solve by cancellation and finding the gcf, then proceed to show the solution, and simplify. 16/30*18/60

Let's solve \(\frac{16}{30} \times \frac{18}{60}\) by canceling common factors and finding the greatest common factor (GCF).

### Step 1: Set Up the Multiplication
We start with:

\[
\frac{16}{30} \times \frac{18}{60}
\]

### Step 2: Cancel Common Factors Before Multiplying
We can simplify the fractions by canceling any common factors directly across numerators and denominators.

**Simplify \(\frac{16}{30}\):**

- The GCF of 16 and 30 is 2.
- Simplify \(\frac{16}{30}\) by dividing both the numerator and the denominator by 2:

\[
\frac{16 \div 2}{30 \div 2} = \frac{8}{15}
\]

**Simplify \(\frac{18}{60}\):**

- The GCF of 18 and 60 is 6.
- Simplify \(\frac{18}{60}\) by dividing both the numerator and the denominator by 6:

\[
\frac{18 \div 6}{60 \div 6} = \frac{3}{10}
\]

Now the expression becomes:

\[
\frac{8}{15} \times \frac{3}{10}
\]

### Step 3: Multiply the Simplified Fractions
Now multiply the simplified fractions:

\[
\frac{8 \times 3}{15 \times 10} = \frac{24}{150}
\]

### Step 4: Simplify \(\frac{24}{150}\) by Finding the GCF
Find the GCF of 24 and 150:

- The GCF of 24 and 150 is 6.
- Simplify \(\frac{24}{150}\) by dividing both the numerator and the denominator by 6:

\[
\frac{24 \div 6}{150

Learn how to simplify and multiply fractions by cancellation and finding the greatest common factor (GCF). This problem involves simplifying the fractions \(\frac{16}{30}\) and \(\frac{18}{60}\) and then multiplying them to obtain the solution \(\frac{24}{150}\). Suitable for students in Grades 5-8.

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