7.5 Systems of Measurement

Before you get started, take this readiness quiz.

Multiply: $4.29 \left(1000\right) .$
If you missed this problem, review the reference.

Simplify: $\frac{30}{54} .$
If you missed this problem, review the reference.

Multiply: $\frac{7}{15} \cdot \frac{25}{28} .$
If you missed this problem, review the reference.

Mary Anne is $66$ inches tall. What is her height in feet?

Lexie is $30$ inches tall. Convert her height to feet.

Rene bought a hose that is $18$ yards long. Convert the length to feet.

Arnold’s SUV weighs about $4.3$ tons. Convert the weight to pounds.

A cruise ship weighs $51,000$ tons. Convert the weight to pounds.

The distance between Earth and the moon is about $250,000$ miles. Convert this length to yards.

A team of astronauts spends $15$ weeks in space. Convert the time to minutes.

How many cups are in $1$ gallon?

How many teaspoons are in $1$ cup?

Laura gave birth to triplets weighing $3$ pounds $12$ ounces, $3$ pounds $3$ ounces, and $2$ pounds $9$ ounces. What was the total birth weight of the three babies?

Seymour cut two pieces of crown molding for his family room that were $8$ feet $7$ inches and $12$ feet $11$ inches. What was the total length of the molding?

Henri wants to triple his spaghetti sauce recipe, which calls for $1$ pound $8$ ounces of ground turkey. How many pounds of ground turkey will he need?

Joellen wants to double a solution of $5$ gallons $3$ quarts. How many gallons of solution will she have in all?

Sandy completed her first $\text{5}-\text{km}$ race. How many meters did she run?

Herman bought a rug $2.5$ meters in length. How many centimeters is the length?

Kari’s newborn baby weighed $2800$ grams. How many kilograms did the baby weigh?

Anderson received a package that was marked $4500$ grams. How many kilograms did this package weigh?

Convert: ⓐ $7.25$ L to kL ⓑ $6.3$ L to mL.

Convert: ⓐ $350$ hL to L ⓑ $4.1$ L to cL.

Ryland is $1.6$ meters tall. His younger brother is $85$ centimeters tall. How much taller is Ryland than his younger brother?

Mariella is $1.58$ meters tall. Her daughter is $75$ centimeters tall. How much taller is Mariella than her daughter? Write the answer in centimeters.

The fence around Hank’s yard is $2$ meters high. Hank is $96$ centimeters tall. How much shorter than the fence is Hank? Write the answer in meters.

Dena’s recipe for lentil soup calls for $150$ milliliters of olive oil. Dena wants to triple the recipe. How many liters of olive oil will she need?

A recipe for Alfredo sauce calls for $250$ milliliters of milk. Renata is making pasta with Alfredo sauce for a big party and needs to multiply the recipe amounts by $8 .$ How many liters of milk will she need?

To make one pan of baklava, Dorothea needs $400$ grams of filo pastry. If Dorothea plans to make $6$ pans of baklava, how many kilograms of filo pastry will she need?

Lee’s water bottle holds $500$ mL of water. How many fluid ounces are in the bottle? Round to the nearest tenth of an ounce.

How many quarts of soda are in a $\text{2}-\text{liter}$ bottle?

How many liters are in $4$ quarts of milk?

Soleil lives in Minnesota but often travels in Canada for work. While driving on a Canadian highway, she passes a sign that says the next rest stop is in $100$ kilometers. How many miles until the next rest stop? Round your answer to the nearest mile.

The height of Mount Kilimanjaro is $5,895$ meters. Convert the height to feet. Round to the nearest foot.

The flight distance from New York City to London is $5,586$ kilometers. Convert the distance to miles. Round to the nearest mile.

Convert the Fahrenheit temperatures to degrees Celsius: $59 °\text{F} .$

Convert the Fahrenheit temperatures to degrees Celsius: $41 °\text{F} .$

Convert the Celsius temperatures to degrees Fahrenheit:

The temperature in Helsinki, Finland was $15 °\text{C} .$

Convert the Celsius temperatures to degrees Fahrenheit:

The temperature in Sydney, Australia was $10 °\text{C} .$

Convert the units.

A floor tile is $2$ feet wide. Convert the width to inches.

Convert the units.

Carson is $45$ inches tall. Convert his height to feet.

Convert the units.

Faye is $4$ feet $10$ inches tall. Convert her height to inches.

Convert the units.

On a baseball diamond, the distance from home plate to first base is $30$ yards. Convert the distance to feet.

