Add Rational Numbers on Number Line - 7th Grade Math
Card 1 of 25
What is $-2+(-6)$?
What is $-2+(-6)$?
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$-8$. Start at $-2$, move left $6$ more units: $-2-6=-8$.
$-8$. Start at $-2$, move left $6$ more units: $-2-6=-8$.
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Interpretation: Your bank balance is $\25$ and you spend $\40$. What is the new balance?
Interpretation: Your bank balance is $\25$ and you spend $\40$. What is the new balance?
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$- \15$. Spending is negative: $25+(-40)=-15$ dollars.
$- \15$. Spending is negative: $25+(-40)=-15$ dollars.
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Identify the sum: starting at $p=4$ and adding $q=-7$, what is $p+q$?
Identify the sum: starting at $p=4$ and adding $q=-7$, what is $p+q$?
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$-3$. Start at $4$, move left $7$ units: $4-7=-3$.
$-3$. Start at $4$, move left $7$ units: $4-7=-3$.
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What is $-5+9$?
What is $-5+9$?
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$4$. Start at $-5$, move right $9$ units: $-5+9=4$.
$4$. Start at $-5$, move right $9$ units: $-5+9=4$.
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What is $7+(-12)$?
What is $7+(-12)$?
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$-5$. Start at $7$, move left $12$ units: $7-12=-5$.
$-5$. Start at $7$, move left $12$ units: $7-12=-5$.
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What is $\frac{3}{4}+\left(-\frac{1}{2}\right)$?
What is $\frac{3}{4}+\left(-\frac{1}{2}\right)$?
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$\frac{1}{4}$. Convert to common denominator: $\frac{3}{4}-\frac{2}{4}=\frac{1}{4}$.
$\frac{1}{4}$. Convert to common denominator: $\frac{3}{4}-\frac{2}{4}=\frac{1}{4}$.
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What is $\frac{5}{8}+\left(-\frac{3}{8}\right)$?
What is $\frac{5}{8}+\left(-\frac{3}{8}\right)$?
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$\frac{1}{4}$. Same denominator: $\frac{5}{8}-\frac{3}{8}=\frac{2}{8}=\frac{1}{4}$.
$\frac{1}{4}$. Same denominator: $\frac{5}{8}-\frac{3}{8}=\frac{2}{8}=\frac{1}{4}$.
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What is $-1.2+0.5$?
What is $-1.2+0.5$?
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$-0.7$. Start at $-1.2$, move right $0.5$: $-1.2+0.5=-0.7$.
$-0.7$. Start at $-1.2$, move right $0.5$: $-1.2+0.5=-0.7$.
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Interpretation: A diver is at $-6$ m and rises $4$ m. What is the new position?
Interpretation: A diver is at $-6$ m and rises $4$ m. What is the new position?
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$-2$ m. Rising means adding positive: $-6+4=-2$ meters.
$-2$ m. Rising means adding positive: $-6+4=-2$ meters.
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Interpretation: The temperature is $-3^\circ\text{C}$ and increases by $7^\circ\text{C}$. What is the new temperature?
Interpretation: The temperature is $-3^\circ\text{C}$ and increases by $7^\circ\text{C}$. What is the new temperature?
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$4^\circ\text{C}$. Temperature increase means add: $-3+7=4$ degrees.
$4^\circ\text{C}$. Temperature increase means add: $-3+7=4$ degrees.
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What is the value of $p$ if $p+q=r$, $q=-6$, and $r=1$?
What is the value of $p$ if $p+q=r$, $q=-6$, and $r=1$?
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$7$. Solve $p+(-6)=1$: $p=1-(-6)=1+6=7$.
$7$. Solve $p+(-6)=1$: $p=1-(-6)=1+6=7$.
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What is $-\frac{2}{3}+\frac{1}{6}$?
What is $-\frac{2}{3}+\frac{1}{6}$?
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$-\frac{1}{2}$. Common denominator: $-\frac{4}{6}+\frac{1}{6}=-\frac{3}{6}=-\frac{1}{2}$
$-\frac{1}{2}$. Common denominator: $-\frac{4}{6}+\frac{1}{6}=-\frac{3}{6}=-\frac{1}{2}$
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What is $p+0$ for any rational number $p$?
What is $p+0$ for any rational number $p$?
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$p$. Adding zero doesn't change the position on the number line.
$p$. Adding zero doesn't change the position on the number line.
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Which direction do you move on the number line when $q<0$ in $p+q$?
Which direction do you move on the number line when $q<0$ in $p+q$?
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Move left. Negative values move left on the number line.
Move left. Negative values move left on the number line.
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Which direction do you move on the number line when $q>0$ in $p+q$?
Which direction do you move on the number line when $q>0$ in $p+q$?
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Move right. Positive values move right on the number line.
Move right. Positive values move right on the number line.
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What is the distance moved from $p$ when adding $q$ in $p+q$?
What is the distance moved from $p$ when adding $q$ in $p+q$?
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A distance of $|q|$ units. The absolute value $|q|$ gives the distance regardless of direction.
A distance of $|q|$ units. The absolute value $|q|$ gives the distance regardless of direction.
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What does $p+q$ represent on a number line in terms of distance from $p$?
What does $p+q$ represent on a number line in terms of distance from $p$?
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The point $|q|$ units from $p$, in the direction of $q$. Adding $q$ means moving $|q|$ units from $p$ in the positive or negative direction.
The point $|q|$ units from $p$, in the direction of $q$. Adding $q$ means moving $|q|$ units from $p$ in the positive or negative direction.
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What is the additive inverse of a number $q$ (the number that makes $q+?=0$)?
What is the additive inverse of a number $q$ (the number that makes $q+?=0$)?
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$-q$. The additive inverse is the opposite sign that sums to zero.
$-q$. The additive inverse is the opposite sign that sums to zero.
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What is the absolute value $|q|$ for a rational number $q$?
What is the absolute value $|q|$ for a rational number $q$?
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The distance from $0$ to $q$ on the number line. Absolute value measures distance without considering direction.
The distance from $0$ to $q$ on the number line. Absolute value measures distance without considering direction.
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Identify the sum: starting at $p=-3$ and adding $q=5$, what is $p+q$?
Identify the sum: starting at $p=-3$ and adding $q=5$, what is $p+q$?
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$2$. Start at $-3$, move right $5$ units: $-3+5=2$.
$2$. Start at $-3$, move right $5$ units: $-3+5=2$.
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What does $|q|$ mean in the interpretation of $p+q$ on a number line?
What does $|q|$ mean in the interpretation of $p+q$ on a number line?
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The distance moved from $p$
The distance moved from $p$
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What does $p+q$ represent on a number line, starting at $p$?
What does $p+q$ represent on a number line, starting at $p$?
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The point $|q|$ units from $p$ in the direction of $q$
The point $|q|$ units from $p$ in the direction of $q$
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Identify the distance moved from $p=7$ when computing $p+q$ for $q=-2$.
Identify the distance moved from $p=7$ when computing $p+q$ for $q=-2$.
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$2$ units
$2$ units
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Identify the distance moved from $p=-4$ when computing $p+q$ for $q=3$.
Identify the distance moved from $p=-4$ when computing $p+q$ for $q=3$.
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$3$ units
$3$ units
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Which direction do you move from $p$ when adding a negative number $q$?
Which direction do you move from $p$ when adding a negative number $q$?
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To the left
To the left
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