What is (7+3 1/8)+(14+6 1/4) ?

The solution to (7+3 1/8)+(14+6 1/4) is 30 3/8

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Popular Pre Algebra >

(7+3 1/8)+(14+6 1/4)

Solution

(7 + 3 \frac{1}{8}) + (14 + 6 \frac{1}{4})

Solution

30 \frac{3}{8}

Decimal

30.375

Solution steps

(7 + 3 \frac{1}{8}) + (14 + 6 \frac{1}{4})

Convert mixed numbers to improper fractions:

3 \frac{1}{8} = \frac{25}{8}

3 \frac{1}{8}

Convert mixed numbers to improper fraction:

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

3 \frac{1}{8} = \frac{3 \cdot 8 + 1}{8}

= \frac{25}{8}

= (7 + \frac{25}{8}) + (14 + 6 \frac{1}{4})

Convert mixed numbers to improper fractions:

6 \frac{1}{4} = \frac{25}{4}

6 \frac{1}{4}

Convert mixed numbers to improper fraction:

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

6 \frac{1}{4} = \frac{6 \cdot 4 + 1}{4}

= \frac{25}{4}

= (7 + \frac{25}{8}) + (14 + \frac{25}{4})

Follow the PEMDAS order of operations

Calculate within parentheses

(7 + \frac{25}{8}) : \frac{81}{8}

7 + \frac{25}{8}

7 + \frac{25}{8} = \frac{81}{8}

7 + \frac{25}{8}

Convert element to fraction:

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

= \frac{7 \cdot 8}{8} + \frac{25}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{7 \cdot 8 + 25}{8}

7 \cdot 8 + 25 = 81

7 \cdot 8 + 25

Multiply the numbers:

7 \cdot 8 = 56

= 56 + 25

Add the numbers:

56 + 25 = 81

= 81

= \frac{81}{8}

= \frac{81}{8}

= \frac{81}{8} + (14 + \frac{25}{4})

Calculate within parentheses

(14 + \frac{25}{4}) : \frac{81}{4}

14 + \frac{25}{4}

14 + \frac{25}{4} = \frac{81}{4}

14 + \frac{25}{4}

Convert element to fraction:

14 = \frac{14 \cdot 4}{4}

= \frac{14 \cdot 4}{4} + \frac{25}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{14 \cdot 4 + 25}{4}

14 \cdot 4 + 25 = 81

14 \cdot 4 + 25

Multiply the numbers:

14 \cdot 4 = 56

= 56 + 25

Add the numbers:

56 + 25 = 81

= 81

= \frac{81}{4}

= \frac{81}{4}

= \frac{81}{8} + \frac{81}{4}

Add and subtract (left to right)

\frac{81}{8} + \frac{81}{4} : \frac{243}{8}

\frac{81}{8} + \frac{81}{4}

\frac{81}{8} + \frac{81}{4} = \frac{243}{8}

\frac{81}{8} + \frac{81}{4}

Least Common Multiplier of

8, 4 : 8

8, 4

Least Common Multiplier (LCM)

Prime factorization of

8 : 2 \cdot 2 \cdot 2

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

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

8

4

= 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 = 8

= 8

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

8

For

\frac{81}{4} :

multiply the denominator and numerator by

2

\frac{81}{4} = \frac{81 \cdot 2}{4 \cdot 2} = \frac{162}{8}

= \frac{81}{8} + \frac{162}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{81 + 162}{8}

Add the numbers:

81 + 162 = 243

= \frac{243}{8}

= \frac{243}{8}

= \frac{243}{8}

Convert improper fractions to mixed numbers:

\frac{243}{8} = 30 \frac{3}{8}

\frac{243}{8} = 30

Remainder

3

\frac{243}{8}

Write the problem in long division format

8 \overline{∣ 243}

Divide

24

8

to get

3

Divide

24

8

to get

3

3 8 \overline{∣ 243}

Multiply the quotient digit

(3)

by the divisor

8

3 8 \overline{∣ 243} \underline{24}

Subtract

24

from

24

3 8 \overline{∣ 243} \underline{24} 0

Bring down the next number of the dividend

3 8 \overline{∣ 243} \underline{24} 03

3 8 \overline{∣ 243} \underline{24} 03

Divide

3

8

to get

0

Divide

3

8

to get

0

30 8 \overline{∣ 243} \underline{24} 03

Multiply the quotient digit

(0)

by the divisor

8

30 8 \overline{∣ 243} \underline{24} 03 \underline{0}

Subtract

0

from

3

30 8 \overline{∣ 243} \underline{24} 03 \underline{0} 3

30 8 \overline{∣ 243} \underline{24} 03 \underline{0} 3

The solution for Long Division of

\frac{243}{8}

30

with remainder of

3

30 Remainder 3

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{243}{8} = 30 \frac{3}{8}

= 30 \frac{3}{8}

= 30 \frac{3}{8}

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Frequently Asked Questions (FAQ)

What is (7+3 1/8)+(14+6 1/4) ?
The solution to (7+3 1/8)+(14+6 1/4) is 30 3/8

(7+3 1/8)+(14+6 1/4)

Solution

Solution

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Frequently Asked Questions (FAQ)

What is (7+3 1/8)+(14+6 1/4) ?

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