Question

Write the ratio in lowest terms in order to decide whether the proportion is true or false.
StartFraction 190 Over 200 EndFraction
equalsStartFraction 270 Over 310 EndFraction
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Question content area right
Part 1
What is the proportion in lowest​ terms?

  
enter your response hereequals
  
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​(Type fractions.)

Answer 1

To determine whether the proportion \( \frac{190}{200} = \frac{270}{310} \) is true, we will simplify both fractions to their lowest terms.

**Step 1: Simplify \( \frac{190}{200} \)**

1. Find the greatest common divisor (GCD) of 190 and 200.
- The GCD of 190 and 200 is 10.
2. Divide both the numerator and denominator by their GCD:
\[
\frac{190 \div 10}{200 \div 10} = \frac{19}{20}
\]

**Step 2: Simplify \( \frac{270}{310} \)**

1. Find the GCD of 270 and 310.
- The GCD of 270 and 310 is 10.
2. Divide both the numerator and denominator by their GCD:
\[
\frac{270 \div 10}{310 \div 10} = \frac{27}{31}
\]

Now we have the simplified fractions:

\[
\frac{190}{200} = \frac{19}{20} \quad \text{and} \quad \frac{270}{310} = \frac{27}{31}
\]

**Final Proportion:**
\[
\frac{19}{20} \neq \frac{27}{31}
\]

Thus, the proportion is **false**.

### Summary:
The proportion in lowest terms is:

\[
\frac{19}{20} \quad \text{and} \quad \frac{27}{31}
\]

So in the boxes, you can enter:
- \( \frac{19}{20} \) equals
- \( \frac{27}{31} \)