_1. A fraction’s value is the quotient obtained by dividing the
numerator by the denominator._
6 6
- = 3 3 is the value of -
2 2
2 2 2 2
- = - - is the value of -
3 3 3 3
_2. Multiplying the denominator of a fraction divides the fraction by
that number._
1 1
- = -
2 × 4 8
3 3
- = --
7 × 3 21
2 2
- = --
3 × 9 27
_3. Dividing the denominator of a fraction multiplies the fraction by
that number._
3 3
- = -
8 ÷ 4 2
10 10
-- = --
9 ÷ 3 3
3 3
-- = -
10 ÷ 5 2
_4. Multiplying the numerator of a fraction multiplies the fraction by
that number._
2 × 2 4
- = -
3 3
1 × 8 8
- = -
9 9
5 × 3 15
- = --
8 8
_5. Dividing the numerator of a fraction divides the fraction by that
number._
4 ÷ 2 2
- = -
7 7
12 ÷ 12 1
-- = --
16 16
3 ÷ 3 1
- = -
7 7
_6. Multiplying both numerator and denominator of a fraction by the same
number does not change the value of the fraction._
1 × 3 3 1
- = - = -
3 × 3 9 3
6 × 2 12 6
- = -- = -
7 × 2 14 7
_7. Dividing both numerator and denominator of a fraction by the same
number does not change the value of the fraction._
12 ÷ 3 4 12
-- = - = --
15 ÷ 3 5 15
18 ÷ 9 2 18
-- = - = --
27 ÷ 9 3 27