Simplify 6/7c − 5/9d − 1/2 c + 1/3d

Answer 1

To simplify the expression, we need to combine like terms. Like terms have the same variable raised to the same power.

6/7c - 1/2c can be simplified by finding a common denominator for 7 and 2. The least common multiple of 7 and 2 is 14. We can rewrite the expression as:

(12/14c - 7/14c)

Simplifying further, we get:

(5/14c)

Similarly, we can simplify -5/9d + 1/3d by finding a common denominator for 9 and 3. The least common multiple of 9 and 3 is 9. We can rewrite the expression as:

(-15/9d + 3/9d)

Simplifying further, we get:

(-12/9d)

Now, we can rewrite the expression with the simplified terms:

(5/14c) + (-12/9d)

To add or subtract fractions with different denominators, we need to find a common denominator. In this case, the least common multiple of 14 and 9 is 126.

The expression can be rewritten as:

(5/14c)*(9/9) + (-12/9d)*(14/14)

Simplifying further, we get:

(45/126c) + (-168/126d)

Finally, we can simplify the expression further by factoring out a common term from the numerator:

(45c - 168d)/126

The simplified expression is (45c - 168d)/126.

Answer 2

Simplify 67c − 59d − 12 c + 13d
.(1 point)
Responses

59c − 412d = 59c −13d
Start Fraction 5 over 9 End Fraction c minus Start Fraction 4 over 12 End Fraction d equals Start Fraction 5 over 9 End Fraction c minus Start Fraction 1 over 3 End Fraction d

59c + 412d = 59c +13d
Start Fraction 5 over 9 End Fraction c plus Start Fraction 4 over 12 End Fraction d equals Start Fraction 5 over 9 End Fraction c plus Start Fraction 1 over 3 End Fraction d

514c + 29d
Start Fraction 5 over 14 End Fraction c plus Start Fraction 2 over 9 End Fraction d

514c − 29d

Answer 3

To simplify the expression, we need to combine like terms. Like terms have the same variable raised to the same power.

67c - 12c can be simplified to 55c.

Similarly, -59d + 13d can be simplified to -46d.

Now, we can rewrite the expression with the simplified terms:

55c - 46d

So, the simplified expression is 55c - 46d.

Answer 4

Simplify 6/7c − 5/9d − 1/2 c + 1/3d
A. 5/9c - 4/12d = 5/9c - 1/3d
B. 5/9c + 4/12d = 5/9c + 1/3d
C. 5/14c + 2/9d
D. 5/14c - 2/9d

Answer 5

To simplify the expression 6/7c - 5/9d - 1/2c + 1/3d, we need to combine like terms.

First, let's combine the c terms: 6/7c - 1/2c. To do this, we find a common denominator for 7 and 2, which is 14. We can rewrite the expression as:

(12/14c - 7/14c)

Simplifying further, we get:

(5/14c)

Next, let's combine the d terms: -5/9d + 1/3d. To do this, we find a common denominator for 9 and 3, which is 9. We can rewrite the expression as:

(-15/9d + 3/9d)

Simplifying further, we get:

(-12/9d)

Now, we can rewrite the expression with the simplified terms:

(5/14c) + (-12/9d)

To add or subtract fractions with different denominators, we need to find a common denominator. In this case, the least common multiple of 14 and 9 is 126.

The expression can be rewritten as:

(5/14c)*(9/9) + (-12/9d)*(14/14)

Simplifying further, we get:

(45/126c) + (-168/126d)

Finally, we can simplify the expression further by factoring out a common term from the numerator:

(45c - 168d)/126

Therefore, the correct simplification is option D. 5/14c - 2/9d.