Addition and Subtraction of Fractions
Addition & Subtraction of Fractions
Slide: 1
Recall: Like Terms Like terms are terms that have the same variables and exponents. Unlike terms are terms that have different variables or the same variables with different exponents.
Like terms
Unlike terms
2x and 43x
4y and 8y2
21y2, −6y2, and 15y2
x2, x, and 1
6xy and –2yx Slide: 2
Recall: Like Terms When adding or subtracting algebraic expressions, first collect the like terms and group them, then add or subtract the coefficients of the like terms.
Example
Slide: 3
Add (3x2 + 7x − 1) and (11x2 − 4x +13).
Addition & Subtraction of Like Algebraic Fractions
To add or subtract fractions with the same denominator (or like fractions), we simply add/subtract the numerators and keep the same denominator.
Numeric Fraction:
1+ 2 = 1 + 2 = 3 5 5 5 5
Algebraic Fraction:
x + 2x = x + 2x = 3x 5 5 5 5
Factor and reduce your answer to simplest terms. Slide: 4
Perform the following arithmetic operations: 3x + y
Slide: 5
5x2 – y
2x y
Add the following fractions: 2a + 4ab – b –2a – ab + 6b + b2 b2
Slide: 6
Subtract the following fractions: 5x2 + 7x + 18 4x2 + 8x – 12 – x2 + 5x x2 + 5x
Slide: 7
Recall: Lowest Common Denominator The Least or Lowest Common Denominator (LCD) of a set of two or more fractions is the smallest whole number that is divisible by each of the denominators.
It is the least common multiple (LCM) of the denominator. 5 3 and , you must find the LCM of 6 and 4. To find the LCD of 6 4 6 is not divisible by 4, so 6 is not the LCD 6 × 2 = 12
12 is a factor of 6
3 5 12 is divisible by 4, so the LCD of and is 12. 4 6 Slide: 8
Lowest Common Multiple – Algebraic Expressions Step 1: Determine the LCM of the coefficients.
Find the LCM of the following terms: Example
2 2 8p q r
3 2 4p q
8 is not divisible by 6. 8 × 2 = 16 is not divisible by 6. 8 × 3 = 24 is divisible by both 4 and 6.
Slide: 9
2 6p qr The LCM of the coefficients is equal to:
24
Lowest Common Multiple – Algebraic Expressions Step 2: Identify all variables in the terms.
Find the LCM of the following terms: Example
8p2q2r
4p3q2
Variables p, q, and r are present.
Slide: 10
Lowest Common Multiple – Algebraic Expressions Step 3: Determine the largest exponent of each variable.
Find the LCM of the following terms: Example
2 2 8p q r
Largest exponent of p: Largest exponent of q: Largest exponent of r: Slide: 11
3 2 1
3 2 4p q Recall:
r = r1
Lowest Common Multiple – Algebraic Expressions Step 4: Combine your answers from Steps 1 – 3.
Find the LCM of the following terms: Example
3 2 4p q
2 2 8p q r
The Lowest Common Multiple is: exponents
24 p q r 3
coefficient Slide: 12
2
variables
1
Expand the following fractions so that the denominator of each is the LCD: 2 3b
10a2c3
Slide: 13
2d 15abc
Expand the following fractions so that the denominator of each is the LCD:
1 3x2 + 3x
Slide: 14
x 4(x + 1)2
Addition & Subtraction of Unlike Algebraic Fractions To add or subtract fractions with different denominators (or unlike fractions), we expand all fractions so that the denominator of each fraction is the Lowest Common Denominator (LCD), then add/subtract normally.
Example
Add the following fractions.
1 2 + 2 3xy 9x
Slide: 15
Perform the following arithmetic operations: 𝟗𝒙 𝟑𝒙 𝟕𝒙 + − 𝟐 𝟓 𝟒
Slide: 16
Add the following fractions: 𝟒𝒂𝒃 + 𝟏 𝟐 − 𝟑𝒃𝟐 + 𝟐 𝒂 𝟑𝒂𝒃
Slide: 17
Subtract the following fractions: 𝒚 − 𝟔 𝟐𝒚 − 𝟏𝟑 − 𝟑𝒚 𝟓𝒚
Slide: 18
Class Problems:
𝟑 𝟏𝟐 + 𝒂 + 𝟒 (𝒂 + 𝟒)𝟐 𝟒𝒑𝟐 𝒒𝒓 𝟓𝒑 − 𝟐+ 𝒒 𝟑𝒑 𝟐
Slide: 19
Slide: 1
Recall: Like Terms Like terms are terms that have the same variables and exponents. Unlike terms are terms that have different variables or the same variables with different exponents.
