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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #12 : Converting Measurements

Convert $\displaystyle 6$ pounds to ounces.

Possible Answers:

$\displaystyle 96$

$\displaystyle 40$

$\displaystyle 48$

0.375 $\displaystyle 0.375$

$\displaystyle 80$

Correct answer:

$\displaystyle 96$

Explanation:

We know $\displaystyle 16$ ounces make up $\displaystyle 1$ pound. Since we are looking for $\displaystyle 6$ pounds in ounces, we can write a proportion.

$\frac{1\ pound}{16\ ounces}=\frac{6\ pounds}{x\ ounces}$ $\displaystyle \frac{1\ pound}{16\ ounces}=\frac{6\ pounds}{x\ ounces}$

Cross-multiply.

$(x\ ounces)(1\ pound)=(16\ ounces)(6\ pounds)$ $\displaystyle (x\ ounces)(1\ pound)=(16\ ounces)(6\ pounds)$

Divide each side by $\displaystyle 1$ pound.

$x\ ounces=6(16\ ounces)$ $\displaystyle x\ ounces=6(16\ ounces)$

$x=96\ ounces$ $\displaystyle x=96\ ounces$

Therefore, $6\ pounds=96\ ounces$ $\displaystyle 6\ pounds=96\ ounces$.

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Example Question #12 : Converting Measurements

Convert $\displaystyle 3$ liters to milliliters.

Possible Answers:

3000 $\displaystyle 3000$

$\displaystyle .03$

30000 $\displaystyle 30000$

300 $\displaystyle 300$

$\displaystyle .003$

Correct answer:

3000 $\displaystyle 3000$

Explanation:

We know 1000 $\displaystyle 1000$ milliliters make up $\displaystyle 1$ liter. Since we are looking for $\displaystyle 3$ liters in milliliters, we can write a proportion.

$\frac{1\ liter}{1000\ milliliters}=\frac{3\ liters}{x\ milliliters}$ $\displaystyle \frac{1\ liter}{1000\ milliliters}=\frac{3\ liters}{x\ milliliters}$

Cross-multiply.

$(x\ milliliters)(1\ liter)=(3\ liters)(1000\ milliliters)$ $\displaystyle (x\ milliliters)(1\ liter)=(3\ liters)(1000\ milliliters)$

Divide by $\displaystyle 1$ liter.

$x\ milliliters=3(1000\ milliliters)$ $\displaystyle x\ milliliters=3(1000\ milliliters)$

$x=3000\ milliliters$ $\displaystyle x=3000\ milliliters$

Therefore, $3\ liters=3000\ milliliters$ $\displaystyle 3\ liters=3000\ milliliters$.

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Example Question #21 : Converting Measurements

Convert 7000 $\displaystyle 7000$ milliliters to liters.

Possible Answers:

7000000 $\displaystyle 7000000$

$\displaystyle 70$

$\displaystyle 10$

$\displaystyle 7$

$\displaystyle 5$

Correct answer:

$\displaystyle 7$

Explanation:

We know 1000 $\displaystyle 1000$ milliliters make up $\displaystyle 1$ liter. Since we are looking for 7000 $\displaystyle 7000$ milliliters in liters, we can write a proportion.

$\frac{1\ liter}{1000\ milliliters}=\frac{x\ liters}{7000\ milliliters}$ $\displaystyle \frac{1\ liter}{1000\ milliliters}=\frac{x\ liters}{7000\ milliliters}$

Cross-multiply.

$(x\ liters)(1000 milliliters)=(1\ liter)(7000\ milliliters)$ $\displaystyle (x\ liters)(1000 milliliters)=(1\ liter)(7000\ milliliters)$

Divide both sides by 1000 $\displaystyle 1000$ milliliters.

$x\ liters= 7(1\ liter)$ $\displaystyle x\ liters= 7(1\ liter)$

$x=7\ liters$ $\displaystyle x=7\ liters$

Therefore, $7000\ millimeters=7\ liters$ $\displaystyle 7000\ millimeters=7\ liters$.

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Example Question #1251 : Linear Equations

Convert $\displaystyle 4$ yards to feet.

Possible Answers:

1.33 $\displaystyle 1.33$

$\displaystyle 12$

$\displaystyle 15$

$\displaystyle 9$

$\displaystyle 6$

Correct answer:

$\displaystyle 12$

Explanation:

We know $\displaystyle 3$ feet make up $\displaystyle 1$ yard. Since we are looking for $\displaystyle 4$ yards in feet, we can write a proportion.

