Test of Essential Academic Skills (TEAS) ATI Mathematics Practice Test

Simplify: 4(2/3) / 1(1/6)

1. 2

2. 3 1/3

3. 4

4. 4 1/2

The correct answer is: 4

To simplify the expression \( 4 \left( \frac{2}{3} \right) \div 1 \left( \frac{1}{6} \right) \), we first convert the mixed number \( 1 \left( \frac{1}{6} \right) \) into an improper fraction. This is done by multiplying the whole number by the denominator and then adding the numerator: \( 1 \times 6 + 1 = 7 \), so \( 1 \left( \frac{1}{6} \right) \) becomes \( \frac{7}{6} \). Next, rewrite the original expression as a fraction: \[ 4 \left( \frac{2}{3} \right) = \frac{8}{3} \] (since \( 4 \times \frac{2}{3} = \frac{8}{3} \)). Now, we convert the division into multiplication by the reciprocal: \[ \frac{8}{3} \div \frac{7}{6} = \frac{8}{3} \times \frac{6}{7} \]. Now, we multiply: \[ \frac{8 \