Express the ratio `(4)/(5):(8)/(7)` in the lowest terms

Answer

To express the ratio \( \frac{4}{5} : \frac{8}{7} \) in the lowest terms, follow these steps:

### Step 1: Write the ratio as a fraction
We start by rewriting the ratio \( \frac{4}{5} : \frac{8}{7} \) as a single fraction:
\[ \frac{4/5}{8/7} \]

### Step 2: Simplify the complex fraction
To simplify this complex fraction, we can multiply by the reciprocal of the denominator:
\[ \frac{4}{5} \times \frac{7}{8} \]

### Step 3: Multiply the numerators and the denominators
Now, we multiply the numerators and the denominators:
\[ \frac{4 \times 7}{5 \times 8} = \frac{28}{40} \]

### Step 4: Simplify the fraction
Next, we simplify \( \frac{28}{40} \) by finding the greatest common divisor (GCD) of 28 and 40. The GCD is 4.
\[ \frac{28 \div 4}{40 \div 4} = \frac{7}{10} \]

### Step 5: Write the final ratio
Now, we can express the simplified ratio:
\[ 7 : 10 \]

Thus, the ratio \( \frac{4}{5} : \frac{8}{7} \) in the lowest terms is \( 7 : 10 \).

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