Question

1. $\frac{-3}{2} + \frac{1}{4}$
2. $\frac{-3}{2} div -2$

Explanation:

Problem 17: $\boldsymbol{\frac{-3}{2} + \frac{1}{4}}$

Step1: Find a common denominator

The denominators are 2 and 4, so the common denominator is 4. Rewrite $\frac{-3}{2}$ with denominator 4: $\frac{-3}{2} = \frac{-3\times2}{2\times2} = \frac{-6}{4}$

Step2: Add the fractions

Now add $\frac{-6}{4}$ and $\frac{1}{4}$: $\frac{-6 + 1}{4} = \frac{-5}{4}$

Step1: Rewrite division as multiplication

Dividing by a number is the same as multiplying by its reciprocal. So, $\frac{-3}{2} \div -2 = \frac{-3}{2} \times \frac{1}{-2}$

Step2: Multiply the fractions

Multiply the numerators and denominators: $\frac{(-3)\times1}{2\times(-2)} = \frac{-3}{-4}$

Step3: Simplify the sign

A negative divided by a negative is positive, so $\frac{-3}{-4} = \frac{3}{4}$

Answer:

$\frac{-5}{4}$

Problem 19: $\boldsymbol{\frac{-3}{2} \div -2}$