Question

Simplify Algebraic Expressions Quick Check
Simplify 6/7c — 5/9d — 1/2c + 1/3d.

Answer 1

Thanks for the help I made a 100

Answer 2

To simplify the expression \( \frac{6}{7}c - \frac{5}{9}d - \frac{1}{2}c + \frac{1}{3}d \), we can group the like terms (the terms involving \( c \) and the terms involving \( d \)).

1. Group the \( c \) terms:
\[
\frac{6}{7}c - \frac{1}{2}c
\]
To combine these, we need a common denominator. The least common multiple of \( 7 \) and \( 2 \) is \( 14 \).
- Convert \( \frac{6}{7}c \):
\[
\frac{6}{7} = \frac{6 \times 2}{7 \times 2} = \frac{12}{14}
\]
- Convert \( \frac{1}{2}c \):
\[
\frac{1}{2} = \frac{1 \times 7}{2 \times 7} = \frac{7}{14}
\]
Now combine:
\[
\frac{12}{14}c - \frac{7}{14}c = \frac{12 - 7}{14}c = \frac{5}{14}c
\]

2. Group the \( d \) terms:
\[
-\frac{5}{9}d + \frac{1}{3}d
\]
Again, we need a common denominator. The least common multiple of \( 9 \) and \( 3 \) is \( 9 \).
- Convert \( \frac{1}{3}d \):
\[
\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}
\]
Now combine:
\[
-\frac{5}{9}d + \frac{3}{9}d = \frac{-5 + 3}{9}d = \frac{-2}{9}d
\]

Putting it all together, the simplified expression is:
\[
\frac{5}{14}c - \frac{2}{9}d
\]

Answer 3

That's fantastic! Congratulations on scoring 100! 🎉 If you have any more questions or need help with anything else, feel free to ask. Keep up the great work!