Question

simplify 4b + 3c - 2b + 7c


4/6x + 10/15y

1/2x + 1 3/10y


1/4x + 13/10y


1 1/4x + 1y

Answer 1

Let's simplify each expression step by step:

1. **For the expression \(4b + 3c - 2b + 7c\)**:
- Combine like terms for \(b\):
\(4b - 2b = 2b\)
- Combine like terms for \(c\):
\(3c + 7c = 10c\)
- Thus, the expression simplifies to:
\[
2b + 10c
\]

2. **For the expression \(\frac{4}{6}x + \frac{10}{15}y\)**:
- Simplify \(\frac{4}{6}\) and \(\frac{10}{15}\):
\(\frac{4}{6} = \frac{2}{3}\) and \(\frac{10}{15} = \frac{2}{3}\)
- So, the expression becomes:
\[
\frac{2}{3}x + \frac{2}{3}y
\]

3. **For the expression \(\frac{1}{2}x + 1 \frac{3}{10}y\)**:
- Convert the mixed number to an improper fraction:
\(1 \frac{3}{10} = \frac{10}{10} + \frac{3}{10} = \frac{13}{10}\)
- The expression is now:
\[
\frac{1}{2}x + \frac{13}{10}y
\]

4. **For the expression \(\frac{1}{4}x + \frac{13}{10}y\)**, it is already simplified.

5. **For the expression \(1 \frac{1}{4}x + 1y\)**:
- Convert the mixed number to an improper fraction:
\(1 \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}\)
- So the expression can be written as:
\[
\frac{5}{4}x + 1y \quad \text{or just} \quad \frac{5}{4}x + y
\]

In summary, the simplified expressions are:

1. \(2b + 10c\)
2. \(\frac{2}{3}x + \frac{2}{3}y\)
3. \(\frac{1}{2}x + \frac{13}{10}y\)
4. \(\frac{1}{4}x + \frac{13}{10}y\) (already simplified)
5. \(\frac{5}{4}x + y\)