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Popular Pre Algebra >

3\div 7+5\div 14-3\div 49+1\div 4-7\div 2

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Solution

3÷7+5÷14−3÷49+1÷4−7÷2

Solution

−196495​
+1
Decimal
−2.52551…
Solution steps
3÷7+5÷14−3÷49+1÷4−7÷2
Follow the PEMDAS order of operations
Multiply and divide (left to right) 3÷7:73​
3÷7
3÷7=73​=73​
=73​+5÷14−3÷49+1÷4−7÷2
Multiply and divide (left to right) 5÷14:145​
5÷14
5÷14=145​=145​
=73​+145​−3÷49+1÷4−7÷2
Multiply and divide (left to right) 3÷49:493​
3÷49
3÷49=493​=493​
=73​+145​−493​+1÷4−7÷2
Multiply and divide (left to right) 1÷4:41​
1÷4
1÷4=41​=41​
=73​+145​−493​+41​−7÷2
Multiply and divide (left to right) 7÷2:27​
7÷2
7÷2=27​=27​
=73​+145​−493​+41​−27​
Add and subtract (left to right) 73​+145​−493​+41​−27​:−196495​
73​+145​−493​+41​−27​
73​+145​=1411​
73​+145​
Least Common Multiplier of 7,14:14
7,14
Least Common Multiplier (LCM)
Prime factorization of 7:7
7
7 is a prime number, therefore no factorization is possible=7
Prime factorization of 14:2⋅7
14
14divides by 214=7⋅2=2⋅7
2,7 are all prime numbers, therefore no further factorization is possible=2⋅7
Multiply each factor the greatest number of times it occurs in either 7 or 14=7⋅2
Multiply the numbers: 7⋅2=14=14
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 14
For 73​:multiply the denominator and numerator by 273​=7⋅23⋅2​=146​
=146​+145​
Since the denominators are equal, combine the fractions: ca​±cb​=ca±b​=146+5​
Add the numbers: 6+5=11=1411​
=1411​−493​+41​−27​
1411​−493​=9871​
1411​−493​
Least Common Multiplier of 14,49:98
14,49
Least Common Multiplier (LCM)
Prime factorization of 14:2⋅7
14
14divides by 214=7⋅2=2⋅7
2,7 are all prime numbers, therefore no further factorization is possible=2⋅7
Prime factorization of 49:7⋅7
49
49divides by 749=7⋅7=7⋅7
Multiply each factor the greatest number of times it occurs in either 14 or 49=2⋅7⋅7
Multiply the numbers: 2⋅7⋅7=98=98
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 98
For 1411​:multiply the denominator and numerator by 71411​=14⋅711⋅7​=9877​
For 493​:multiply the denominator and numerator by 2493​=49⋅23⋅2​=986​
=9877​−986​
Since the denominators are equal, combine the fractions: ca​±cb​=ca±b​=9877−6​
Subtract the numbers: 77−6=71=9871​
=9871​+41​−27​
9871​+41​=196191​
9871​+41​
Least Common Multiplier of 98,4:196
98,4
Least Common Multiplier (LCM)
Prime factorization of 98:2⋅7⋅7
98
98divides by 298=49⋅2=2⋅49
49divides by 749=7⋅7=2⋅7⋅7
2,7 are all prime numbers, therefore no further factorization is possible=2⋅7⋅7
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 98 or 4=2⋅2⋅7⋅7
Multiply the numbers: 2⋅2⋅7⋅7=196=196
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 196
For 9871​:multiply the denominator and numerator by 29871​=98⋅271⋅2​=196142​
For 41​:multiply the denominator and numerator by 4941​=4⋅491⋅49​=19649​
=196142​+19649​
Since the denominators are equal, combine the fractions: ca​±cb​=ca±b​=196142+49​
Add the numbers: 142+49=191=196191​
=196191​−27​
196191​−27​=−196495​
196191​−27​
Least Common Multiplier of 196,2:196
196,2
Least Common Multiplier (LCM)
Prime factorization of 196:2⋅2⋅7⋅7
196
196divides by 2196=98⋅2=2⋅98
98divides by 298=49⋅2=2⋅2⋅49
49divides by 749=7⋅7=2⋅2⋅7⋅7
2,7 are all prime numbers, therefore no further factorization is possible=2⋅2⋅7⋅7
Prime factorization of 2:2
2
2 is a prime number, therefore no factorization is possible=2
Multiply each factor the greatest number of times it occurs in either 196 or 2=2⋅2⋅7⋅7
Multiply the numbers: 2⋅2⋅7⋅7=196=196
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 196
For 27​:multiply the denominator and numerator by 9827​=2⋅987⋅98​=196686​
=196191​−196686​
Since the denominators are equal, combine the fractions: ca​±cb​=ca±b​=196191−686​
Subtract the numbers: 191−686=−495=196−495​
Apply the fraction rule: b−a​=−ba​=−196495​
=−196495​
=−196495​

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Frequently Asked Questions (FAQ)

  • What is 3\div 7+5\div 14-3\div 49+1\div 4-7\div 2 ?

    The solution to 3\div 7+5\div 14-3\div 49+1\div 4-7\div 2 is -495/196

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