2. Multiply and express in the lowest form:

(a) [tex]\frac{2}{-3}[/tex] and [tex]\frac{4}{5}[/tex]

(b) [tex]\frac{-3}{5}[/tex] and [tex]\frac{4}{3}[/tex]

(c) [tex]\frac{16}{15}[/tex] and [tex]\frac{3}{4}[/tex]



Answer :

Let's solve each part of the problem step by step:

### Part (a)

We need to multiply the fractions [tex]\(\frac{2}{-3}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex].

Step 1: Multiply the numerators together:
[tex]\[ 2 \times 4 = 8 \][/tex]

Step 2: Multiply the denominators together:
[tex]\[ (-3) \times 5 = -15 \][/tex]

Step 3: Combine the results to form a new fraction:
[tex]\[ \frac{8}{-15} = -\frac{8}{15} \][/tex]

The fraction [tex]\(-\frac{8}{15}\)[/tex] is already in its lowest form. So the answer is:
[tex]\[ -\frac{8}{15} \][/tex]

### Part (b)

Next, we multiply the fractions [tex]\(\frac{-3}{5}\)[/tex] and [tex]\(\frac{4}{3}\)[/tex].

Step 1: Multiply the numerators together:
[tex]\[ -3 \times 4 = -12 \][/tex]

Step 2: Multiply the denominators together:
[tex]\[ 5 \times 3 = 15 \][/tex]

Step 3: Combine the results to form a new fraction:
[tex]\[ \frac{-12}{15} \][/tex]

Step 4: Simplify the fraction [tex]\(\frac{-12}{15}\)[/tex]. The greatest common divisor (GCD) of 12 and 15 is 3, so we divide both the numerator and the denominator by 3:
[tex]\[ \frac{-12 \div 3}{15 \div 3} = \frac{-4}{5} \][/tex]

The fraction [tex]\(\frac{-4}{5}\)[/tex] is in its lowest form. So the answer is:
[tex]\[ -\frac{4}{5} \][/tex]

### Part (c)

Lastly, we multiply the fractions [tex]\(\frac{16}{15}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex].

Step 1: Multiply the numerators together:
[tex]\[ 16 \times 3 = 48 \][/tex]

Step 2: Multiply the denominators together:
[tex]\[ 15 \times 4 = 60 \][/tex]

Step 3: Combine the results to form a new fraction:
[tex]\[ \frac{48}{60} \][/tex]

Step 4: Simplify the fraction [tex]\(\frac{48}{60}\)[/tex]. The GCD of 48 and 60 is 12, so we divide both the numerator and the denominator by 12:
[tex]\[ \frac{48 \div 12}{60 \div 12} = \frac{4}{5} \][/tex]

The fraction [tex]\(\frac{4}{5}\)[/tex] is in its lowest form. So the answer is:
[tex]\[ \frac{4}{5} \][/tex]

### Summary of the Answers:
(a) [tex]\(-\frac{8}{15}\)[/tex]
(b) [tex]\(-\frac{4}{5}\)[/tex]
(c) [tex]\(\frac{4}{5}\)[/tex]

Therefore, the results of the multiplications are:
(a) [tex]\(-\frac{8}{15}\)[/tex]
(b) [tex]\(-\frac{4}{5}\)[/tex]
(c) [tex]\(\frac{4}{5}\)[/tex]