Solve Problems With Rational Numbers - 7th Grade Math
Card 1 of 25
What is the value of $\frac{7}{8}-\left(-\frac{1}{4}\right)$?
What is the value of $\frac{7}{8}-\left(-\frac{1}{4}\right)$?
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$\frac{9}{8}$. Subtracting negative is adding: $\frac{7}{8}+\frac{1}{4}=\frac{7}{8}+\frac{2}{8}$.
$\frac{9}{8}$. Subtracting negative is adding: $\frac{7}{8}+\frac{1}{4}=\frac{7}{8}+\frac{2}{8}$.
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What is the reciprocal of $-\frac{3}{5}$?
What is the reciprocal of $-\frac{3}{5}$?
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$-\frac{5}{3}$. Flip the fraction and keep the negative sign.
$-\frac{5}{3}$. Flip the fraction and keep the negative sign.
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What is the sign of the quotient of a positive rational number and a negative rational number?
What is the sign of the quotient of a positive rational number and a negative rational number?
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Negative. Positive divided by negative equals negative.
Negative. Positive divided by negative equals negative.
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What is the value of $\left(-\frac{3}{2}\right)^2$?
What is the value of $\left(-\frac{3}{2}\right)^2$?
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$\frac{9}{4}$. Square of negative fraction: $\frac{(-3)^2}{2^2}=\frac{9}{4}$.
$\frac{9}{4}$. Square of negative fraction: $\frac{(-3)^2}{2^2}=\frac{9}{4}$.
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What is the value of $\left(-\frac{5}{6}\right)\div\left(\frac{10}{3}\right)$?
What is the value of $\left(-\frac{5}{6}\right)\div\left(\frac{10}{3}\right)$?
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$-\frac{1}{4}$. Multiply by reciprocal: $\frac{-5}{6} \times \frac{3}{10}=\frac{-15}{60}=\frac{-1}{4}$.
$-\frac{1}{4}$. Multiply by reciprocal: $\frac{-5}{6} \times \frac{3}{10}=\frac{-15}{60}=\frac{-1}{4}$.
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What is the value of $\frac{2}{3}+\frac{1}{9}+\left(-\frac{4}{9}\right)$?
What is the value of $\frac{2}{3}+\frac{1}{9}+\left(-\frac{4}{9}\right)$?
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$\frac{1}{3}$. Common denominator: $\frac{6}{9}+\frac{1}{9}-\frac{4}{9}=\frac{3}{9}=\frac{1}{3}$.
$\frac{1}{3}$. Common denominator: $\frac{6}{9}+\frac{1}{9}-\frac{4}{9}=\frac{3}{9}=\frac{1}{3}$.
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What is the value of $-\left(-\frac{7}{3}\right)$?
What is the value of $-\left(-\frac{7}{3}\right)$?
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$\frac{7}{3}$. Negative of negative equals positive.
$\frac{7}{3}$. Negative of negative equals positive.
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What is the value of $\left| -\frac{11}{6} \right|$?
What is the value of $\left| -\frac{11}{6} \right|$?
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$\frac{11}{6}$. Absolute value removes the negative sign.
$\frac{11}{6}$. Absolute value removes the negative sign.
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What is the value of $-1.2\div(-0.3)$?
What is the value of $-1.2\div(-0.3)$?
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$4$. Negative divided by negative equals positive.
$4$. Negative divided by negative equals positive.
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What is the value of $-0.75\times 0.4$?
What is the value of $-0.75\times 0.4$?
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$-0.3$. Negative times positive equals negative.
$-0.3$. Negative times positive equals negative.
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What is the value of $\frac{3}{5}\div\left(-\frac{9}{10}\right)$?
What is the value of $\frac{3}{5}\div\left(-\frac{9}{10}\right)$?
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$-\frac{2}{3}$. Multiply by reciprocal: $\frac{3}{5} \times \frac{-10}{9}=\frac{-30}{45}=\frac{-2}{3}$.
$-\frac{2}{3}$. Multiply by reciprocal: $\frac{3}{5} \times \frac{-10}{9}=\frac{-30}{45}=\frac{-2}{3}$.
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What is the value of $\left(-2\frac{1}{2}\right)\times\left(\frac{4}{5}\right)$?
What is the value of $\left(-2\frac{1}{2}\right)\times\left(\frac{4}{5}\right)$?
