To simplify the given expression \(\frac{\frac{150}{160}}{\frac{70}{100}}\), follow these steps:

### Step 1: Rewrite the expression
We have:
\[
\frac{\frac{150}{160}}{\frac{70}{100}} = \frac{150}{160} \times \frac{100}{70}
\]

### Step 2: Simplify the fractions
First, simplify both fractions:

- \(\frac{150}{160}\): The greatest common divisor (GCD) of 150 and 160 is 10, so:
  \[
  \frac{150}{160} = \frac{150 \div 10}{160 \div 10} = \frac{15}{16}
  \]

- \(\frac{100}{70}\): The GCD of 100 and 70 is 10, so:
  \[
  \frac{100}{70} = \frac{100 \div 10}{70 \div 10} = \frac{10}{7}
  \]

### Step 3: Multiply the simplified fractions
Now multiply \(\frac{15}{16}\) by \(\frac{10}{7}\):
\[
\frac{15}{16} \times \frac{10}{7} = \frac{15 \times 10}{16 \times 7} = \frac{150}{112}
\]

### Step 4: Simplify the final fraction
Now simplify \(\frac{150}{112}\). The GCD of 150 and 112 is 2, so:
\[
\frac{150}{112} = \frac{150 \div 2}{112 \div 2} = \frac{75}{56}
\]

Thus, the simplified expression is \(\frac{75}{56}\), which is in its simplest form.

Would you like more details or have any further questions?

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**Related questions:**
1. How do you find the GCD of two numbers?
2. Can you multiply fractions directly without simplifying?
3. How do you convert an improper fraction to a mixed number?
4. What happens if you multiply decimals instead of fractions?
5. What is the decimal form of \(\frac{75}{56}\)?

**Tip:** Always simplify fractions as early as possible to make calculations easier.

Learn how to simplify the fraction expression 150/160:70/100 using the greatest common divisor (GCD). This step-by-step solution explains the multiplication and simplification of fractions, suitable for students in Grades 6-8.

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