Divide Rational Numbers - 7th Grade Math
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What identity shows a negative sign can be placed outside or in the numerator: $ -\left(\frac{p}{q}\right) $?
What identity shows a negative sign can be placed outside or in the numerator: $ -\left(\frac{p}{q}\right) $?
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$ -\left(\frac{p}{q}\right) = \frac{-p}{q} $. The negative can be moved from outside to the numerator.
$ -\left(\frac{p}{q}\right) = \frac{-p}{q} $. The negative can be moved from outside to the numerator.
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What identity shows a negative sign can be placed in the denominator: $ -\left(\frac{p}{q}\right) $?
What identity shows a negative sign can be placed in the denominator: $ -\left(\frac{p}{q}\right) $?
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$ -\left(\frac{p}{q}\right) = \frac{p}{-q} $. The negative can also be placed in the denominator.
$ -\left(\frac{p}{q}\right) = \frac{p}{-q} $. The negative can also be placed in the denominator.
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What complete identity connects all three equivalent forms of a negative rational quotient?
What complete identity connects all three equivalent forms of a negative rational quotient?
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$-\left(\frac{p}{q}\right)=\frac{-p}{q}=\frac{p}{-q}$. All three forms represent the same negative rational number.
$-\left(\frac{p}{q}\right)=\frac{-p}{q}=\frac{p}{-q}$. All three forms represent the same negative rational number.
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What is the result of dividing any nonzero integer by $0$, such as $\frac{5}{0}$?
What is the result of dividing any nonzero integer by $0$, such as $\frac{5}{0}$?
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Undefined (division by $0$ is not allowed). Division by zero violates the fundamental rule of division.
Undefined (division by $0$ is not allowed). Division by zero violates the fundamental rule of division.
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Identify the value: $(-12) \div 3$.
Identify the value: $(-12) \div 3$.
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$-4$. Negative divided by positive gives negative: $-12 \div 3 = -4$.
$-4$. Negative divided by positive gives negative: $-12 \div 3 = -4$.
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Identify the value: $12 \div (-3)$.
Identify the value: $12 \div (-3)$.
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$-4$. Positive divided by negative gives negative: $12 \div (-3) = -4$.
$-4$. Positive divided by negative gives negative: $12 \div (-3) = -4$.
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Identify the value: $(-12) \div (-3)$.
Identify the value: $(-12) \div (-3)$.
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$4$. Negative divided by negative gives positive: $(-12) \div (-3) = 4$.
$4$. Negative divided by negative gives positive: $(-12) \div (-3) = 4$.
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Identify the value: $(-15) \div 5$.
Identify the value: $(-15) \div 5$.
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$-3$. Different signs yield negative: $(-15) \div 5 = -3$.
$-3$. Different signs yield negative: $(-15) \div 5 = -3$.
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What is the sign rule for dividing two integers with the same sign?
What is the sign rule for dividing two integers with the same sign?
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The quotient is positive. Same signs divide to give a positive result.
The quotient is positive. Same signs divide to give a positive result.
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Identify the value: $7 \div (-1)$.
Identify the value: $7 \div (-1)$.
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$-7$. Dividing by $-1$ changes the sign: $7 \div (-1) = -7$.
$-7$. Dividing by $-1$ changes the sign: $7 \div (-1) = -7$.
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Which is equivalent to $-\left(\frac{8}{5}\right)$: $\frac{-8}{5}$ or $\frac{8}{-5}$?
Which is equivalent to $-\left(\frac{8}{5}\right)$: $\frac{-8}{5}$ or $\frac{8}{-5}$?
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Both: $\frac{-8}{5}$ and $\frac{8}{-5}$. By the identity, negative can be in numerator or denominator.
Both: $\frac{-8}{5}$ and $\frac{8}{-5}$. By the identity, negative can be in numerator or denominator.
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What is the sign rule for integer division when the signs are the same?
What is the sign rule for integer division when the signs are the same?
