26 Algebraic Fractions
By studying this lesson you will be able to;
² identify algebraic fractions,
² add and subtract algebraic fractions with integral denominators (equal/ unequal
denominators)
² add and subtract algebraic fractions with equal algebraic denominators.
We have already learnt to add and subtract numerical fractions and simplify, expand
and factorize algebraic expressions.
Do the following review exercise to recall what has been learnt earlier.
Review Exercise
1. Simplify.
i. 2 +1 ii. 5 − 2 iii. 1 − 7 +4 iv. 12 − 2 − 1
5 5 7 7 9 9 9 13 13 13
2. Fill in each box with the appropriate number.
i. 1 −1 ii. 3 − 2 iii. 4 − 3 −1
2 4 4 3 5 10 3
=1× −1 = 3 × − × 4 = 4 × − 3 × − 1 × 10
2×2 4 4×3 3×4 5×6 10 × 3 3×
= −1 = − = − − 10
4 12 30
= = =
4 12 30
= ÷5
30 ÷ 5
=
6
65
For free distribution.
, 3. Simplify the algebraic expressions given below.
a. 2x + 3x b. 3y − y
c. 5a + 4a + a d. 5x + 3y + x + 3y
e. 3y + 2 − y − 2 f. 4n −1 + 5 −2n
g. −3y + 2 − y − 3 + 2y h. 5xy − 6xy + 3x + y
4. Expand and simplify.
a. 2 (x + y) + 3x b. 3 (2x − 4y) + 12y
c. −(4 − 3x) − 1 d. 2 (3x − 2) + 3(x + 2)
e. 3 (m + 1) − 2 (2m −1) f. x ( x − y ) + 2xy
5. For each of the statements given below, if it is true, mark a zzZZ and if it is false,
mark a zzZZ in the box to the right of the statement.
a. The value of 2 + 1 is the same as the value of 2+ 1 '
3 4 3+4
b. To obtain the sum or the difference of two fractions, their
numerators should be equal; if they are not equal, then they should
be made equal.
c. The numerator of the sum of two unit fractions is the sum of the
denominators of the original two fractions and the denominator is
the product of the denominators of the original two fractions.
d. When adding or subtracting two fractions with unequal
denominators, the common denominator that should be used is the
L. C. M. of the denominators of the original two fractions.
e. By multiplying the numerator and the denominator of a fraction
by the same number, we can convert it into its simplest equivalent
form.
f. By dividing the numerator and the denominator of a fraction by the
same number, we can convert it into its simplest equivalent form.
g. − 3x − 2x can be considered as (− 3x) + (− 2x) '
h. To expand − 3(2x − 5), the terms 2x and − 5 need to be multiplied
by 3.
i. When − x − x is simplified we obtain 2x .
j. When 3x + 4y is simplified we obtain 7xy.
66
For free distribution.
By studying this lesson you will be able to;
² identify algebraic fractions,
² add and subtract algebraic fractions with integral denominators (equal/ unequal
denominators)
² add and subtract algebraic fractions with equal algebraic denominators.
We have already learnt to add and subtract numerical fractions and simplify, expand
and factorize algebraic expressions.
Do the following review exercise to recall what has been learnt earlier.
Review Exercise
1. Simplify.
i. 2 +1 ii. 5 − 2 iii. 1 − 7 +4 iv. 12 − 2 − 1
5 5 7 7 9 9 9 13 13 13
2. Fill in each box with the appropriate number.
i. 1 −1 ii. 3 − 2 iii. 4 − 3 −1
2 4 4 3 5 10 3
=1× −1 = 3 × − × 4 = 4 × − 3 × − 1 × 10
2×2 4 4×3 3×4 5×6 10 × 3 3×
= −1 = − = − − 10
4 12 30
= = =
4 12 30
= ÷5
30 ÷ 5
=
6
65
For free distribution.
, 3. Simplify the algebraic expressions given below.
a. 2x + 3x b. 3y − y
c. 5a + 4a + a d. 5x + 3y + x + 3y
e. 3y + 2 − y − 2 f. 4n −1 + 5 −2n
g. −3y + 2 − y − 3 + 2y h. 5xy − 6xy + 3x + y
4. Expand and simplify.
a. 2 (x + y) + 3x b. 3 (2x − 4y) + 12y
c. −(4 − 3x) − 1 d. 2 (3x − 2) + 3(x + 2)
e. 3 (m + 1) − 2 (2m −1) f. x ( x − y ) + 2xy
5. For each of the statements given below, if it is true, mark a zzZZ and if it is false,
mark a zzZZ in the box to the right of the statement.
a. The value of 2 + 1 is the same as the value of 2+ 1 '
3 4 3+4
b. To obtain the sum or the difference of two fractions, their
numerators should be equal; if they are not equal, then they should
be made equal.
c. The numerator of the sum of two unit fractions is the sum of the
denominators of the original two fractions and the denominator is
the product of the denominators of the original two fractions.
d. When adding or subtracting two fractions with unequal
denominators, the common denominator that should be used is the
L. C. M. of the denominators of the original two fractions.
e. By multiplying the numerator and the denominator of a fraction
by the same number, we can convert it into its simplest equivalent
form.
f. By dividing the numerator and the denominator of a fraction by the
same number, we can convert it into its simplest equivalent form.
g. − 3x − 2x can be considered as (− 3x) + (− 2x) '
h. To expand − 3(2x − 5), the terms 2x and − 5 need to be multiplied
by 3.
i. When − x − x is simplified we obtain 2x .
j. When 3x + 4y is simplified we obtain 7xy.
66
For free distribution.
