Middle School

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Find the error in the work below. Then show the correct calculation.

Given Calculation:
\[ \frac{8}{12} \times 6 = 8 \times \frac{1}{12} \times 6 = 8 \times \frac{1}{72} = \frac{8}{72} = \frac{1}{9} \]

Correct Calculation:
\[ \frac{8}{12} \times 6 = \frac{8 \times 6}{12} = \frac{48}{12} = 4 \]

Answer :

  • The calculation is as follows;

Here we have to use BODMAS

(Bracket, Of, Division, Multiplication, Addition and Subtraction).

Like

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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Rewritten by : Barada

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:

  1. Simplify 8/12 by dividing both the numerator and denominator by their greatest common divisor, which is 4. This gives us 2/3.
  2. Multiply the resulting fraction by 6: 2/3 x 6.
  3. 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.
  4. Finally, we simplify 12/3 to get the answer: 4.

The correct calculation is therefore 8/12 x 6 = 2/3 x 6 = 4.