Question

1/6 + 3/4 + 2/3 + 1 1/5 = 4/5 + 6/7 + 1 2/5 + 1 5/7 =

Answer 1

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Answer 2

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Answer 3

To simplify the expressions on both sides of the equation, we need to find a common denominator for each set of fractions. The common denominator for the first set of fractions is 12 (the least common multiple of 6, 4, and 3), and for the second set, it is 35 (the least common multiple of 5 and 7).

Let's simplify each side of the equation:

Left side: 1/6 + 3/4 + 2/3 + 1 1/5

To express the mixed number 1 1/5 as an improper fraction, we perform the following calculation: 1 1/5 = (1 * 5 + 1)/5 = 6/5

Now, we have: 1/6 + 3/4 + 2/3 + 6/5

To find the common denominator, we multiply each fraction by the appropriate factor:

(1/6)(2/2) + (3/4)(3/3) + (2/3)*(4/4) + 6/5

Now, we get: 2/12 + 9/12 + 8/12 + 6/5

Next, add the fractions: (2 + 9 + 8)/12 + 6/5

Sum the numerators: 19/12 + 6/5

To find the common denominator, we multiply 19/12 by 5/5 and 6/5 by 12/12:

(19/12)(5/5) + (6/5)(12/12)

Now, we get: 95/60 + 72/60

Finally, add the fractions: (95 + 72)/60 = 167/60

Right side: 4/5 + 6/7 + 1 2/5 + 1 5/7

To express the mixed numbers as improper fractions: 1 2/5 = (1 * 5 + 2)/5 = 7/5 1 5/7 = (1 * 7 + 5)/7 = 12/7

Now, we have: 4/5 + 6/7 + 7/5 + 12/7

To find the common denominator, we multiply each fraction by the appropriate factor:

(4/5)(7/7) + (6/7)(5/5) + 7/5 + (12/7)*(5/5)

Now, we get: 28/35 + 30/35 + 7/5 + 60/35

Next, add the fractions: (28 + 30 + 7 + 60)/35 = 125/35

Now, we simplify the fractions on both sides of the equation:

Left side: 167/60 Right side: 125/35

To compare the two sides, we need to find a common denominator, which is the least common multiple of 60 and 35, which is 420.

Now, we convert both fractions to have a denominator of 420:

Left side: (167/60)(7/7)(70/70) = 11690/420

Right side: (125/35)(12/12)(12/12) = 1500/420

Now, the equation becomes:

11690/420 = 1500/420

Since the denominators are the same, we can compare the numerators:

11690 = 1500

However, 11690 is not equal to 1500, so the equation is not true. The original statement "1/6 + 3/4 + 2/3 + 1 1/5 = 4/5 + 6/7 + 1 2/5 + 1 5/7" is incorrect.