Solve the Arithmetic Puzzle: a×b×8c : (2a : (72b×c))

Video Solution

Solution Steps

00:00 Solve

00:09 Let's write division as a fraction

00:18 Division is also multiplication by the reciprocal

00:30 Let's reduce what we can

00:37 Let's factor 8 into factors 2 and 4

00:47 Let's reduce what we can

00:57 Use the distribution law and split 72 into 70 plus 2

01:10 Open parentheses properly

01:13 The outer factor will multiply each term in parentheses

01:26 And this is the solution to the question

Step-by-Step Solution

To solve the problem, follow these detailed steps:

Step 1: Simplify the innermost expression:
Calculate $2a : (72b \cdot c)$ . This equates to dividing $2a$ by $72b \cdot c$ :
$2a : (72b \cdot c) = \frac{2a}{72b \cdot c}$
Step 2: Simplification
$= \frac{2a}{72b \cdot c} = \frac{2a}{72bc} = \frac{a}{36bc}$
Step 3: Complete the outer expression:
Now, substitute this back into the outer expression:
$a \cdot b \cdot 8c : \left(\frac{a}{36bc}\right)$
Step 4: Simplify this result:
This means multiplying $a \cdot b \cdot 8c$ by the reciprocal of $\frac{a}{36bc}$ ):
$= a \cdot b \cdot 8c \cdot \frac{36bc}{a}$
Step 5: Cancel and compute:
Notice $a$ cancels out:
$= b \cdot 8c \cdot 36bc$
Step 6: Final simplification:
$= 8 \cdot 36 \cdot b^2 \cdot c^2$
$= 288b^2c^2$

Therefore, the solution to the given expression is $288b^2c^2$ , which corresponds to choice ID 4.