$\frac{1\ yard}{3\ feet}=\frac{4\ yards}{x\ feet}$ $\displaystyle \frac{1\ yard}{3\ feet}=\frac{4\ yards}{x\ feet}$

Cross-multiply.

$(x\ feet)(1\ yard)=(3\ feet)(4\ yards)$ $\displaystyle (x\ feet)(1\ yard)=(3\ feet)(4\ yards)$

Divide each side by $\displaystyle 1$ yard.

$x\ feet=4(3\ feet)$ $\displaystyle x\ feet=4(3\ feet)$

$x=12\ feet$ $\displaystyle x=12\ feet$

Therefore, $4\ yards=12\ feet$ $\displaystyle 4\ yards=12\ feet$.

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Example Question #21 : Converting Measurements

Convert $\displaystyle 21$ feet to yards.

Possible Answers:

$\displaystyle 15$

$\displaystyle 6$

$\displaystyle 9$

$\displaystyle 63$

$\displaystyle 7$

Correct answer:

$\displaystyle 7$

Explanation:

We know $\displaystyle 3$ feet make up $\displaystyle 1$ yard. Since we are looking for $\displaystyle 21$ feet in yards, we can write a proportion.

$\frac{1\ yard}{3\ feet}=\frac{x\ yards}{21\ feet}$ $\displaystyle \frac{1\ yard}{3\ feet}=\frac{x\ yards}{21\ feet}$

Cross-multiply.

$(x\ yards)(3\ feet)=(1\ yard)(21\ feet)$ $\displaystyle (x\ yards)(3\ feet)=(1\ yard)(21\ feet)$

Divide both sides by $\displaystyle 3$ feet.

$x\ yards=7(1\ yard)$ $\displaystyle x\ yards=7(1\ yard)$

$x=7\ yards$ $\displaystyle x=7\ yards$

Therefore, $21\ feet=7\ yards$ $\displaystyle 21\ feet=7\ yards$.

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Example Question #21 : Converting Measurements

Convert 5.75 $\displaystyle 5.75$ pounds to ounces.

Possible Answers:

$\displaystyle 88$

9200 $\displaystyle 9200$

$\displaystyle 82$

$\displaystyle 96$

$\displaystyle 92$

Correct answer:

$\displaystyle 92$

Explanation:

We know $\displaystyle 16$ ounces make up $\displaystyle 1$ pound. Since we are looking for 5.75 $\displaystyle 5.75$ pounds in ounces, we can write a proportion.

$\frac{1\ pound}{16\ ounces}=\frac{5.75\ pounds}{x\ ounces}$ $\displaystyle \frac{1\ pound}{16\ ounces}=\frac{5.75\ pounds}{x\ ounces}$

Cross-multiply.

$(x\ ounces)(1\ pound)=(16\ ounces)(5.75\ pounds)$ $\displaystyle (x\ ounces)(1\ pound)=(16\ ounces)(5.75\ pounds)$

Divide each side by $\displaystyle 1$ pound.

$x\ ounces= 5.75(16\ ounces)$ $\displaystyle x\ ounces= 5.75(16\ ounces)$

$x=92\ ounces$ $\displaystyle x=92\ ounces$

Remember, we have to place the decimal point between the $\displaystyle 2$ and $\displaystyle 0$ since we are dealing with a decimal value and we shift two decimal places to the right (92.00) $\displaystyle (92.00)$.

Therefore, $5.75\ pounds=92\ ounces$ $\displaystyle 5.75\ pounds=92\ ounces$.

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Example Question #1251 : Linear Equations

Convert $\displaystyle 18$ inches to feet.

Possible Answers:

1.6 $\displaystyle 1.6$

1.7 $\displaystyle 1.7$

$\displaystyle 2$

1.5 $\displaystyle 1.5$

1.8 $\displaystyle 1.8$

Correct answer:

1.5 $\displaystyle 1.5$

Explanation:

We know $\displaystyle 12$ inches make up $\displaystyle 1$ foot. Since we are looking for $\displaystyle 18$ inches in feet, we can write a proportion.

$\frac{1\ foot}{12\ inches}=\frac{x\ feet}{18\ inches}$ $\displaystyle \frac{1\ foot}{12\ inches}=\frac{x\ feet}{18\ inches}$

Cross-multiply.

