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1. Grade 8 – Mathematics
Quarter I
ADDITION AND SUBTRACTION OF
RATIONAL ALGEBRAIC EXPRESSIONS
(LIKE DENOMINATORS)

2. 1. recall addition and subtraction of
similar fractions; and
2. add and subtract rational
algebraic expressions with like
denominators.

3. How do we add and subtract similar
fractions?
𝟐
𝟒
+
𝟏
𝟒
Similar Fractions
1. Add or subtract the numerator then copy
the common denominator.
2. Simplify, if possible.
=
𝟑
𝟒
𝟒
𝟔
-
𝟐
𝟔
=
𝟐
𝟔
=
𝟏
𝟑

4. How do we add and subtract similar
fractions?
𝟑
𝟓
+
𝟏
𝟓
Similar Fractions
1. Add or subtract the numerator then copy
the common denominator.
2. Simplify, if possible.
=
𝟒
𝟓
𝟑
𝟔
-
𝟐
𝟔
=
𝟏
𝟔

5. ADDING AND SUBTRACTING RATIONAL
EXPRESSIONS WITH LIKE DENOMINATORS
1. Add or subtract the numerator.
2. Copy the common denominator.
3. Factor the numerator and cancel out or
divide the common factor then simplify.
𝒂
𝒄
+
𝒃
𝒄
=
𝒂+𝒃
𝒄
𝒂
𝒄
-
𝒃
𝒄
=
𝒂−𝒃
𝒄
𝒄 ≠ 𝟎

6. ADDING AND SUBTRACTING RATIONAL
EXPRESSIONS WITH LIKE DENOMINATORS
𝟐𝒂
𝟒𝒃
+
𝟑
𝟒𝒃
Add the numerator
=
𝟐𝒂 + 𝟑
𝟒𝒃
Copy the common
denominator.
Factor the numerator.
Simplify.

7. ADDING AND SUBTRACTING RATIONAL
EXPRESSIONS WITH LIKE DENOMINATORS
𝟏𝟎𝒄
𝟏𝟑
+
𝟏𝟔𝒄
𝟏𝟑Add the numerator
=
𝟐𝟔𝒄
𝟏𝟑
Copy the common
denominator.
Factor the numerator.
=
𝟏𝟑(𝟐𝒄)
𝟏𝟑
Simplify.
= 𝟐𝒄

8. ADDING AND SUBTRACTING RATIONAL
EXPRESSIONS WITH LIKE DENOMINATORS
𝟖𝒅−𝟑
𝟗
+
𝟒𝒅+𝟏𝟐
𝟗Add the numerator
=
𝟖𝒅 − 𝟑 + 𝟒𝒅 + 𝟏𝟐
𝟗Copy the common
denominator.
Factor the numerator.
Simplify.
=
𝟏𝟐𝒅 + 𝟗
𝟗 =
𝟑(𝟒𝒅 + 𝟑)
𝟗
𝟑
𝟏
=
𝟒𝒅 + 𝟑
𝟑

9. ADDING AND SUBTRACTING RATIONAL
EXPRESSIONS WITH LIKE DENOMINATORS
𝟗𝒙 𝟐
𝟑𝒙−𝟓
-
𝟐𝟓
𝟑𝒙−𝟓
Subtract the numerator = 𝟗𝒙 𝟐 − 𝟐𝟓
𝟑𝒙 − 𝟓
Copy the common
denominator.
Factor.
Simplify.
𝟗𝒙 𝟐
− (𝟐𝟓)
=
(𝟑𝒙 + 𝟓)(𝟑𝒙 − 𝟓)
𝟑𝒙 − 𝟓
= 𝟑𝒙 + 𝟓

10. ADDING AND SUBTRACTING RATIONAL
EXPRESSIONS WITH LIKE DENOMINATORS
𝟗𝒚 𝟐
𝒚−𝟐
-
𝒚 𝟐+𝟏𝟔𝒚
𝒚−𝟐
Subtract the numerator =
𝟗𝒚 𝟐
− 𝒚 𝟐
− 𝟏𝟔𝒚
𝒚 − 𝟐
Copy the common
denominator.
Factor.
Simplify.
𝟗𝒚 𝟐
− (𝒚 𝟐
+ 𝟏𝟔𝒚)
=
8𝒚(𝒚 − 𝟐)
𝒚 − 𝟐
= 𝟖𝒚
= 𝟖𝒚 𝟐
− 𝟏𝟔𝒚
𝒚 − 𝟐

11. ADDING AND SUBTRACTING RATIONAL
EXPRESSIONS WITH LIKE DENOMINATORS
𝒉 𝟐+𝟖𝒉−𝟏𝟓
𝟑𝒉 𝟐−𝟗𝒉
-
𝟒𝒉+𝟔
𝟑𝒉 𝟐−𝟗𝒉
Subtract the numerator
=
𝒉 𝟐 + 𝟖𝒉 − 𝟏𝟓 − 𝟒𝒉 − 𝟔
𝟑𝒉 𝟐
− 𝟗𝒉Copy the common
denominator.
Factor.
Simplify.
=
𝒉 𝟐
+ 𝟒𝒉 − 𝟐𝟏
𝟑𝒉 𝟐
− 𝟗𝒉
𝒉 𝟐
+ 𝟖𝒉 − 𝟏𝟓 − (𝟒𝒉 + 𝟔)
=
(𝒉 + 𝟕)(𝒉 − 𝟑)
𝟑𝒉(𝒉 − 𝟑) =
𝒉 + 𝟕
𝟑𝒉