**Multiply and divide rational numbers :**

To find the product of two rational numbers, simplify the numerator and denominator as much as possible.

Now multiply the numerators and multiply the denominators separately and put them as new rational number.Simplify the new rational number into its lowest form.

**Division of rational numbers**

To divide one rational number by another rational number, multiply the first rational number with the multiplicative inverse of the second rational number.

Note : In case we have mixed fractions, first we have to convert them as improper and then we can simplify and multiply the numerators and denominators.

**Example 1 :**

Find the product of (4/-11) and (-22/8)

**Solution :**

= (4/-11) x (-22/8)

Simplify the denominator of the first fraction and numerator of the second fraction by using 11 times table.

= 2/2

Again simplifying using 2 times table, we get

= 1

Hence the product of given fraction is 1.

**Example 2 :**

Find (2/3) ÷ (-5/10)

**Solution :**

** = (2/3) ÷ (-5/10)**

Hence the answer is 4/3

**Example 3 :**

Find (-4/9) ÷ (9/-4)

**Solution :**

** = **(-4/9) ÷ (9/-4)

** = **(-4/9) x (-4/9)

= 16/81

Hence the answer is 16/81.

**Example 4 :**

Find -9 3/4 ÷ 1 3/40

**Solution :**

** = **-9 3/4 ÷ 1 3/40

Converting the mixed fraction into improper fraction

** = **(-39/4) ÷ (43/40)

= (-39/4) x (40/43)

= (-39/1) x (10/43)

= -390/43

= - 9 3/43

Hence the answer is -9 3/43.

**Example 5 :**

Find the product of -2 4/15 and -3 2/49

**Solution :**

= (-2 4/15) x (-3 2/49)

Converting the mixed fractions into improper fractions.

= - (30 + 4)/15 x -(147 + 2)/49

= (-34/15) x (-149/49)

= 5066/735

= 6 656/735

Hence the product of the given fraction is 6 656/735

**Example 6 :**

Find the product of -12/5 and 6/5

**Solution :**

= (-12/5) x (6/5)

Multiplying the numerators, we get

= -12(6) = -72

Multiplying the denominators, we get 5(5) = 25

= -72/25

Converting the improper fraction into mixed fraction.

= 2 22/25

Hence the product of the given fraction is 2 22/25

**Example 7 :**

Find the product of -7/13 and 5/13

**Solution :**

= (-7/13) x (5/13)

Multiplying the numerators, we get

= -7(5) = -35

Multiplying the denominators, we get 13(13) = 169

= -35/169

Hence the product of the given fraction is -35/169

**Example 8 :**

Find the product of -3/9 and 7/8

**Solution :**

= (-3/9) x (7/8)

= (-1/3) x (7/8)

= -7/24

Hence the product of the given fraction is -7/24

**Example 9 :**

Find the product of -6/11 and 44/22

**Solution :**

= (-6/11) x (44/22)

= (-6/11) x (2/1)

= -12/11

Converting the improper fraction into mixed fraction, we get -1 1/11

Hence the product of the given fraction is -1 1/11.

**Example 10 :**

Find the product of (3/6) x (9/7) x (10/4)

**Solution :**

= (3/6) x (9/7) x (10/4)

= 45/28

After having gone through the stuff given above, we hope that the students would have understood "Multiply and divide rational numbers".

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