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$-2$. Convert: $-\frac{5}{2} \times \frac{4}{5}=\frac{-20}{10}=-2$.
$-2$. Convert: $-\frac{5}{2} \times \frac{4}{5}=\frac{-20}{10}=-2$.
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What is the sign of the product of two negative rational numbers?
What is the sign of the product of two negative rational numbers?
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Positive. Negative times negative equals positive.
Positive. Negative times negative equals positive.
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What is the value of $\left(-\frac{3}{4}\right)\times\left(\frac{8}{9}\right)$?
What is the value of $\left(-\frac{3}{4}\right)\times\left(\frac{8}{9}\right)$?
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$-\frac{2}{3}$. Multiply: $\frac{-3 \times 8}{4 \times 9}=\frac{-24}{36}=\frac{-2}{3}$.
$-\frac{2}{3}$. Multiply: $\frac{-3 \times 8}{4 \times 9}=\frac{-24}{36}=\frac{-2}{3}$.
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What is the value of $-3.6-(-1.2)$?
What is the value of $-3.6-(-1.2)$?
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$-2.4$. Subtracting negative is adding: $-3.6+1.2=-2.4$.
$-2.4$. Subtracting negative is adding: $-3.6+1.2=-2.4$.
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What is the value of $-4.2+1.7$?
What is the value of $-4.2+1.7$?
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$-2.5$. Add the values: $-4.2+1.7=-2.5$.
$-2.5$. Add the values: $-4.2+1.7=-2.5$.
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What is the reciprocal of a nonzero rational number $\frac{a}{b}$?
What is the reciprocal of a nonzero rational number $\frac{a}{b}$?
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$\frac{b}{a}$
$\frac{b}{a}$
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What is the rule for the sign of a product $(a)(b)$ when $a$ and $b$ have the same sign?
What is the rule for the sign of a product $(a)(b)$ when $a$ and $b$ have the same sign?
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The product is positive.
The product is positive.
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What is $-2.5\div 0.5$?
What is $-2.5\div 0.5$?
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$-5$. Negative divided by positive gives negative: $-2.5 \div 0.5=-5$.
$-5$. Negative divided by positive gives negative: $-2.5 \div 0.5=-5$.
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What is the average of $-2$, $3$, and $-4$?
What is the average of $-2$, $3$, and $-4$?
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$-1$. Sum and divide by count: $\frac{-2+3+(-4)}{3}=\frac{-3}{3}=-1$.
$-1$. Sum and divide by count: $\frac{-2+3+(-4)}{3}=\frac{-3}{3}=-1$.
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What is $\left| -\frac{11}{6} \right|$?
What is $\left| -\frac{11}{6} \right|$?
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$\frac{11}{6}$. Absolute value removes negative sign.
$\frac{11}{6}$. Absolute value removes negative sign.
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What is the total change after $-2.3$ and then $+1.8$?
What is the total change after $-2.3$ and then $+1.8$?
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$-0.5$. Add changes: $-2.3+1.8=-0.5$.
$-0.5$. Add changes: $-2.3+1.8=-0.5$.
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What is the net gain/loss for $4$ deposits of $\frac{3}{2}$ and $3$ withdrawals of $\frac{5}{2}$?
What is the net gain/loss for $4$ deposits of $\frac{3}{2}$ and $3$ withdrawals of $\frac{5}{2}$?
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$-\frac{3}{2}$. Total: $4(\frac{3}{2})-3(\frac{5}{2})=6-\frac{15}{2}=\frac{12}{2}-\frac{15}{2}=-\frac{3}{2}$.
$-\frac{3}{2}$. Total: $4(\frac{3}{2})-3(\frac{5}{2})=6-\frac{15}{2}=\frac{12}{2}-\frac{15}{2}=-\frac{3}{2}$.
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What is the value of $-3^2$ (no parentheses around $-3$)?
What is the value of $-3^2$ (no parentheses around $-3$)?
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$-9$. Order of operations: $-3^2=-(3^2)=-9$.
$-9$. Order of operations: $-3^2=-(3^2)=-9$.
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What is the value of $(-3)^2$?
What is the value of $(-3)^2$?
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$9$. Parentheses mean square the negative: $(-3)(-3)=9$.
$9$. Parentheses mean square the negative: $(-3)(-3)=9$.
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