Rational and Irrational Number Operations - Algebra
Card 1 of 30
Identify the correct classification of $\frac{7}{9}+\frac{2}{3}$: rational or irrational?
Identify the correct classification of $\frac{7}{9}+\frac{2}{3}$: rational or irrational?
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Rational. Sum of two rational numbers.
Rational. Sum of two rational numbers.
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Identify the correct classification of $\frac{2}{7}+\left(-\frac{2}{7}\right)$: rational or irrational?
Identify the correct classification of $\frac{2}{7}+\left(-\frac{2}{7}\right)$: rational or irrational?
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Rational. Sum equals zero, which is rational.
Rational. Sum equals zero, which is rational.
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Identify the correct classification of $\frac{5}{6}\cdot 0$: rational or irrational?
Identify the correct classification of $\frac{5}{6}\cdot 0$: rational or irrational?
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Rational. Any number times zero equals zero.
Rational. Any number times zero equals zero.
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Identify the correct classification of $\left(\frac{1}{2}\right)\pi$: rational or irrational?
Identify the correct classification of $\left(\frac{1}{2}\right)\pi$: rational or irrational?
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Irrational. Nonzero rational times irrational is irrational.
Irrational. Nonzero rational times irrational is irrational.
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Identify the correct classification of $\pi+3$: rational or irrational?
Identify the correct classification of $\pi+3$: rational or irrational?
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Irrational. Rational plus irrational is irrational.
Irrational. Rational plus irrational is irrational.
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Identify the correct classification of $\pi-\pi$: rational or irrational?
Identify the correct classification of $\pi-\pi$: rational or irrational?
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Rational. Any number minus itself equals zero.
Rational. Any number minus itself equals zero.
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Identify the correct classification of $\sqrt{5}+\sqrt{5}$ written as $2\sqrt{5}$: rational or irrational?
Identify the correct classification of $\sqrt{5}+\sqrt{5}$ written as $2\sqrt{5}$: rational or irrational?
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Irrational. $2\sqrt{5}$ is irrational.
Irrational. $2\sqrt{5}$ is irrational.
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What is the correct conclusion if $r$ is rational and $r+i$ is irrational?
What is the correct conclusion if $r$ is rational and $r+i$ is irrational?
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$i$ can be irrational (this is consistent with the rule). This confirms the rule holds.
$i$ can be irrational (this is consistent with the rule). This confirms the rule holds.
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What is the correct conclusion if $r$ is nonzero rational and $ri$ is irrational?
What is the correct conclusion if $r$ is nonzero rational and $ri$ is irrational?
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$i$ can be irrational (this is consistent with the rule). This confirms the rule holds.
$i$ can be irrational (this is consistent with the rule). This confirms the rule holds.
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Identify the correct classification of $\left(-\frac{3}{4}\right)+\sqrt{8}$: rational or irrational?
Identify the correct classification of $\left(-\frac{3}{4}\right)+\sqrt{8}$: rational or irrational?
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Irrational. Rational plus irrational is irrational.
Irrational. Rational plus irrational is irrational.
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Identify the correct classification of $\left(\frac{3}{4}\right)\left(\sqrt{8}\right)$: rational or irrational?
Identify the correct classification of $\left(\frac{3}{4}\right)\left(\sqrt{8}\right)$: rational or irrational?
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Irrational. Nonzero rational times irrational is irrational.
Irrational. Nonzero rational times irrational is irrational.
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Which statement is always true about $\frac{m}{n}+\frac{p}{q}$ for integers $m,n,p,q$ with $nq \ne 0$?
Which statement is always true about $\frac{m}{n}+\frac{p}{q}$ for integers $m,n,p,q$ with $nq \ne 0$?
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$\frac{m}{n}+\frac{p}{q}$ is rational. Sum of rational fractions is rational.
$\frac{m}{n}+\frac{p}{q}$ is rational. Sum of rational fractions is rational.
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Which statement is always true about $\frac{m}{n}\cdot\frac{p}{q}$ for integers $m,n,p,q$ with $nq \ne 0$?
Which statement is always true about $\frac{m}{n}\cdot\frac{p}{q}$ for integers $m,n,p,q$ with $nq \ne 0$?
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$\frac{m}{n}\cdot\frac{p}{q}$ is rational. Product of rational fractions is rational.
$\frac{m}{n}\cdot\frac{p}{q}$ is rational. Product of rational fractions is rational.
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Identify the correct classification of $\left(\frac{2}{3}\right)+\left(\frac{4}{9}\right)$: rational or irrational?
Identify the correct classification of $\left(\frac{2}{3}\right)+\left(\frac{4}{9}\right)$: rational or irrational?
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Rational. Sum of two rational numbers.
Rational. Sum of two rational numbers.
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Identify the correct classification of $\left(\frac{-5}{8}\right)\left(\frac{12}{7}\right)$: rational or irrational?
