Use the properties of operations and rules for multiplying and dividing to solve: (8/9)×(−3/4)÷(1/9)×(−4/5)÷(3/5) (1 point)

Answer 1

To solve this expression, we can use the associative property of multiplication and division to rearrange the terms:

(8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5)

= [(8/9) × (-3/4) × (-4/5)] ÷ [(1/9) × (3/5)]

= [(8 × -3 × -4)/ (9 × 4 × 5)] ÷ [(1 × 3) / (9 × 5)]

= [(8 × 3 × 4)/ (9 × 4 × 5)] ÷ [(1 × 3) / (9 × 5)]

= [96/(180)] ÷ [3/45]

= 96/180 ÷ 3/45

Now, we can simplify the fractions by dividing the numerators and denominators:

= (96 ÷ 180) ÷ (3 ÷ 45)

= (2/5) ÷ (1/15)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

= (2/5) × (15/1)

= 30/5

= 6

Therefore, (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5) equals 6.