Answer :
Final answer:
The error was in the handling of the multiplication and division in the expression 8/12 x 6. The proper calculation should simplify the fraction before multiplying, leading to the correct answer of 4.
Explanation:
To find the error in the mathematical operation 8/12 x 6, let us examine each step that was provided:
The original equation was manipulated incorrectly; the mistake lies in the manipulation of the division and multiplication steps. The student incorrectly changed the operation into 8 x 1/12 x 6, which then led to 8 x 1/72 and finally an incorrect simplification to 8/72, which they further reduced to 1/9. However, the correct approach is to either simplify the fraction first or perform the multiplication as shown:
- Simplify 8/12 by dividing both the numerator and denominator by their greatest common divisor, which is 4. This gives us 2/3.
- Multiply the resulting fraction by 6: 2/3 x 6.
- Since 6 is equivalent to 6/1, we multiply the numerators together (2 x 6) and the denominators together (3 x 1), resulting in 12/3.
- Finally, we simplify 12/3 to get the answer: 4.
The correct calculation is therefore 8/12 x 6 = 2/3 x 6 = 4.
- The calculation is as follows;
Here we have to use BODMAS
(Bracket, Of, Division, Multiplication, Addition and Subtraction).
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We can re- write it as
[tex]= (8\div 12) \times 6\\\\= (2\div 3) \times 6\\\\= (2) \times 2[/tex]
= 4
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