Convert the units.

Denver, Colorado, is $5,183$ feet above sea level. Convert the height to miles.

Convert the units.

Blue whales can weigh as much as $150$ tons. Convert the weight to pounds.

Convert the units.

At take-off, an airplane weighs $220,000$ pounds. Convert the weight to tons.

Convert the units.

Lynn’s cruise lasted $6$ days and $18$ hours. Convert the time to hours.

Convert the units.

Misty’s surgery lasted $2 \frac{1}{4}$ hours. Convert the time to seconds.

Convert the units.

How many tablespoons are in a gallon?

Convert the units.

April’s dog, Beans, weighs $8$ pounds. Convert his weight to ounces.

Convert the units.

Baby Audrey weighed $6$ pounds $15$ ounces at birth. Convert her weight to ounces.

Convert the units.

Lance needs $500$ cups of water for the runners in a race. Convert the volume to gallons.

Solve and write your answer in mixed units.

Judy bought $1$ pound $6$ ounces of almonds, $2$ pounds $3$ ounces of walnuts, and $8$ ounces of cashews. What was the total weight of the nuts?

Solve and write your answer in mixed units.

Last year Eric went on $6$ business trips. The number of days of each was $5 , 2 , 8 , 12 , 6 , \text{and 3}.$ How much time (in weeks and days) did Eric spend on business trips last year?

Solve and write your answer in mixed units.

Fawzi’s SUV is $6$ feet $4$ inches tall. If he puts a $\text{2}-\text{foot}-\text{10}-\text{inch}$ box on top of his SUV, what is the total height of the SUV and the box?

Solve and write your answer in mixed units.

Mireille needs to cut $24$ inches of ribbon for each of the $12$ girls in her dance class. How many yards of ribbon will she need altogether?

Convert the units.

Kitaka hiked $8$ kilometers. Convert the length to meters.

Convert the units.

The width of the wading pool is $2.45$ meters. Convert the width to centimeters.

Convert the units.

The depth of the Mariana Trench is $10,911$ meters. Convert the depth to kilometers.

Convert the units.

A typical ruby-throated hummingbird weights $3$ grams. Convert this to milligrams.

Convert the units.

One serving of gourmet ice cream has $25$ grams of fat. Convert this to milligrams.

Convert the units.

Dimitri’s daughter weighed $3.8$ kilograms at birth. Convert this to grams.

Convert the units.

A bottle of medicine contained $300$ milliliters. Convert this to liters.

Solve and write your answer in mixed units.

Stavros is $1.6$ meters tall. His sister is $95$ centimeters tall. How much taller, in centimeters, is Stavros than his sister?

Solve and write your answer in mixed units.

Concetta had a $\text{2}-\text{kilogram}$ bag of flour. She used $180$ grams of flour to make biscotti. How many kilograms of flour are left in the bag?

Solve and write your answer in mixed units.

One glass of orange juice provides $560$ milligrams of potassium. Linda drinks one glass of orange juice every morning. How many grams of potassium does Linda get from her orange juice in $30$ days?

Solve and write your answer in mixed units.

One serving of whole grain sandwich bread provides $6$ grams of protein. How many milligrams of protein are provided by $7$ servings of whole grain sandwich bread?

Make the unit conversions. Round to the nearest tenth.

Frankie is $42$ inches tall. Convert his height to centimeters.

Make the unit conversions. Round to the nearest tenth.

Connie bought $9$ yards of fabric to make drapes. Convert the fabric length to meters.

Make the unit conversions. Round to the nearest tenth.

An average American will throw away $90,000$ pounds of trash over his or her lifetime. Convert this weight to kilograms (2.20 pounds = 1 kilogram).

Make the unit conversions. Round to the nearest tenth.

Kathryn is $1.6$ meters tall. Convert her height to feet.

Make the unit conversions. Round to the nearest tenth.

Jackson’s backpack weighs $15$ kilograms. Convert the weight to pounds.

Make the unit conversions. Round to the nearest tenth.

Bernard bought $8$ gallons of paint. Convert the volume to liters.

Convert the Fahrenheit temperature to degrees Celsius. Round to the nearest tenth.

$77 °\text{F}$

Convert the Fahrenheit temperature to degrees Celsius. Round to the nearest tenth.

$14 °\text{F}$

Convert the Fahrenheit temperature to degrees Celsius. Round to the nearest tenth.

$4 °\text{F}$

Convert the Fahrenheit temperature to degrees Celsius. Round to the nearest tenth.

