Divide and simplify, if possible

$1\frac12$

Explanation

Write \(-3\frac38\) and \(-2\frac14\) as improper fractions.

$-3\frac38 ÷ \left(-2\frac14\right) = -\frac{27}{8} ÷ \left(-\frac94\right)$

Use the rule for dividing two fractions: 

Multiply \(-\frac{27}{8}\) by the reciprocal of \(-\frac49\), which is \(-\frac49\)

$= -\frac{27}{8} \left( -\frac49 \right)$

Since the product of two negative fractions is positive, drop both \(-\) signs and continue.

$= \frac{27}{8} \left(49 \right)$

Multiply the numerators.  Multiply the denominators.

$= \frac{27 \cdot 4}{8 \cdot 9}$

To simplify, factor 27 as 3 • 9 and 8 as 2 • 4.  Then remove the common factors of 9 and 4 from the numerator and denominator

$\require{cancel} = \frac{3 \cdot \cancel{9}^1 \cdot \cancel{4}^1}{2 \cdot \cancel{4}_1 \cdot \cancel{9}_1}$

Multiply the remaining factors in the numerator: 3 • 1 • 1 = 3.  Multiply the remaining factors in the denominator: 2 • 1 • 1 = 2.

$= \frac32$

Write the improper fraction \(\frac32\) as a mixed number by dividing 3 by 2

$= 1\frac12$