What is 400-1/5-1/4-9/30 ?

The solution to 400-1/5-1/4-9/30 is 399 1/4

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400-1/5-1/4-9/30

Solution

400 - \frac{1}{5} - \frac{1}{4} - \frac{9}{30}

Solution

399 \frac{1}{4}

Solution steps

400 - \frac{1}{5} - \frac{1}{4} - \frac{9}{30}

\frac{9}{30} = \frac{3}{10}

Cancel the common factor:

3

\frac{3}{10}

= 400 - \frac{1}{5} - \frac{1}{4} - \frac{3}{10}

Follow the PEMDAS order of operations

Add and subtract (left to right)

400 - \frac{1}{5} - \frac{1}{4} - \frac{3}{10} : \frac{1597}{4}

400 - \frac{1}{5} - \frac{1}{4} - \frac{3}{10}

400 - \frac{1}{5} = \frac{1999}{5}

400 - \frac{1}{5}

Convert element to fraction:

400 = \frac{400 \cdot 5}{5}

= \frac{400 \cdot 5}{5} - \frac{1}{5}

Since the denominators are equal, combine the fractions:

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

= \frac{400 \cdot 5 - 1}{5}

400 \cdot 5 - 1 = 1999

400 \cdot 5 - 1

Multiply the numbers:

400 \cdot 5 = 2000

= 2000 - 1

Subtract the numbers:

2000 - 1 = 1999

= 1999

= \frac{1999}{5}

= \frac{1999}{5} - \frac{1}{4} - \frac{3}{10}

\frac{1999}{5} - \frac{1}{4} = \frac{7991}{20}

\frac{1999}{5} - \frac{1}{4}

Least Common Multiplier of

5, 4 : 20

5, 4

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

5

4

= 5 \cdot 2 \cdot 2

Multiply the numbers:

5 \cdot 2 \cdot 2 = 20

= 20

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

20

For

\frac{1999}{5} :

multiply the denominator and numerator by

4

\frac{1999}{5} = \frac{1999 \cdot 4}{5 \cdot 4} = \frac{7996}{20}

For

\frac{1}{4} :

multiply the denominator and numerator by

5

\frac{1}{4} = \frac{1 \cdot 5}{4 \cdot 5} = \frac{5}{20}

= \frac{7996}{20} - \frac{5}{20}

Since the denominators are equal, combine the fractions:

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

= \frac{7996 - 5}{20}

Subtract the numbers:

7996 - 5 = 7991

= \frac{7991}{20}

= \frac{7991}{20} - \frac{3}{10}

\frac{7991}{20} - \frac{3}{10} = \frac{1597}{4}

\frac{7991}{20} - \frac{3}{10}

Least Common Multiplier of

20, 10 : 20

20, 10

Least Common Multiplier (LCM)

Prime factorization of

20 : 2 \cdot 2 \cdot 5

20

20

divides by

220 = 10 \cdot 2

= 2 \cdot 10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 5

Prime factorization of

10 : 2 \cdot 5

10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 5

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

20

10

= 2 \cdot 2 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 5 = 20

= 20

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

20

For

\frac{3}{10} :

multiply the denominator and numerator by

2

\frac{3}{10} = \frac{3 \cdot 2}{10 \cdot 2} = \frac{6}{20}

= \frac{7991}{20} - \frac{6}{20}

Since the denominators are equal, combine the fractions:

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

= \frac{7991 - 6}{20}

Subtract the numbers:

7991 - 6 = 7985

= \frac{7985}{20}

Cancel the common factor:

5

= \frac{1597}{4}

= \frac{1597}{4}

= \frac{1597}{4}

Convert improper fractions to mixed numbers:

\frac{1597}{4} = 399 \frac{1}{4}

\frac{1597}{4} = 399

Remainder

1

\frac{1597}{4}

Write the problem in long division format

4 \overline{∣ 1597}

Divide

15

4

to get

3

Divide

15

4

to get

3

3 4 \overline{∣ 1597}

Multiply the quotient digit

(3)

by the divisor

4

3 4 \overline{∣ 1597} \underline{12}

Subtract

12

from

15

3 4 \overline{∣ 1597} \underline{12} 3

Bring down the next number of the dividend

3 4 \overline{∣ 1597} \underline{12} 39

3 4 \overline{∣ 1597} \underline{12} 39

Divide

39

4

to get

9

Divide

39

4

to get

9

39 4 \overline{∣ 1597} \underline{12} 39

Multiply the quotient digit

(9)

by the divisor

4

39 4 \overline{∣ 1597} \underline{12} 39 \underline{36}

Subtract

36

from

39

39 4 \overline{∣ 1597} \underline{12} 39 \underline{36} 3

Bring down the next number of the dividend

39 4 \overline{∣ 1597} \underline{12} 39 \underline{36} 37

39 4 \overline{∣ 1597} \underline{12} 39 \underline{36} 37

Divide

37

4

to get

9

Divide

37

4

to get

9

399 4 \overline{∣ 1597} \underline{12} 39 \underline{36} 37

Multiply the quotient digit

(9)

by the divisor

4

399 4 \overline{∣ 1597} \underline{12} 39 \underline{36} 37 \underline{36}

Subtract

36

from

37

399 4 \overline{∣ 1597} \underline{12} 39 \underline{36} 37 \underline{36} 1

399 4 \overline{∣ 1597} \underline{12} 39 \underline{36} 37 \underline{36} 1

The solution for Long Division of

\frac{1597}{4}

399

with remainder of

1

399 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{1597}{4} = 399 \frac{1}{4}

= 399 \frac{1}{4}

= 399 \frac{1}{4}

Popular Examples

6^2-5

6^{2} - 5

6^2-1

6^{2} - 1

6^2+4

6^{2} + 4

6-(-4)(-2)(+1)

6 - (- 4) (- 2) (+ 1)

2/3 \times 22/7 \times 7^3

\frac{2}{3} \times \frac{22}{7} \times 7^{3}

Frequently Asked Questions (FAQ)

What is 400-1/5-1/4-9/30 ?
The solution to 400-1/5-1/4-9/30 is 399 1/4