Multiplication and Division of Fractions
Multiplication & Division of Fractions
Slide: 1
Multiplication of Simple Algebraic Fractions
Step 1: Reduce the numerical coefficients.
Slide: 2
Multiplication of Simple Algebraic Fractions
Step 2: Reduce the variables by subtracting exponents of like bases.
Slide: 3
Multiplication of Simple Algebraic Fractions
Step 3: Multiply the numerators and denominators.
Slide: 4
Multiply the following fractions:
–a2c 3b3 × 6ab 4ac
Slide: 5
Perform the following multiplication:
4r ×
Slide: 6
2pr2 6p2r3
Multiplication of Algebraic Fractions Containing Multinomials When multiplying fractions containing multinomials, you must first factor the multinomials, then multiply following the same steps.
HCF = 3z
2 xy
z + 2xz
×
3yz – 12z 6y
HCF = z Factor. Slide: 7
Multiplication of Algebraic Fractions Containing Multinomials When multiplying fractions containing multinomials, you must first factor the multinomials, then multiply following the same steps.
2 xy
× z(1 + 2x)
3z(y – 4) 2
6y
ReduceFactor. coefficients. Slide: 8
Multiplication of Algebraic Fractions Containing Multinomials When multiplying fractions containing multinomials, you must first factor the multinomials, then multiply following the same steps.
2 xy
1
× z(1 + 2x)
z(y – 4) 2y
Reduce Reduce common coefficients. factors. Slide: 9
Multiply the following fractions: 3ab2 – 18b2 cb
Slide: 10
×
bc + 2ac a–6
Multiply the following fractions:
4 x2
Slide: 11
– 4x – 12
×
6xy – x2y –2y
Division of Algebraic Fractions The division of fractions is done by multiplying one fraction by the reciprocal of the dividing fraction.
Numeric Fraction:
5 7 Slide: 12
÷
Algebraic Fraction:
2
1
3
x
÷
y 2x
Divide the following fractions: 4pr2 3p ÷ 2 7q r 21r
Slide: 13
Divide the following fractions: ac b2c ÷ 6a + 15 4a2 – 25
Slide: 14
Complex Algebraic Fractions A complex fraction is a fraction in which one or more fractions are found in the numerator or denominator.
Complex fractions are easier to work with when written horizontally.
2x y – 3z x2
4– xz2 Slide: 15
=
2x y – 3z
÷
4 – x2 xz2
Class Problems: a)
b)
2x3
3ab
z2
2a4 + 5a2 – 12
8xyz2 z4
Slide: 16
=
b2 4a4 – 9
=
Slide: 1
Multiplication of Simple Algebraic Fractions
Step 1: Reduce the numerical coefficients.
Slide: 2
Multiplication of Simple Algebraic Fractions
Step 2: Reduce the variables by subtracting exponents of like bases.
Slide: 3
Multiplication of Simple Algebraic Fractions
Step 3: Multiply the numerators and denominators.
Slide: 4
Multiply the following fractions:
–a2c 3b3 × 6ab 4ac
Slide: 5
Perform the following multiplication:
4r ×
Slide: 6
2pr2 6p2r3
Multiplication of Algebraic Fractions Containing Multinomials When multiplying fractions containing multinomials, you must first factor the multinomials, then multiply following the same steps.
HCF = 3z
2 xy
z + 2xz
×
3yz – 12z 6y
HCF = z Factor. Slide: 7
Multiplication of Algebraic Fractions Containing Multinomials When multiplying fractions containing multinomials, you must first factor the multinomials, then multiply following the same steps.
2 xy
× z(1 + 2x)
3z(y – 4) 2
6y
ReduceFactor. coefficients. Slide: 8
Multiplication of Algebraic Fractions Containing Multinomials When multiplying fractions containing multinomials, you must first factor the multinomials, then multiply following the same steps.
2 xy
1
× z(1 + 2x)
z(y – 4) 2y
Reduce Reduce common coefficients. factors. Slide: 9
Multiply the following fractions: 3ab2 – 18b2 cb
Slide: 10
×
bc + 2ac a–6
Multiply the following fractions:
4 x2
Slide: 11
– 4x – 12
×
6xy – x2y –2y
Division of Algebraic Fractions The division of fractions is done by multiplying one fraction by the reciprocal of the dividing fraction.
Numeric Fraction:
5 7 Slide: 12
÷
Algebraic Fraction:
2
1
3
x
÷
y 2x
Divide the following fractions: 4pr2 3p ÷ 2 7q r 21r
Slide: 13
Divide the following fractions: ac b2c ÷ 6a + 15 4a2 – 25
Slide: 14
Complex Algebraic Fractions A complex fraction is a fraction in which one or more fractions are found in the numerator or denominator.
Complex fractions are easier to work with when written horizontally.
2x y – 3z x2
4– xz2 Slide: 15
=
2x y – 3z
÷
4 – x2 xz2
Class Problems: a)
b)
2x3
3ab
z2
2a4 + 5a2 – 12
8xyz2 z4
Slide: 16
=
b2 4a4 – 9
=