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Same signs: the quotient is positive.
Same signs: the quotient is positive.
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What is $-\left(\frac{p}{q}\right)$ equal to in terms of $p$ and $q$?
What is $-\left(\frac{p}{q}\right)$ equal to in terms of $p$ and $q$?
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$-\left(\frac{p}{q}\right)=\frac{-p}{q}=\frac{p}{-q}$.
$-\left(\frac{p}{q}\right)=\frac{-p}{q}=\frac{p}{-q}$.
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What is the definition of a rational number in terms of integers $p$ and $q$?
What is the definition of a rational number in terms of integers $p$ and $q$?
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A number that can be written as $\frac{p}{q}$ with $p,q$ integers and $q \ne 0$.
A number that can be written as $\frac{p}{q}$ with $p,q$ integers and $q \ne 0$.
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What is the sign rule for integer division when the signs are different?
What is the sign rule for integer division when the signs are different?
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Different signs: the quotient is negative.
Different signs: the quotient is negative.
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What quotient represents splitting a debt of $\$24$ equally among $6$ people?
What quotient represents splitting a debt of $\$24$ equally among $6$ people?
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$\frac{-24}{6}$.
$\frac{-24}{6}$.
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Which is greater: $\frac{-3}{5}$ or $\frac{3}{-5}$?
Which is greater: $\frac{-3}{5}$ or $\frac{3}{-5}$?
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They are equal: $\frac{-3}{5}=\frac{3}{-5}$.
They are equal: $\frac{-3}{5}=\frac{3}{-5}$.
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What is the simplified form of $\frac{-10}{15}$ in lowest terms?
What is the simplified form of $\frac{-10}{15}$ in lowest terms?
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$-\frac{2}{3}$.
$-\frac{2}{3}$.
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What is the simplified form of $\frac{9}{-12}$ in lowest terms?
What is the simplified form of $\frac{9}{-12}$ in lowest terms?
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$-\frac{3}{4}$.
$-\frac{3}{4}$.
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Identify the correct statement: $\frac{-p}{-q}=\frac{p}{q}$ or $\frac{-p}{-q}=-\frac{p}{q}$.
Identify the correct statement: $\frac{-p}{-q}=\frac{p}{q}$ or $\frac{-p}{-q}=-\frac{p}{q}$.
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$\frac{-p}{-q}=\frac{p}{q}$.
$\frac{-p}{-q}=\frac{p}{q}$.
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What is the unit rate if a temperature changes by $ -12^\circ\text{C} $ over $ 4 $ hours?
What is the unit rate if a temperature changes by $ -12^\circ\text{C} $ over $ 4 $ hours?
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$ \frac{-12}{4} = -3^\circ\text{C} $ per hour.
$ \frac{-12}{4} = -3^\circ\text{C} $ per hour.
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What is the equivalent form of $-\left(\frac{p}{q}\right)$ using a negative numerator?
What is the equivalent form of $-\left(\frac{p}{q}\right)$ using a negative numerator?
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$\frac{-p}{q}$. The negative sign can be placed on the numerator.
$\frac{-p}{q}$. The negative sign can be placed on the numerator.
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What is the sign of $\frac{p}{q}$ when $p<0$ and $q<0$?
What is the sign of $\frac{p}{q}$ when $p<0$ and $q<0$?
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Positive. Two negatives make a positive when dividing.
Positive. Two negatives make a positive when dividing.
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Find the value of $\frac{-7}{5}$.
Find the value of $\frac{-7}{5}$.
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$-\frac{7}{5}$. Negative numerator makes the fraction negative.
$-\frac{7}{5}$. Negative numerator makes the fraction negative.
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What is the sign of $\frac{p}{q}$ when $p<0$ and $q>0$?
What is the sign of $\frac{p}{q}$ when $p<0$ and $q>0$?
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Negative. Negative divided by positive yields negative.
Negative. Negative divided by positive yields negative.
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