Question

(-1/6)×(3/7)×(-1 1/4)/-1/8×(-1 1/2)×5/6

Answer 1

-1/6*3/7=-3/42
-3/42*(-1 1/4)=-3/42*5/4=-15/168
-1/8*(-1 1/2)=-1/8*(-3/2)=3/16
3/16*5/6=15/96
-15/168:15/96=-15/168*96/15=96/168=4/7

Answer 2

To simplify the expression, follow these steps:

Step 1: Convert mixed numbers to improper fractions. Step 2: Perform the operations (multiplications and divisions) from left to right.

Let's start with the expression:

(-1/6) × (3/7) × (-1 1/4) / (-1/8) × (-1 1/2) × 5/6

Step 1: Convert mixed numbers to improper fractions.

(-1 1/4) can be converted to an improper fraction as follows: -1 1/4 = -(1 + 1/4) = -5/4

(-1 1/2) can be converted to an improper fraction as follows: -1 1/2 = -(1 + 1/2) = -3/2

Step 2: Perform the operations from left to right.

Now, let's perform the multiplication and division:

(-1/6) × (3/7) × (-5/4) / (-1/8) × (-3/2) × 5/6

Now, perform the multiplications:

= (-1/6) × (3/7) × (-5/4) / (1/4) × (3/2) × 5/6 [Multiplying -1/8 with -1 gives us 1/8]

Next, simplify the fractions:

= (-1/2) × (1/2) × (-5/4) / (1/4) × (3/2) × 5/6 [Simplified -1/6 × 3/7]

Now, perform the remaining multiplication:

= (-1/4) × (-5/4) / (1/4) × (3/2) × 5/6 [Simplified -1/2 × 1/2]

Simplify further:

= 5/16 / (3/8) × 5/6 [Simplified -1/4 × -5/4]

Now, perform the division:

= 5/16 × (8/3) × 5/6 [Dividing by 3/8 is the same as multiplying by its reciprocal, which is 8/3]

Now, simplify the fractions:

= 5/16 × 40/18

Now, multiply the numerators and denominators:

= (5 × 40) / (16 × 18)

Finally, perform the division:

= 200 / 288

Now, reduce the fraction to its simplest form:

= 25/36

So, the simplified expression is 25/36.