Like terms
Unlike terms
2x and 43x
4y and 8y2
21y2, −6y2, and 15y2
x2, x, and 1
6xy and –2yx Slide: 2
Recall: Like Terms When adding or subtracting algebraic expressions, first collect the like terms and group them, then add or subtract the coefficients of the like terms.
Example
Slide: 3
Add (3x2 + 7x − 1) and (11x2 − 4x +13).
Addition & Subtraction of Like Algebraic Fractions
To add or subtract fractions with the same denominator (or like fractions), we simply add/subtract the numerators and keep the same denominator.
Numeric Fraction:
1+ 2 = 1 + 2 = 3 5 5 5 5
Algebraic Fraction:
x + 2x = x + 2x = 3x 5 5 5 5
Factor and reduce your answer to simplest terms. Slide: 4
Perform the following arithmetic operations: 3x + y
Slide: 5
5x2 – y
2x y
Add the following fractions: 2a + 4ab – b –2a – ab + 6b + b2 b2
Slide: 6
Subtract the following fractions: 5x2 + 7x + 18 4x2 + 8x – 12 – x2 + 5x x2 + 5x
Slide: 7
Recall: Lowest Common Denominator The Least or Lowest Common Denominator (LCD) of a set of two or more fractions is the smallest whole number that is divisible by each of the denominators.
It is the least common multiple (LCM) of the denominator. 5 3 and , you must find the LCM of 6 and 4. To find the LCD of 6 4 6 is not divisible by 4, so 6 is not the LCD 6 × 2 = 12
12 is a factor of 6
3 5 12 is divisible by 4, so the LCD of and is 12. 4 6 Slide: 8
Lowest Common Multiple – Algebraic Expressions Step 1: Determine the LCM of the coefficients.
Find the LCM of the following terms: Example
2 2 8p q r
3 2 4p q
8 is not divisible by 6. 8 × 2 = 16 is not divisible by 6. 8 × 3 = 24 is divisible by both 4 and 6.
Slide: 9
2 6p qr The LCM of the coefficients is equal to:
24
Lowest Common Multiple – Algebraic Expressions Step 2: Identify all variables in the terms.
Find the LCM of the following terms: Example
8p2q2r
4p3q2
Variables p, q, and r are present.
Slide: 10
Lowest Common Multiple – Algebraic Expressions Step 3: Determine the largest exponent of each variable.
Find the LCM of the following terms: Example
2 2 8p q r
Largest exponent of p: Largest exponent of q: Largest exponent of r: Slide: 11
3 2 1
3 2 4p q Recall:
r = r1
Lowest Common Multiple – Algebraic Expressions Step 4: Combine your answers from Steps 1 – 3.
Find the LCM of the following terms: Example
3 2 4p q
2 2 8p q r
The Lowest Common Multiple is: exponents
24 p q r 3
coefficient Slide: 12
2
variables
1
Expand the following fractions so that the denominator of each is the LCD: 2 3b
10a2c3
Slide: 13
2d 15abc
Expand the following fractions so that the denominator of each is the LCD:
1 3x2 + 3x
Slide: 14
x 4(x + 1)2
Addition & Subtraction of Unlike Algebraic Fractions To add or subtract fractions with different denominators (or unlike fractions), we expand all fractions so that the denominator of each fraction is the Lowest Common Denominator (LCD), then add/subtract normally.
Example
Add the following fractions.
1 2 + 2 3xy 9x
Slide: 15
Perform the following arithmetic operations: 𝟗𝒙 𝟑𝒙 𝟕𝒙 + − 𝟐 𝟓 𝟒
Slide: 16
Add the following fractions: 𝟒𝒂𝒃 + 𝟏 𝟐 − 𝟑𝒃𝟐 + 𝟐 𝒂 𝟑𝒂𝒃
Slide: 17
Subtract the following fractions: 𝒚 − 𝟔 𝟐𝒚 − 𝟏𝟑 − 𝟑𝒚 𝟓𝒚
Slide: 18
Class Problems:
𝟑 𝟏𝟐 + 𝒂 + 𝟒 (𝒂 + 𝟒)𝟐 𝟒𝒑𝟐 𝒒𝒓 𝟓𝒑 − 𝟐+ 𝒒 𝟑𝒑 𝟐
Slide: 19
