What is 343 1/3+625 1/4-2^2 ?

The solution to 343 1/3+625 1/4-2^2 is 964 7/12

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Popular Pre Algebra >

343 1/3+625 1/4-2^2

Solution

343 \frac{1}{3} + 625 \frac{1}{4} - 2^{2}

Solution

964 \frac{7}{12}

Decimal

964.58333 \dots

Solution steps

343 \frac{1}{3} + 625 \frac{1}{4} - 2^{2}

Convert mixed numbers to improper fractions:

343 \frac{1}{3} = \frac{1030}{3}

343 \frac{1}{3}

Convert mixed numbers to improper fraction:

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

343 \frac{1}{3} = \frac{343 \cdot 3 + 1}{3}

= \frac{1030}{3}

= \frac{1030}{3} + 625 \frac{1}{4} - 2^{2}

Convert mixed numbers to improper fractions:

625 \frac{1}{4} = \frac{2501}{4}

625 \frac{1}{4}

Convert mixed numbers to improper fraction:

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

625 \frac{1}{4} = \frac{625 \cdot 4 + 1}{4}

= \frac{2501}{4}

= \frac{1030}{3} + \frac{2501}{4} - 2^{2}

Follow the PEMDAS order of operations

Calculate exponents

2^{2} : 4

2^{2}

2^{2} = 4

= 4

= \frac{1030}{3} + \frac{2501}{4} - 4

Add and subtract (left to right)

\frac{1030}{3} + \frac{2501}{4} - 4 : \frac{11575}{12}

\frac{1030}{3} + \frac{2501}{4} - 4

\frac{1030}{3} + \frac{2501}{4} = \frac{11623}{12}

\frac{1030}{3} + \frac{2501}{4}

Least Common Multiplier of

3, 4 : 12

3, 4

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

3

4

= 3 \cdot 2 \cdot 2

Multiply the numbers:

3 \cdot 2 \cdot 2 = 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{1030}{3} :

multiply the denominator and numerator by

4

\frac{1030}{3} = \frac{1030 \cdot 4}{3 \cdot 4} = \frac{4120}{12}

For

\frac{2501}{4} :

multiply the denominator and numerator by

3

\frac{2501}{4} = \frac{2501 \cdot 3}{4 \cdot 3} = \frac{7503}{12}

= \frac{4120}{12} + \frac{7503}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{4120 + 7503}{12}

Add the numbers:

4120 + 7503 = 11623

= \frac{11623}{12}

= \frac{11623}{12} - 4

\frac{11623}{12} - 4 = \frac{11575}{12}

\frac{11623}{12} - 4

Convert element to fraction:

4 = \frac{4 \cdot 12}{12}

= - \frac{4 \cdot 12}{12} + \frac{11623}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{- 4 \cdot 12 + 11623}{12}

- 4 \cdot 12 + 11623 = 11575

- 4 \cdot 12 + 11623

Multiply the numbers:

4 \cdot 12 = 48

= - 48 + 11623

Add/Subtract the numbers:

- 48 + 11623 = 11575

= 11575

= \frac{11575}{12}

= \frac{11575}{12}

= \frac{11575}{12}

Convert improper fractions to mixed numbers:

\frac{11575}{12} = 964 \frac{7}{12}

\frac{11575}{12} = 964

Remainder

7

\frac{11575}{12}

Write the problem in long division format

12 \overline{∣ 11575}

Divide

115

12

to get

9

Divide

115

12

to get

9

9 12 \overline{∣ 11575}

Multiply the quotient digit

(9)

by the divisor

12

9 12 \overline{∣ 11575} \underline{108}

Subtract

108

from

115

9 12 \overline{∣ 11575} \underline{108} 7

Bring down the next number of the dividend

9 12 \overline{∣ 11575} \underline{108} 77

9 12 \overline{∣ 11575} \underline{108} 77

Divide

77

12

to get

6

Divide

77

12

to get

6

96 12 \overline{∣ 11575} \underline{108} 77

Multiply the quotient digit

(6)

by the divisor

12

96 12 \overline{∣ 11575} \underline{108} 77 \underline{72}

Subtract

72

from

77

96 12 \overline{∣ 11575} \underline{108} 77 \underline{72} 5

Bring down the next number of the dividend

96 12 \overline{∣ 11575} \underline{108} 77 \underline{72} 55

96 12 \overline{∣ 11575} \underline{108} 77 \underline{72} 55

Divide

55

12

to get

4

Divide

55

12

to get

4

964 12 \overline{∣ 11575} \underline{108} 77 \underline{72} 55

Multiply the quotient digit

(4)

by the divisor

12

964 12 \overline{∣ 11575} \underline{108} 77 \underline{72} 55 \underline{48}

Subtract

48

from

55

964 12 \overline{∣ 11575} \underline{108} 77 \underline{72} 55 \underline{48} 7

964 12 \overline{∣ 11575} \underline{108} 77 \underline{72} 55 \underline{48} 7

The solution for Long Division of

\frac{11575}{12}

964

with remainder of

7

964 Remainder 7

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{11575}{12} = 964 \frac{7}{12}

= 964 \frac{7}{12}

= 964 \frac{7}{12}

Popular Examples

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Frequently Asked Questions (FAQ)

What is 343 1/3+625 1/4-2^2 ?
The solution to 343 1/3+625 1/4-2^2 is 964 7/12

343 1/3+625 1/4-2^2

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 343 1/3+625 1/4-2^2 ?

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