What is the value of the expression −6 4/9−1 1/3?

Question

A 7 7/9
B -7 7/9
C 5 1/9
D -5 1/9

Answer 1

To subtract mixed numbers, we need to find a common denominator. The least common multiple of 9 and 3 is 9, so we can convert the mixed numbers into fractions with a denominator of 9.

Converting -6 4/9 to a fraction:
-6 4/9 = -6 * 9/9 + 4/9 = -54/9 + 4/9 = -50/9

Converting 1 1/3 to a fraction:
1 1/3 = 1 * 3/3 + 1/3 = 3/3 + 1/3 = 4/3

Now we can subtract the fractions:
-50/9 - 4/3

To subtract fractions, we need a common denominator. The least common multiple of 9 and 3 is 9, so we can convert the fractions to have the same denominator.

-50/9 - 4/3 = -50/9 - (4/3)(3/3) = -50/9 - 12/9 = -62/9

The expression −6 4/9−1 1/3 is equal to -62/9.

Converting -62/9 to a mixed number:
-62/9 = -6 remainder -8/9 = -6 8/9

So, the value of the expression −6 4/9−1 1/3 is -6 8/9.

The correct answer is D) -5 1/9.

Answer 2

When subtracting a positive and negative integers simply combine the two terms and keep the negative. With fractions you have to find the common denominator of each term. -6 4/9 - 1 1/3 = -6 4/9 - 1 3/9 = -7 7/9.

Answer 3

You are absolutely correct. I apologize for the incorrect explanation in my previous response. When subtracting mixed numbers, we indeed combine the whole number parts and fractions separately, find a common denominator, and then subtract.

-6 4/9 - 1 1/3 can be rewritten as -6 4/9 - 1 3/9.

Combining the whole number parts, we have -6 - 1 = -7.

For the fraction parts, the common denominator is 9.
Then, we have 4/9 - 3/9 = 1/9.

Putting it all together, the simplified expression is -7 1/9.

The correct answer is B) -7 1/9. Thank you for pointing out the mistake and providing the correct explanation.