$(x\ feet)(12\ inches)=(1\ foot)(18\ inches)$ $\displaystyle (x\ feet)(12\ inches)=(1\ foot)(18\ inches)$

Divide each side by $\displaystyle 12$ inches.

$x\ feet=(1\ foot) (\frac{18\ inches}{12\ inches})$ $\displaystyle x\ feet=(1\ foot) (\frac{18\ inches}{12\ inches})$

Solve for $(\frac{18\ inches}{12\ inches})$ $\displaystyle (\frac{18\ inches}{12\ inches})$.

Inches will cross out and leave the fraction $\tfrac{18}{12}$ $\displaystyle \tfrac{18}{12}$.

$\frac{18}{12}=\frac{3}{2}=1\frac{1}{2}=1.5$ $\displaystyle \frac{18}{12}=\frac{3}{2}=1\frac{1}{2}=1.5$

Replace the fraction $(\frac{18\ inches}{12\ inches})$ $\displaystyle (\frac{18\ inches}{12\ inches})$ with 1.5 $\displaystyle 1.5$ in the equation $x\ feet=(1\ foot) (\frac{18\ inches}{12\ inches})$ $\displaystyle x\ feet=(1\ foot) (\frac{18\ inches}{12\ inches})$.

$x\ feet=1.5(1\ foot)$ $\displaystyle x\ feet=1.5(1\ foot)$

$x=1.5\ feet$ $\displaystyle x=1.5\ feet$

Therefore, $18\ inches=1.5\ feet$ $\displaystyle 18\ inches=1.5\ feet$.

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Example Question #26 : Converting Measurements

Convert $\displaystyle 3$ yards to inches.

Possible Answers:

$\displaystyle 54$

$\displaystyle 48$

$\displaystyle 9$

108 $\displaystyle 108$

$\displaystyle 36$

Correct answer:

108 $\displaystyle 108$

Explanation:

First, let's go from yards to feet.

We know $\displaystyle 3$ feet make up $\displaystyle 1$ yard. Since we are looking for $\displaystyle 3$ yards in feet, we can write a proportion.

$\frac{1\ yard}{3\ feet}=\frac{3\ yards}{x\ feet}$ $\displaystyle \frac{1\ yard}{3\ feet}=\frac{3\ yards}{x\ feet}$

Cross-multiply.

$(x\ feet)(1\ yard)=(3\ feet)(3\ yards)$ $\displaystyle (x\ feet)(1\ yard)=(3\ feet)(3\ yards)$

Divide each side by $\displaystyle 1$ yard.

$(x\ feet)=3(3\ feet)$ $\displaystyle (x\ feet)=3(3\ feet)$

$x=9\ feet$ $\displaystyle x=9\ feet$

Therefore, $3\ yards=9\ feet$ $\displaystyle 3\ yards=9\ feet$.

Now we convert feet to inches.

We know $\displaystyle 12$ inches make up $\displaystyle 1$ foot. Since we are looking for inches in $\displaystyle 9$ feet, we can write a proportion.

$\frac{1\ foot}{12\ inches}=\frac{9\ feet}{x\ inches}$ $\displaystyle \frac{1\ foot}{12\ inches}=\frac{9\ feet}{x\ inches}$

Cross-multiply.

$(x\ inches)(1\ foot)= (12\ inches)(9\ feet)$ $\displaystyle (x\ inches)(1\ foot)= (12\ inches)(9\ feet)$

Divide each side by $\displaystyle 1$ foot.

$x\ inches=9(12\ inches)$ $\displaystyle x\ inches=9(12\ inches)$

$x=108\ inches$ $\displaystyle x=108\ inches$

Therefore, $9\ feet =108\ inches$ $\displaystyle 9\ feet =108\ inches$.

So overall: $3\ yards=108\ inches$ $\displaystyle 3\ yards=108\ inches$.

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Example Question #1251 : Linear Equations

Convert $\displaystyle 80$ ounces to pounds.

Possible Answers:

120 $\displaystyle 120$

$\displaystyle 3$

1080 $\displaystyle 1080$

$\displaystyle 5$

540 $\displaystyle 540$

Correct answer:

$\displaystyle 5$

Explanation:

We know $\displaystyle 16$ ounces make up $\displaystyle 1$ pound. Since we are looking for the number of pounds in $\displaystyle 80$ ounces, we can write a proportion.