Identify the correct classification of $\left(\frac{-5}{8}\right)\left(\frac{12}{7}\right)$: rational or irrational?
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Rational. Product of two rational numbers.
Rational. Product of two rational numbers.
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Which property justifies that $bd \ne 0$ if $b \ne 0$ and $d \ne 0$?
Which property justifies that $bd \ne 0$ if $b \ne 0$ and $d \ne 0$?
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Nonzero numbers have a nonzero product: $bd \ne 0$. Product of nonzero numbers is nonzero.
Nonzero numbers have a nonzero product: $bd \ne 0$. Product of nonzero numbers is nonzero.
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What is the fraction form of $\frac{a}{b}\cdot\frac{c}{d}$ that shows it is rational?
What is the fraction form of $\frac{a}{b}\cdot\frac{c}{d}$ that shows it is rational?
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$\frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd}$. Shows product as fraction with integer parts.
$\frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd}$. Shows product as fraction with integer parts.
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What is the fraction form of $\frac{a}{b}+\frac{c}{d}$ that shows it is rational?
What is the fraction form of $\frac{a}{b}+\frac{c}{d}$ that shows it is rational?
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$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$. Shows sum as fraction with integer parts.
$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$. Shows sum as fraction with integer parts.
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Identify the correct conclusion: if $r$ is rational and $i$ is irrational, what is $-r+i$?
Identify the correct conclusion: if $r$ is rational and $i$ is irrational, what is $-r+i$?
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$-r+i$ is irrational. Negative rational plus irrational is irrational.
$-r+i$ is irrational. Negative rational plus irrational is irrational.
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Identify the correct conclusion: if $r$ is rational and $i$ is irrational, what is $i-r$?
Identify the correct conclusion: if $r$ is rational and $i$ is irrational, what is $i-r$?
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$i-r$ is irrational. Irrational minus rational is still irrational.
$i-r$ is irrational. Irrational minus rational is still irrational.
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What special case makes $ri$ rational when $r$ is rational and $i$ is irrational?
What special case makes $ri$ rational when $r$ is rational and $i$ is irrational?
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If $r=0$, then $ri=0$ is rational. Zero times any number equals zero, which is rational.
If $r=0$, then $ri=0$ is rational. Zero times any number equals zero, which is rational.
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What is always true about $ri$ if $r$ is nonzero rational and $i$ is irrational?
What is always true about $ri$ if $r$ is nonzero rational and $i$ is irrational?
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$ri$ is irrational. Nonzero rational times irrational is irrational.
$ri$ is irrational. Nonzero rational times irrational is irrational.
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What is always true about $r-i$ if $r$ is rational and $i$ is irrational?
What is always true about $r-i$ if $r$ is rational and $i$ is irrational?
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$r-i$ is irrational. Subtracting irrational from rational gives irrational.
$r-i$ is irrational. Subtracting irrational from rational gives irrational.
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What is always true about $r+i$ if $r$ is rational and $i$ is irrational?
What is always true about $r+i$ if $r$ is rational and $i$ is irrational?
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$r+i$ is irrational. Adding rational to irrational gives irrational.
$r+i$ is irrational. Adding rational to irrational gives irrational.
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Which statement is always true: if $r$ and $s$ are rational, what is $rs$?
Which statement is always true: if $r$ and $s$ are rational, what is $rs$?
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$rs$ is rational. Product of two rationals is always rational.
$rs$ is rational. Product of two rationals is always rational.
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Which statement is always true: if $r$ and $s$ are rational, what is $r+s$?
Which statement is always true: if $r$ and $s$ are rational, what is $r+s$?
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$r+s$ is rational. Sum of two rationals is always rational.
$r+s$ is rational. Sum of two rationals is always rational.
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What is the closure property of rational numbers under multiplication?
What is the closure property of rational numbers under multiplication?
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If $r$ and $s$ are rational, then $rs$ is rational. Rational numbers are closed under multiplication.
If $r$ and $s$ are rational, then $rs$ is rational. Rational numbers are closed under multiplication.
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What is the closure property of rational numbers under addition?
What is the closure property of rational numbers under addition?
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If $r$ and $s$ are rational, then $r+s$ is rational. Rational numbers are closed under addition.
If $r$ and $s$ are rational, then $r+s$ is rational. Rational numbers are closed under addition.
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Identify the correct classification of $\left(\frac{1}{3}\right)\sqrt{6}$: rational or irrational?
Identify the correct classification of $\left(\frac{1}{3}\right)\sqrt{6}$: rational or irrational?
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Irrational. Nonzero rational times irrational is irrational.
Irrational. Nonzero rational times irrational is irrational.
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Identify the correct classification of $\left(\frac{3}{5}\right)\sqrt{7}$: rational or irrational?
Identify the correct classification of $\left(\frac{3}{5}\right)\sqrt{7}$: rational or irrational?
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Irrational. Nonzero rational times irrational is irrational.
Irrational. Nonzero rational times irrational is irrational.
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