what is operation on fraction
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Fraction Operations
To add (or subtract) two fractions :
1) Find the least common denominator .
2) Write both original fractions asequivalent fractions with the least common denominator.
3) Add (or subtract) the numerators.
4) Write the result with the denominator.
Example 1:
Add 13+3713+37 .
The least common denominator is 2121 .
13+37=1 ⋅ 73 ⋅ 7+3 ⋅ 37 ⋅ 3 =721+921 =162113+37=1 ⋅ 73 ⋅ 7+3 ⋅ 37 ⋅ 3 =721+921 =1621
To multiply two fractions:
1) Multiply the numerator by the numerator.
2) Multiply the denominator by the denominator.
For all real numbers a,b,c,d(b≠0,d≠0)a,b,c,d(b≠0,d≠0)
ab⋅cd=acbdab⋅cd=acbd
Example 2:
Multiply 14⋅5614⋅56 .
14⋅56=1 ⋅ 54 ⋅ 6 =52414⋅56=1 ⋅ 54 ⋅ 6 =524
To divide by a fraction, multiply by itsreciprocal .
For all real numbers a,b,c,d(b≠0,c≠,d≠0)a,b,c,d(b≠0,c≠,d≠0)
ab÷cd=ab⋅dc=adbcab÷cd=ab⋅dc=adbc
Example 3:
Divide 34÷5734÷57 .
34÷57=34⋅75 =3 ⋅ 74 ⋅ 5 =212034÷57=34⋅75 =3 ⋅ 74 ⋅ 5 =2120
Mixed numbers can be written as an improper fraction and an improper fraction can be written as a mixed number.
Example 4:
Write 725725 as an improper fraction.
725=71+25 =7 ⋅ 51 ⋅ 5+25 =355+25 =375725=71+25 =7 ⋅ 51 ⋅ 5+25 =355+25 =375
Example 5:
Write 117117 as a mixed number in simple form.
117=11÷7=1 R 4117=11÷7=1 R 4
Therefore, 117=147117=147 .
A fraction is in lowest terms when the numerator and denominator have no common factor other than 11 . To write a fraction in lowest terms, divide the numerator and denominator by the greatest common factor .
Example 6:
Write 45754575 in lowest terms.
4545 and 7575 have a common factor of 1515 .
4575=45 ÷ 1575 ÷ 15=35
To add (or subtract) two fractions :
1) Find the least common denominator .
2) Write both original fractions asequivalent fractions with the least common denominator.
3) Add (or subtract) the numerators.
4) Write the result with the denominator.
Example 1:
Add 13+3713+37 .
The least common denominator is 2121 .
13+37=1 ⋅ 73 ⋅ 7+3 ⋅ 37 ⋅ 3 =721+921 =162113+37=1 ⋅ 73 ⋅ 7+3 ⋅ 37 ⋅ 3 =721+921 =1621
To multiply two fractions:
1) Multiply the numerator by the numerator.
2) Multiply the denominator by the denominator.
For all real numbers a,b,c,d(b≠0,d≠0)a,b,c,d(b≠0,d≠0)
ab⋅cd=acbdab⋅cd=acbd
Example 2:
Multiply 14⋅5614⋅56 .
14⋅56=1 ⋅ 54 ⋅ 6 =52414⋅56=1 ⋅ 54 ⋅ 6 =524
To divide by a fraction, multiply by itsreciprocal .
For all real numbers a,b,c,d(b≠0,c≠,d≠0)a,b,c,d(b≠0,c≠,d≠0)
ab÷cd=ab⋅dc=adbcab÷cd=ab⋅dc=adbc
Example 3:
Divide 34÷5734÷57 .
34÷57=34⋅75 =3 ⋅ 74 ⋅ 5 =212034÷57=34⋅75 =3 ⋅ 74 ⋅ 5 =2120
Mixed numbers can be written as an improper fraction and an improper fraction can be written as a mixed number.
Example 4:
Write 725725 as an improper fraction.
725=71+25 =7 ⋅ 51 ⋅ 5+25 =355+25 =375725=71+25 =7 ⋅ 51 ⋅ 5+25 =355+25 =375
Example 5:
Write 117117 as a mixed number in simple form.
117=11÷7=1 R 4117=11÷7=1 R 4
Therefore, 117=147117=147 .
A fraction is in lowest terms when the numerator and denominator have no common factor other than 11 . To write a fraction in lowest terms, divide the numerator and denominator by the greatest common factor .
Example 6:
Write 45754575 in lowest terms.
4545 and 7575 have a common factor of 1515 .
4575=45 ÷ 1575 ÷ 15=35
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