Multiply the quotient digit

(0)

by the divisor

12

850 12 \overline{∣ 10207} \underline{96} 60 \underline{60} 07 \underline{0}

Subtract

0

from

7

850 12 \overline{∣ 10207} \underline{96} 60 \underline{60} 07 \underline{0} 7

850 12 \overline{∣ 10207} \underline{96} 60 \underline{60} 07 \underline{0} 7

The solution for Long Division of

\frac{10207}{12}

850

with remainder of

7

850 Remainder 7

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{10207}{12} = 850 \frac{7}{12}

= 850 \frac{7}{12}

= 850 \frac{7}{12}

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Frequently Asked Questions (FAQ)

What is 24(6)^2+29/24 (6)-62/3 ?
The solution to 24(6)^2+29/24 (6)-62/3 is 850 7/12

24(6)^2+29/24 (6)-62/3

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 24(6)^2+29/24 (6)-62/3 ?

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