Verify the Equation: Is (8+3×4)/(6×2+8) = 1?

Question

Determine if the simplification below is correct:

8+3462+8=1 \frac{8+3\cdot4}{6\cdot2+8}=1

Video Solution

Solution Steps

00:00 Determine if the reduction is correct
00:08 Let's calculate the multiplications
00:23 Use the commutative law and arrange the denominator to match the numerator
00:36 Reduce what's possible, when we reduce the entire fraction we always get 1
00:41 Compare between the expressions
00:45 And this is the solution to the question

Step-by-Step Solution

Let's examine the given problem:

8+3462+8=?1 \frac{8+3\cdot4}{6\cdot2+8}\stackrel{?}{= }1 Note that in the numerator there is a product between the number 8 and the number34 3\cdot4 and in the denominator there is a product between the number 8 and the number 62 6\cdot2 , since these two multiplications give the same result:

34=62=12 3\cdot4=6\cdot2=12 Both in the numerator and denominator it's the same number:

8+34=62+8 8+3\cdot4=6\cdot2+8 Now we'll remember that dividing a number by itself always yields 1, therefore indeed:

8+3462+8=8+1212+8=!1 \frac{8+3\cdot4}{6\cdot2+8}= \frac{8+12}{12+8}\stackrel{!}{= }1 and thus answer A is the correct answer

Answer

Correct