Using Units in Problem Solving, Modeling - Algebra
Card 1 of 30
What happens to units when you multiply two quantities?
What happens to units when you multiply two quantities?
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Units multiply (for example, $\text{m}\cdot\text{s}$). Multiplication combines units as products.
Units multiply (for example, $\text{m}\cdot\text{s}$). Multiplication combines units as products.
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Which conversion factor is valid for centimeters to meters?
Which conversion factor is valid for centimeters to meters?
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$\frac{1 \text{m}}{100 \text{cm}}$. Conversion factor equals 1 and cancels unwanted units.
$\frac{1 \text{m}}{100 \text{cm}}$. Conversion factor equals 1 and cancels unwanted units.
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Find the unit of $\frac{\text{miles}}{\text{hour}}\times\text{hours}$.
Find the unit of $\frac{\text{miles}}{\text{hour}}\times\text{hours}$.
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$\text{miles}$. Hours cancel, leaving miles.
$\text{miles}$. Hours cancel, leaving miles.
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What is the unit of $C$ in $C=\pi d$ if $d$ is in meters?
What is the unit of $C$ in $C=\pi d$ if $d$ is in meters?
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$\text{m}$. Circumference has the same units as diameter.
$\text{m}$. Circumference has the same units as diameter.
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What cancels in $5\ \frac{\text{m}}{\text{s}}\times 2\ \text{s}$ to leave the final unit?
What cancels in $5\ \frac{\text{m}}{\text{s}}\times 2\ \text{s}$ to leave the final unit?
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$\text{s}$ cancels, leaving $\text{m}$. Unit cancellation follows multiplication rules.
$\text{s}$ cancels, leaving $\text{m}$. Unit cancellation follows multiplication rules.
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Identify the correct setup to convert $250\ \text{cm}$ to meters.
Identify the correct setup to convert $250\ \text{cm}$ to meters.
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$250\ \text{cm}\times\frac{1\ \text{m}}{100\ \text{cm}}$. Centimeters cancel, leaving meters as final unit.
$250\ \text{cm}\times\frac{1\ \text{m}}{100\ \text{cm}}$. Centimeters cancel, leaving meters as final unit.
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Identify the correct setup to convert $3\ \text{h}$ to minutes using factor-label method.
Identify the correct setup to convert $3\ \text{h}$ to minutes using factor-label method.
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$3\ \text{h}\times\frac{60\ \text{min}}{1\ \text{h}}$. Hours cancel, leaving minutes as final unit.
$3\ \text{h}\times\frac{60\ \text{min}}{1\ \text{h}}$. Hours cancel, leaving minutes as final unit.
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What must be true about a conversion factor to keep the value unchanged?
What must be true about a conversion factor to keep the value unchanged?
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It must equal $1$ (a ratio of equivalent measures). Ratios of equivalent measurements equal 1.
It must equal $1$ (a ratio of equivalent measures). Ratios of equivalent measurements equal 1.
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Which conversion factor is valid for centimeters to meters?
Which conversion factor is valid for centimeters to meters?
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$\frac{1\ \text{m}}{100\ \text{cm}}$. Conversion factor equals 1 and cancels unwanted units.
$\frac{1\ \text{m}}{100\ \text{cm}}$. Conversion factor equals 1 and cancels unwanted units.
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Which conversion factor is valid for minutes to hours?
Which conversion factor is valid for minutes to hours?
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$\frac{1\ \text{h}}{60\ \text{min}}$. Conversion factor equals 1 and cancels unwanted units.
$\frac{1\ \text{h}}{60\ \text{min}}$. Conversion factor equals 1 and cancels unwanted units.
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What is dimensional analysis used for in problem solving?
What is dimensional analysis used for in problem solving?
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Tracking units to choose operations and verify a formula’s output unit. Units guide calculation setup and result verification.
Tracking units to choose operations and verify a formula’s output unit. Units guide calculation setup and result verification.
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What is a “unit rate” in terms of units?
What is a “unit rate” in terms of units?
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A rate with denominator $1$ unit (for example, $\frac{\text{dollars}}{1\ \text{hour}}$). Rate per single unit of denominator.
A rate with denominator $1$ unit (for example, $\frac{\text{dollars}}{1\ \text{hour}}$). Rate per single unit of denominator.
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Identify the unit mistake: reporting a rectangle area as $24\ \text{cm}$ instead of square units.
Identify the unit mistake: reporting a rectangle area as $24\ \text{cm}$ instead of square units.
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Area must be in $\text{cm}^2$, not $\text{cm}$. Area requires square units, not linear units.
Area must be in $\text{cm}^2$, not $\text{cm}$. Area requires square units, not linear units.
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Identify the unit mistake: adding $3\ \text{ft}$ and $10\ \text{in}$ without converting.
Identify the unit mistake: adding $3\ \text{ft}$ and $10\ \text{in}$ without converting.
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Units do not match; convert to a common unit first. Different units cannot be directly combined.
Units do not match; convert to a common unit first. Different units cannot be directly combined.
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Which unit is appropriate for speed: $\text{mi}$, $\text{h}$, or $\frac{\text{mi}}{\text{h}}$?
Which unit is appropriate for speed: $\text{mi}$, $\text{h}$, or $\frac{\text{mi}}{\text{h}}$?
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$\frac{\text{mi}}{\text{h}}$. Speed is distance per time.
$\frac{\text{mi}}{\text{h}}$. Speed is distance per time.
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Which unit is appropriate for the volume of a box: $\text{cm}$, $\text{cm}^2$, or $\text{cm}^3$?
Which unit is appropriate for the volume of a box: $\text{cm}$, $\text{cm}^2$, or $\text{cm}^3$?
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$\text{cm}^3$. Volume requires cubed units.
