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Popular Pre Algebra >

5/4+2/3+7/4+5/3+9/4+7/3+11/4+9/3

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Solution

5/4+2/3+7/4+5/3+9/4+7/3+11/4+9/3

Solution

1532​
+1
Decimal
15.66666…
Solution steps
5/4+2/3+7/4+5/3+9/4+7/3+11/4+9/3
Follow the PEMDAS order of operations
Multiply and divide (left to right) 5/4:45​
5/4
5/4=45​=45​
=45​+2/3+7/4+5/3+9/4+7/3+11/4+9/3
Multiply and divide (left to right) 2/3:32​
2/3
2/3=32​=32​
=45​+32​+7/4+5/3+9/4+7/3+11/4+9/3
Multiply and divide (left to right) 7/4:47​
7/4
7/4=47​=47​
=45​+32​+47​+5/3+9/4+7/3+11/4+9/3
Multiply and divide (left to right) 5/3:35​
5/3
5/3=35​=35​
=45​+32​+47​+35​+9/4+7/3+11/4+9/3
Multiply and divide (left to right) 9/4:49​
9/4
9/4=49​=49​
=45​+32​+47​+35​+49​+7/3+11/4+9/3
Multiply and divide (left to right) 7/3:37​
7/3
7/3=37​=37​
=45​+32​+47​+35​+49​+37​+11/4+9/3
Multiply and divide (left to right) 11/4:411​
11/4
11/4=411​=411​
=45​+32​+47​+35​+49​+37​+411​+9/3
Multiply and divide (left to right) 9/3:3
9/3
9/3=3=3
=45​+32​+47​+35​+49​+37​+411​+3
Add and subtract (left to right) 45​+32​+47​+35​+49​+37​+411​+3:347​
45​+32​+47​+35​+49​+37​+411​+3
45​+32​=1223​
45​+32​
Least Common Multiplier of 4,3:12
4,3
Least Common Multiplier (LCM)
Prime factorization of 4:2⋅2
4
4divides by 24=2⋅2=2⋅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 or 3=2⋅2⋅3
Multiply the numbers: 2⋅2⋅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 45​:multiply the denominator and numerator by 345​=4⋅35⋅3​=1215​
For 32​:multiply the denominator and numerator by 432​=3⋅42⋅4​=128​
=1215​+128​
Since the denominators are equal, combine the fractions: ca​±cb​=ca±b​=1215+8​
Add the numbers: 15+8=23=1223​
=1223​+47​+35​+49​+37​+411​+3
1223​+47​=311​
1223​+47​
Least Common Multiplier of 12,4:12
12,4
Least Common Multiplier (LCM)
Prime factorization of 12:2⋅2⋅3
12
12divides by 212=6⋅2=2⋅6
6divides by 26=3⋅2=2⋅2⋅3
2,3 are all prime numbers, therefore no further factorization is possible=2⋅2⋅3
Prime factorization of 4:2⋅2
4
4divides by 24=2⋅2=2⋅2
Multiply each factor the greatest number of times it occurs in either 12 or 4=2⋅2⋅3
Multiply the numbers: 2⋅2⋅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 47​:multiply the denominator and numerator by 347​=4⋅37⋅3​=1221​
=1223​+1221​
Since the denominators are equal, combine the fractions: ca​±cb​=ca±b​=1223+21​
Add the numbers: 23+21=44=1244​
Cancel the common factor: 4=311​
=311​+35​+49​+37​+411​+3
311​+35​=316​
311​+35​
Apply rule ca​±cb​=ca±b​=311+5​
Add the numbers: 11+5=16=316​
=316​+49​+37​+411​+3
316​+49​=1291​
316​+49​
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⋅2
4
4divides by 24=2⋅2=2⋅2
Multiply each factor the greatest number of times it occurs in either 3 or 4=3⋅2⋅2
Multiply the numbers: 3⋅2⋅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 316​:multiply the denominator and numerator by 4316​=3⋅416⋅4​=1264​
For 49​:multiply the denominator and numerator by 349​=4⋅39⋅3​=1227​
=1264​+1227​
Since the denominators are equal, combine the fractions: ca​±cb​=ca±b​=1264+27​
Add the numbers: 64+27=91=1291​
=1291​+37​+411​+3
1291​+37​=12119​
1291​+37​
Least Common Multiplier of 12,3:12
12,3
Least Common Multiplier (LCM)
Prime factorization of 12:2⋅2⋅3
12
12divides by 212=6⋅2=2⋅6
6divides by 26=3⋅2=2⋅2⋅3
2,3 are all prime numbers, therefore no further factorization is possible=2⋅2⋅3
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 12 or 3=2⋅2⋅3
Multiply the numbers: 2⋅2⋅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 37​:multiply the denominator and numerator by 437​=3⋅47⋅4​=1228​
=1291​+1228​
Since the denominators are equal, combine the fractions: ca​±cb​=ca±b​=1291+28​
Add the numbers: 91+28=119=12119​
=12119​+411​+3
12119​+411​=338​
12119​+411​
Least Common Multiplier of 12,4:12
12,4
Least Common Multiplier (LCM)
Prime factorization of 12:2⋅2⋅3
12
12divides by 212=6⋅2=2⋅6
6divides by 26=3⋅2=2⋅2⋅3
2,3 are all prime numbers, therefore no further factorization is possible=2⋅2⋅3
Prime factorization of 4:2⋅2
4
4divides by 24=2⋅2=2⋅2
Multiply each factor the greatest number of times it occurs in either 12 or 4=2⋅2⋅3
Multiply the numbers: 2⋅2⋅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 411​:multiply the denominator and numerator by 3411​=4⋅311⋅3​=1233​
=12119​+1233​
Since the denominators are equal, combine the fractions: ca​±cb​=ca±b​=12119+33​
Add the numbers: 119+33=152=12152​
Cancel the common factor: 4=338​
=338​+3
338​+3=347​
338​+3
Convert element to fraction: 3=33⋅3​=33⋅3​+338​
Since the denominators are equal, combine the fractions: ca​±cb​=ca±b​=33⋅3+38​
3⋅3+38=47
3⋅3+38
Multiply the numbers: 3⋅3=9=9+38
Add the numbers: 9+38=47=47
=347​
=347​
=347​
Convert improper fractions to mixed numbers:347​=1532​
347​=15Remainder2
347​
Write the problem in long division format3∣47​​
Divide 4by 3to get 1
Divide 4by 3to get 113∣47​​
Multiply the quotient digit (1)by the divisor 313∣47​3​​
Subtract 3from 413∣47​3​1​
Bring down the next number of the dividend13∣47​3​17​
13∣47​3​17​
Divide 17by 3to get 5
Divide 17by 3to get 5153∣47​3​17​
Multiply the quotient digit (5)by the divisor 3153∣47​3​1715​​
Subtract 15from 17153∣47​3​1715​2​
153∣47​3​1715​2​
The solution for Long Division of 347​is 15with remainder of 215Remainder2
Convert to mixed number: QuotientDivisorRemainder​347​=1532​
=1532​
=1532​

Popular Examples

3-4+5-6+7-8-101(1)^2-2× (3-(5-2× (8-16)))2(1)^2-4(1)+11-3(0)

Frequently Asked Questions (FAQ)

  • What is 5/4+2/3+7/4+5/3+9/4+7/3+11/4+9/3 ?

    The solution to 5/4+2/3+7/4+5/3+9/4+7/3+11/4+9/3 is 15 2/3

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