Multiply Rational Numbers - 7th Grade Math
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Use distribution: What is $-3(2-5)$?
Use distribution: What is $-3(2-5)$?
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$9$. $-3(2-5) = -3(-3) = 9$.
$9$. $-3(2-5) = -3(-3) = 9$.
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What is the value of $\frac{7}{8} \times \frac{-4}{7}$?
What is the value of $\frac{7}{8} \times \frac{-4}{7}$?
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$\frac{-1}{2}$. Cancel $7$s: $\frac{-4}{8} = \frac{-1}{2}$
$\frac{-1}{2}$. Cancel $7$s: $\frac{-4}{8} = \frac{-1}{2}$
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What is the sign of the product when multiplying two negative rational numbers?
What is the sign of the product when multiplying two negative rational numbers?
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Positive. Two negatives multiply to give a positive result.
Positive. Two negatives multiply to give a positive result.
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What does $(-2)(-6)=12$ represent if $-2$ means $2$ units below $0$ and $-6$ means reversing direction $6$ times?
What does $(-2)(-6)=12$ represent if $-2$ means $2$ units below $0$ and $-6$ means reversing direction $6$ times?
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Reversing a negative gives a positive result: $12$ units above $0$. Reversing a negative direction results in positive movement.
Reversing a negative gives a positive result: $12$ units above $0$. Reversing a negative direction results in positive movement.
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What does the product $(-3)(4)$ represent for a $4$-day change of $-3$ units per day?
What does the product $(-3)(4)$ represent for a $4$-day change of $-3$ units per day?
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A total change of $-12$ units. Repeated addition: $4$ days of $-3$ units each.
A total change of $-12$ units. Repeated addition: $4$ days of $-3$ units each.
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What is the value of $(0.6)(-5)$?
What is the value of $(0.6)(-5)$?
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$-3$. Positive times negative: $0.6 imes -5 = -3$.
$-3$. Positive times negative: $0.6 imes -5 = -3$.
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What is the value of $(-2.5)(-4)$?
What is the value of $(-2.5)(-4)$?
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$10$. Two negatives make positive: $2.5 imes 4 = 10$.
$10$. Two negatives make positive: $2.5 imes 4 = 10$.
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What is the sign of the product when multiplying a positive and a negative rational number?
What is the sign of the product when multiplying a positive and a negative rational number?
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Negative. Different signs multiply to give a negative product.
Negative. Different signs multiply to give a negative product.
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What is the value of $(-1)(-1)$?
What is the value of $(-1)(-1)$?
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$1$. Negative times negative equals positive.
$1$. Negative times negative equals positive.
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What is the value of $(-1)(7)$?
What is the value of $(-1)(7)$?
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$-7$. Negative one times any number gives its opposite.
$-7$. Negative one times any number gives its opposite.
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What is the value of $(1)(-9)$?
What is the value of $(1)(-9)$?
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$-9$. Positive times negative gives negative.
$-9$. Positive times negative gives negative.
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What is the value of $(0)(-15)$?
What is the value of $(0)(-15)$?
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$0$. Zero times any number equals zero.
$0$. Zero times any number equals zero.
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What is the value of $(-3)(4)$?
What is the value of $(-3)(4)$?
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$-12$. Different signs: $(-3)(4) = -12$.
$-12$. Different signs: $(-3)(4) = -12$.
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What is the value of $-2(3+5)$?
What is the value of $-2(3+5)$?
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$-16$. First add inside parentheses: $-2(8) = -16$.
$-16$. First add inside parentheses: $-2(8) = -16$.
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What is the value of $\frac{-2}{3} \times \frac{9}{4}$?
What is the value of $\frac{-2}{3} \times \frac{9}{4}$?
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$\frac{-3}{2}$. Multiply numerators and denominators: $\frac{-18}{12} = \frac{-3}{2}$
$\frac{-3}{2}$. Multiply numerators and denominators: $\frac{-18}{12} = \frac{-3}{2}$
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What is the value of $(-3)\big( \frac{1}{2} \big)$?
What is the value of $(-3)\big( \frac{1}{2} \big)$?
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$\frac{-3}{2}$. Negative times positive fraction gives negative.
$\frac{-3}{2}$. Negative times positive fraction gives negative.
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Which expression is equivalent to $-4(x-3)$?
Which expression is equivalent to $-4(x-3)$?
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$-4x+12$. Distribute $-4$: $-4(x) + -4(-3) = -4x + 12$.
$-4x+12$. Distribute $-4$: $-4(x) + -4(-3) = -4x + 12$.
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What property justifies rewriting $a(b+c)$ as $ab+ac$ for rational numbers?
What property justifies rewriting $a(b+c)$ as $ab+ac$ for rational numbers?
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Distributive property. Allows multiplying each term inside parentheses separately.
Distributive property. Allows multiplying each term inside parentheses separately.
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What is the value of $-2(3)+-2(5)$?
What is the value of $-2(3)+-2(5)$?
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$-16$. Distributive property: $-6 + -10 = -16$.
$-16$. Distributive property: $-6 + -10 = -16$.
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What is the value of $-3(4+2)$?
What is the value of $-3(4+2)$?
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$-18$. Distribute $-3$: $-3(4) + -3(2) = -12 + -6 = -18$.
$-18$. Distribute $-3$: $-3(4) + -3(2) = -12 + -6 = -18$.
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What is the value of $-3igl(4+(-2)igr)$?
What is the value of $-3igl(4+(-2)igr)$?
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$-6$. First simplify inside: $4 + (-2) = 2$, then $-3(2) = -6$.
$-6$. First simplify inside: $4 + (-2) = 2$, then $-3(2) = -6$.
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What does $(-3)(5)$ represent if $-3$ means “a loss of $\$3$” and $5$ is the number of days?
What does $(-3)(5)$ represent if $-3$ means “a loss of $\$3$” and $5$ is the number of days?
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A total loss of $\$15$. Negative (loss) times positive (days) = total negative (total loss).
A total loss of $\$15$. Negative (loss) times positive (days) = total negative (total loss).
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What is the sign of a product when both factors are positive, such as $(+3)(+5)$?
What is the sign of a product when both factors are positive, such as $(+3)(+5)$?
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Positive. Two positive numbers always multiply to give a positive product.
Positive. Two positive numbers always multiply to give a positive product.
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What is the sign of a product when one factor is negative and the other is positive, such as $(-3)(+5)$?
What is the sign of a product when one factor is negative and the other is positive, such as $(-3)(+5)$?
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Negative. A positive times a negative (or vice versa) always gives a negative product.
Negative. A positive times a negative (or vice versa) always gives a negative product.
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What is the sign of a product when both factors are negative, such as $(-3)(-5)$?
What is the sign of a product when both factors are negative, such as $(-3)(-5)$?
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Positive. Two negatives multiply to give a positive (negative × negative = positive).
Positive. Two negatives multiply to give a positive (negative × negative = positive).
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