$\text{cm}^3$. Volume requires cubed units.
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Which unit is appropriate for the area of a classroom floor: $\text{m}$, $\text{m}^2$, or $\text{m}^3$?
Which unit is appropriate for the area of a classroom floor: $\text{m}$, $\text{m}^2$, or $\text{m}^3$?
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$\text{m}^2$. Area requires squared units.
$\text{m}^2$. Area requires squared units.
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What is the unit of $\frac{\text{calories}}{\text{serving}}\times\text{servings}$?
What is the unit of $\frac{\text{calories}}{\text{serving}}\times\text{servings}$?
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$\text{calories}$. Servings cancel, leaving calories.
$\text{calories}$. Servings cancel, leaving calories.
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What is the unit of $\frac{\text{dollars}}{\text{item}}\times\text{items}$?
What is the unit of $\frac{\text{dollars}}{\text{item}}\times\text{items}$?
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$\text{dollars}$. Items cancel, leaving dollars.
$\text{dollars}$. Items cancel, leaving dollars.
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Find the unit of $\text{N}\cdot\text{m}$ if you are only combining units symbolically.
Find the unit of $\text{N}\cdot\text{m}$ if you are only combining units symbolically.
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$\text{N}\cdot\text{m}$. Units multiply when quantities are multiplied.
$\text{N}\cdot\text{m}$. Units multiply when quantities are multiplied.
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Find the unit of $\text{m}\div\text{s}$.
Find the unit of $\text{m}\div\text{s}$.
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$\frac{\text{m}}{\text{s}}$. Division creates rate units.
$\frac{\text{m}}{\text{s}}$. Division creates rate units.
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Find the unit of $\frac{\text{miles}}{\text{hour}}\times\text{hours}$.
Find the unit of $\frac{\text{miles}}{\text{hour}}\times\text{hours}$.
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$\text{miles}$. Hours cancel, leaving miles.
$\text{miles}$. Hours cancel, leaving miles.
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What unit should $m$ have in $y=mx$ if $x$ is $\text{s}$ and $y$ is $\text{m}$?
What unit should $m$ have in $y=mx$ if $x$ is $\text{s}$ and $y$ is $\text{m}$?
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$\frac{\text{m}}{\text{s}}$. Slope unit is $\frac{\text{output unit}}{\text{input unit}}$.
$\frac{\text{m}}{\text{s}}$. Slope unit is $\frac{\text{output unit}}{\text{input unit}}$.
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What is the unit of $E$ in $E=pt$ if $p$ is $\frac{\text{dollars}}{\text{month}}$ and $t$ is $\text{month}$?
What is the unit of $E$ in $E=pt$ if $p$ is $\frac{\text{dollars}}{\text{month}}$ and $t$ is $\text{month}$?
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$\text{dollars}$. Rate times time cancels time unit, leaving dollars.
$\text{dollars}$. Rate times time cancels time unit, leaving dollars.
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What is the unit of $A$ in $A=\pi r^2$ if $r$ is in inches?
What is the unit of $A$ in $A=\pi r^2$ if $r$ is in inches?
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$\text{in}^2$. Area uses squared radius units.
$\text{in}^2$. Area uses squared radius units.
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What is the unit of $C$ in $C=\pi d$ if $d$ is in meters?
What is the unit of $C$ in $C=\pi d$ if $d$ is in meters?
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$\text{m}$. Circumference has the same units as diameter.
$\text{m}$. Circumference has the same units as diameter.
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What is the unit of density $\rho$ in $\rho=\frac{m}{V}$ if $m$ is $\text{g}$ and $V$ is $\text{cm}^3$?
What is the unit of density $\rho$ in $\rho=\frac{m}{V}$ if $m$ is $\text{g}$ and $V$ is $\text{cm}^3$?
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$\frac{\text{g}}{\text{cm}^3}$. Density is mass per volume: $\frac{\text{mass}}{\text{volume}}$.
$\frac{\text{g}}{\text{cm}^3}$. Density is mass per volume: $\frac{\text{mass}}{\text{volume}}$.
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What is the unit of $r$ in $r=\frac{d}{t}$ if $d$ is $\text{m}$ and $t$ is $\text{s}$?
What is the unit of $r$ in $r=\frac{d}{t}$ if $d$ is $\text{m}$ and $t$ is $\text{s}$?
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$\frac{\text{m}}{\text{s}}$. Rate equals distance over time: $\frac{\text{m}}{\text{s}}$.
$\frac{\text{m}}{\text{s}}$. Rate equals distance over time: $\frac{\text{m}}{\text{s}}$.
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What is the unit of $t$ in $t=\frac{d}{r}$ if $d$ is $\text{km}$ and $r$ is $\frac{\text{km}}{\text{min}}$?
What is the unit of $t$ in $t=\frac{d}{r}$ if $d$ is $\text{km}$ and $r$ is $\frac{\text{km}}{\text{min}}$?
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$\text{min}$. Distance divided by rate gives time: $\text{km} \div \frac{\text{km}}{\text{min}} = \text{min}$.
$\text{min}$. Distance divided by rate gives time: $\text{km} \div \frac{\text{km}}{\text{min}} = \text{min}$.
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What is the unit of $d$ in $d=rt$ if $r$ is $\frac{\text{mi}}{\text{h}}$ and $t$ is $\text{h}$?
What is the unit of $d$ in $d=rt$ if $r$ is $\frac{\text{mi}}{\text{h}}$ and $t$ is $\text{h}$?
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$\text{mi}$. Rate times time gives distance: $\frac{\text{mi}}{\text{h}} \times \text{h} = \text{mi}$.
$\text{mi}$. Rate times time gives distance: $\frac{\text{mi}}{\text{h}} \times \text{h} = \text{mi}$.
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