Question

simplify the the following and Express the product as a rational number in standard form :
(a) -7/15 × 4/14
(b) -5/9 × 11/-20
(c) -45/32 × 4/9
(d) 3/-11 × -55/2​

Answer 1

(a) Simplification: -28/210 and Standard Form: 14/105

(b) Simplification: 55/180 and Standard Form: 11/36

(c) Simplification: -180/288 and Standard Form: -5/8

(d) Simplification: 165/22 and Standard Form:15/2

Step-by-step explanation:

(a)

$\frac{ - 7}{15} \times \frac{4}{14}$

Simplification:

$\frac{ - 7 \times 4}{15 \times 14} \\ \\ = \frac{ - 28}{210}$

In Standard form:

$\frac{ - 28}{210} \\ \\ = \frac{14}{105}$

(b)

$\frac{ - 5}{9} \times \frac{11}{ - 20}$

Simplification:

$\frac{ - 5 \times 11}{9 \times ( - 20)} \\ \\ = \frac{ - 55}{ - 180} \\ \\ = \frac{55}{180}$

In Standard form:

$\frac{55}{180} \\ \\ = \frac{11}{36}$

(c)

$\frac{ - 45}{32} \times \frac{4}{9}$

Simplification:

$\frac{ - 45 \times 4}{32 \times 9} \\ \\ = \frac{ - 180}{288}$

In Standard form:

$\frac{ - 180}{288} \\ \\ = \frac{ - 5}{8}$

(d)

$\frac{ 3}{ - 11} \times \frac{ - 55}{2}$

Simplification:

$\frac{ 3 \times - 55}{ - 11 \times 2} \\ \\ = \frac{ - 165}{ - 22} \\ \\ = \frac{165}{22}$

In Standard form:

$\frac{165}{22} \\ \\ = \frac{3 \times 5 \times 11}{2 \times 11} \\ \\ = \frac{3 \times 5}{2} \\ \\ = \frac{15}{2}$