Google

Add two numerical fractions that share the denominator $$18$$, then simplify the result by factoring out common factors:

$$\frac{5}{18} + \frac{7}{18}$$

**Step 1 — Add the numerators over the common denominator.** Since both fractions already share the denominator $$18$$, combine the numerators directly:

$$\frac{5 + 7}{18} = \frac{12}{18}$$

**Step 2 — Factor the numerator and denominator to reveal common factors.** Write $$12 = 6 \cdot 2$$ and $$18 = 6 \cdot 3$$:

$$\frac{6 \cdot 2}{6 \cdot 3}$$

**Step 3 — Divide out the common factor.** Cancel the shared factor of $$6$$ from the numerator and denominator:

$$\frac{2}{3}$$

This numerical example previews the same three-step procedure used for adding rational expressions with a common denominator: combine the numerators, factor completely, and simplify by removing common factors. The only difference when working with rational expressions is that the numerators and denominators are polynomials rather than plain numbers.

Adding $$\frac{5}{18} + \frac{7}{18}$$

A logistics coordinator is combining two shipments of liquid fertilizer. One shipment fills $\frac{5}{18}$ of a transport tank, and the second shipment fills $\frac{7}{18}$ of the same tank. What is the total fraction of the tank filled by these two shipments? Provide your answer as a fraction in simplest form.

Consolidating Material Shipments

Add and simplify: $$\frac{5}{18} + \frac{7}{18}$$

Arrange the steps in the correct order to add and simplify: $$\frac{5}{18} + \frac{7}{18}$$

The sum of $$\frac{5}{18}$$ and $$\frac{7}{18}$$, expressed in simplest form, is $$\frac{2}{3}$$.

What is the result of adding $$\frac{5}{18} + \frac{7}{18}$$ before any simplification occurs?

Case context:
$$\frac{5}{18}+\frac{7}{18}$$

Question:
Add and simplify the fractions. Show the sum before and after simplifying.

Sample answer:
Add the numerators: $$\frac{5+7}{18}=\frac{12}{18}$$. Divide the numerator and denominator by the common factor $$6$$: $$\frac{12}{18}=\frac{2}{3}$$.

Key points:
- Add the numerators to get $$\frac{12}{18}$$.
- Use the common factor $$6$$.
- Simplify to $$\frac{2}{3}$$.

Rubric:
Full credit requires $$\frac{12}{18}$$, the common factor $$6$$, and the simplified answer $$\frac{2}{3}$$.

Add and simplify the fractions. Show the sum before and after simplifying.

The greatest common factor of $$12$$ and $$18$$ is _____.

Complete the factorization: $$12=6\cdot\,?$$

These fractions have the same denominator. Explain the procedure you would use to combine them and write the sum in simplest form.

Learn Before

Related