$\frac{1\ pound}{16\ ounces}=\frac{x\ pounds}{80\ ounces}$ $\displaystyle \frac{1\ pound}{16\ ounces}=\frac{x\ pounds}{80\ ounces}$

Cross-multiply.

$(x\ pounds)(16\ ounces)=(1\ pound)(80\ ounces)$ $\displaystyle (x\ pounds)(16\ ounces)=(1\ pound)(80\ ounces)$

Divide both sides by $\displaystyle 16$ ounces.

$x\ pounds=5(1\ pound)$ $\displaystyle x\ pounds=5(1\ pound)$

$x=5\ pounds$ $\displaystyle x=5\ pounds$

Therefore, $80\ ounces = 5\ pounds$ $\displaystyle 80\ ounces = 5\ pounds$.

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Example Question #1252 : Linear Equations

How many eggs are in $4\tfrac{1}{3}$ $\displaystyle 4\tfrac{1}{3}$ dozen if there are $\displaystyle 12$ eggs in a dozen?

Possible Answers:

$\displaystyle 52$

$\displaystyle 53$

$\displaystyle 51$

$\displaystyle 48$

$\displaystyle 61$

Correct answer:

$\displaystyle 52$

Explanation:

We know $\displaystyle 12$ eggs make up $\displaystyle 1$ dozen. Since we are looking for $4\tfrac{1}{3}$ $\displaystyle 4\tfrac{1}{3}$ dozen in eggs, we can write a proportion.

$\frac{1\ dozen}{12\ eggs}=\frac{4\tfrac{1}{3}\ dozen}{x\ eggs}$ $\displaystyle \frac{1\ dozen}{12\ eggs}=\frac{4\tfrac{1}{3}\ dozen}{x\ eggs}$

Cross-multiply.

$(x\ eggs)(1\ dozen)=(12\ eggs)(4\tfrac{1}{3}\ dozen )$ $\displaystyle (x\ eggs)(1\ dozen)=(12\ eggs)(4\tfrac{1}{3}\ dozen )$

Divide each side by $\displaystyle 1$ dozen.

$x\ eggs=4\tfrac{1}{3}(12\ eggs)$ $\displaystyle x\ eggs=4\tfrac{1}{3}(12\ eggs)$

Convert the mixed number into an improper fraction by multiplying denominator with the whole number followed by adding the numerator. Then we write that value over the denominator.

$\frac{(3*4)+1}{3}=\frac{13}{3}$ $\displaystyle \frac{(3*4)+1}{3}=\frac{13}{3}$

Replace the mixed number $4\tfrac{1}{3}$ $\displaystyle 4\tfrac{1}{3}$ with the improper fraction $\tfrac{13}{3}$ $\displaystyle \tfrac{13}{3}$ in the equation $x\ eggs=4\tfrac{1}{3}(12\ eggs)$ $\displaystyle x\ eggs=4\tfrac{1}{3}(12\ eggs)$.

$x\ eggs=\frac{13}{3}(12\ eggs)$ $\displaystyle x\ eggs=\frac{13}{3}(12\ eggs)$

Solve.

$x\ eggs=\frac{13}{3}*\frac{12\ eggs}{1}$ $\displaystyle x\ eggs=\frac{13}{3}*\frac{12\ eggs}{1}$

Cross out the $\displaystyle 3$ and reduce.

$x\ eggs=\frac{13}{1}*\frac{4\ eggs}{1}$ $\displaystyle x\ eggs=\frac{13}{1}*\frac{4\ eggs}{1}$

$x\ eggs=13(4\ eggs)$ $\displaystyle x\ eggs=13(4\ eggs)$

$x=52\ eggs$ $\displaystyle x=52\ eggs$

Therefore, $4\tfrac{1}{3}\ dozen = 52\ eggs$ $\displaystyle 4\tfrac{1}{3}\ dozen = 52\ eggs$.

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #12 : Converting Measurements

Example Question #12 : Converting Measurements

Example Question #21 : Converting Measurements

Example Question #1251 : Linear Equations

Example Question #21 : Converting Measurements

Example Question #21 : Converting Measurements

Example Question #1251 : Linear Equations

Example Question #26 : Converting Measurements

Example Question #1251 : Linear Equations

Example Question #1252 : Linear Equations

All Algebra 1 Resources

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