What is 1\div 4+3\div 16+5\div 36 ?

The solution to 1\div 4+3\div 16+5\div 36 is 83/144

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Popular >

1\div 4+3\div 16+5\div 36

Solution

1 \div 4 + 3 \div 16 + 5 \div 36

Solution

\frac{83}{144}

Solution steps

1 \div 4 + 3 \div 16 + 5 \div 36

Follow the PEMDAS order of operations

Multiply and divide (left to right)

1 \div 4 : \frac{1}{4}

1 \div 4

1 \div 4 = \frac{1}{4}

= \frac{1}{4}

= \frac{1}{4} + 3 \div 16 + 5 \div 36

Multiply and divide (left to right)

3 \div 16 : \frac{3}{16}

3 \div 16

3 \div 16 = \frac{3}{16}

= \frac{3}{16}

= \frac{1}{4} + \frac{3}{16} + 5 \div 36

Multiply and divide (left to right)

5 \div 36 : \frac{5}{36}

5 \div 36

5 \div 36 = \frac{5}{36}

= \frac{5}{36}

= \frac{1}{4} + \frac{3}{16} + \frac{5}{36}

Add and subtract (left to right)

\frac{1}{4} + \frac{3}{16} + \frac{5}{36} : \frac{83}{144}

\frac{1}{4} + \frac{3}{16} + \frac{5}{36}

\frac{1}{4} + \frac{3}{16} = \frac{7}{16}

\frac{1}{4} + \frac{3}{16}

Least Common Multiplier of

4, 16 : 16

4, 16

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

16 : 2 \cdot 2 \cdot 2 \cdot 2

16

16

divides by

216 = 8 \cdot 2

= 2 \cdot 8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2

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

4

16

= 2 \cdot 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 2 = 16

= 16

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

16

For

\frac{1}{4} :

multiply the denominator and numerator by

4

\frac{1}{4} = \frac{1 \cdot 4}{4 \cdot 4} = \frac{4}{16}

= \frac{4}{16} + \frac{3}{16}

Since the denominators are equal, combine the fractions:

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

= \frac{4 + 3}{16}

Add the numbers:

4 + 3 = 7

= \frac{7}{16}

= \frac{7}{16} + \frac{5}{36}

\frac{7}{16} + \frac{5}{36} = \frac{83}{144}

\frac{7}{16} + \frac{5}{36}

Least Common Multiplier of

16, 36 : 144

16, 36

Least Common Multiplier (LCM)

Prime factorization of

16 : 2 \cdot 2 \cdot 2 \cdot 2

16

16

divides by

216 = 8 \cdot 2

= 2 \cdot 8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2

Prime factorization of

36 : 2 \cdot 2 \cdot 3 \cdot 3

36

36

divides by

236 = 18 \cdot 2

= 2 \cdot 18

18

divides by

218 = 9 \cdot 2

= 2 \cdot 2 \cdot 9

9

divides by

39 = 3 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3 \cdot 3

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

16

36

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 = 144

= 144

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

144

For

\frac{7}{16} :

multiply the denominator and numerator by

9

\frac{7}{16} = \frac{7 \cdot 9}{16 \cdot 9} = \frac{63}{144}

For

\frac{5}{36} :

multiply the denominator and numerator by

4

\frac{5}{36} = \frac{5 \cdot 4}{36 \cdot 4} = \frac{20}{144}

= \frac{63}{144} + \frac{20}{144}

Since the denominators are equal, combine the fractions:

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

= \frac{63 + 20}{144}

Add the numbers:

63 + 20 = 83

= \frac{83}{144}

= \frac{83}{144}

= \frac{83}{144}

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Frequently Asked Questions (FAQ)

What is 1\div 4+3\div 16+5\div 36 ?
The solution to 1\div 4+3\div 16+5\div 36 is 83/144