Let's remind ourselves of the three rules for dividing with negative numbers:

  • A negative number divided by a positive number gives a negative number. \begin{align*} \mathbf{\color{red}(-)} \:\mathbf{\div}\: \mathbf{\color{blue}(+)} \:=\: \mathbf{\color{red}(-)} \end{align*}

  • A positive number divided by a negative number is also a negative number. \begin{align*} \mathbf{\color{blue}(+)} \:\mathbf{\div}\: \mathbf{\color{red}(-)} \:=\: \mathbf{\color{red}(-)} \end{align*}

  • A negative number divided by a negative number is a positive number. \begin{align*} \mathbf{\color{red}(-)} \:\mathbf{\div}\: \mathbf{\color{red}(-)} \:=\: \mathbf{\color{blue}(+)} \end{align*}

FLAG

As an example, let's find the value of

2.4 \div (-4).

Dividing a positive number by a negative number gives a negative number. Hence, the result will be negative.

Therefore, since

2.4\div 4=0.6,

we obtain

2.4 \div (-4) = -0.6.

FLAG

Calculate 2.4 \div (-1.2).

EXPLANATION

Dividing a positive number by a negative number gives a negative number. Hence, the result will be negative.

Therefore, since

2.4\div 1.2 = 2,

we obtain

2.4 \div (-1.2) = -2.

FLAG

Find the value of $(-5.2) \div (-4).$

a
$1.3$
b
$1.2$
c
$-1.2$
d
$1.4$
e
$-1.3$

Calculate $(-4.5) \div 0.5.$

a
$-9$
b
$-5$
c
$2.5$
d
$5$
e
$9$

Find the value of \dfrac{4}{7} \div (-2).

EXPLANATION

Dividing a positive number by a negative number gives a negative number. Hence, the result will be negative.

Therefore, since \dfrac{4}{7} \div 2 = \dfrac{4}{7 \times 2} = \dfrac{4}{14} = \dfrac{2}{7}, we obtain \dfrac{4}{7} \div (-2) = -\dfrac {2}{7}.

FLAG

Find the value of $\left(-\dfrac{10}{13}\right) \div 5.$

a
$\dfrac{12}{13}$
b
$\dfrac {2}{13}$
c
$\dfrac{7}{65}$
d
$-\dfrac{7}{65}$
e
$-\dfrac {2}{13}$

What is the value of $(-10) \div \left(-\dfrac 2 3\right)?$

a
$-15$
b
$15$
c
$5$
d
$20$
e
$-20$

Find the value of \left(-\dfrac{2}{5}\right) \div \dfrac{1}{10}.

EXPLANATION

Dividing a negative number by a positive number gives a negative number. Hence, the result will be negative.

Therefore, since \dfrac{2}{5} \div \dfrac{1}{10} = \dfrac {2 \times 10}{5 \times 1} = \dfrac{20}{5} =4, we obtain \left(-\dfrac{2}{5}\right) \div \dfrac{1}{10} = -4.

FLAG

Find the value of $\dfrac{1}{8} \div \left( -\dfrac 1 {24} \right).$

a
$-\dfrac{1}{3}$
b
$3$
c
$\dfrac{1}{3}$
d
$1$
e
$-3$

What is the value of $\left(-\dfrac{5}{8}\right) \div \left(-\dfrac 3 4\right)?$

a
$\dfrac{5}{6}$
b
$-\dfrac{2}{3}$
c
$\dfrac{2}{3}$
d
$-\dfrac{5}{6}$
e
$2$
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