$120 °\text{F}$

Convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

$25 °\text{C}$

Convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

$−15 °\text{C}$

Convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

$8 °\text{C}$

Convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

$16 °\text{C}$

Reflectors The reflectors in each lane-marking stripe on a highway are spaced $16$ yards apart. How many reflectors are needed for a one-mile-long stretch of highway?

Write as the ratio of two integers.

$−5$

Write as the ratio of two integers.

$1.8$

Determine which of the numbers is rational.

$\text{0}.\text{75319}\ldots , 0. \overset{—}{16} , 1.95$

Identify whether each given number is rational or irrational.

ⓐ $\sqrt{72}$ ⓑ $\sqrt{64}$

List the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.

$−5 , - 2 \frac{1}{4} , - \sqrt{4} , 0. \overset{—}{25} , \frac{13}{5} , 4$

Use the commutative property to rewrite the given expression.

$−14 \cdot 5 = ____$

Use the commutative property to rewrite the given expression.

$a + 8 = ____$

Use the associative property to rewrite the given expression.

$\left(22 + 7\right) + 3 = _____$

Use the associative property to rewrite the given expression.

$\frac{1}{2} \left(22 y\right) = _____$

Evaluate each expression for the given value.

If $z = - \frac{5}{3} ,$ evaluate:
ⓐ $z + 5.39 + \left(- z\right)$
ⓑ $z + \left(- z\right) + 5.39$

Evaluate each expression for the given value.

If $m = −13 ,$ evaluate:
ⓐ $- \frac{2}{5} \left(\frac{5}{2} m\right)$
ⓑ $\left(- \frac{2}{5} \cdot \frac{5}{2}\right) m$

Simplify using the commutative and associative properties.

$\frac{1}{4} + \frac{11}{15} + \left(- \frac{1}{4}\right)$

Simplify using the commutative and associative properties.

$−18 \cdot 15 \cdot \frac{2}{9}$

Simplify using the commutative and associative properties.

$\left(3.98 d + 0.75 d\right) + 1.25 d$

Simplify using the commutative and associative properties.

$30 \left(\frac{5}{6} q\right)$

Simplify using the commutative and associative properties.

$52 m + \left(−20 n\right) + \left(−18 m\right) + \left(−5 n\right)$

Simplify using the distributive property.

$9 \left(u - 4\right)$

Simplify using the distributive property.

$−8 \left(−7 a - 12\right)$

Simplify using the distributive property.

$\left(y + 10\right) \cdot p$

Simplify using the distributive property.

$4 \left(x + 3\right) - 8 \left(x - 7\right)$

Evaluate using the distributive property.

If $n = \frac{7}{8} ,$ evaluate
ⓐ $8 \left(n + \frac{1}{4}\right)$ and
ⓑ $8 \cdot n + 8 \cdot \frac{1}{4}$ to show that $8 \left(n + \frac{1}{4}\right) = 8 \cdot n + 8 \cdot \frac{1}{4}$

Evaluate using the distributive property.

If $y = −18 ,$ evaluate
ⓐ $- \left(y - 18\right)$ and
ⓑ $- y + 18$ to show that $- \left(y - 18\right) = - y + 18$

Identify whether each example is using the identity property of addition or multiplication.

$29 + 0 = 29$

Identify whether each example is using the identity property of addition or multiplication.

$9 \cdot 1 + \left(- 3\right) = 9 + \left(- 3\right)$

Find the additive inverse.

$19.4$

Find the additive inverse.

$- \frac{7}{15}$

Find the multiplicative inverse.

$−5$

Find the multiplicative inverse.

$- \frac{4}{9}$

Simplify.

$\frac{0}{9}$

Simplify.

$0 \div \frac{2}{3}$

Simplify.

$\left(n + 6.75\right) + 0.25$

Simplify.

$\frac{1}{6} \cdot 17 \cdot 12$

Simplify.

$9 \left(6 x - 11\right) + 15$

Convert between U.S. units. Round to the nearest tenth.

A picture frame is $42$ inches wide. Convert the width to feet.

Convert between U.S. units. Round to the nearest tenth.

A playground is $45$ feet wide. Convert the width to yards.

Convert between U.S. units. Round to the nearest tenth.

Shamu weighs $4.5$ tons. Convert the weight to pounds.

Convert between U.S. units. Round to the nearest tenth.

How many tablespoons are in a quart?

Convert between U.S. units. Round to the nearest tenth.

Trinh needs $30$ cups of paint for her class art project. Convert the volume to gallons.

Solve, and state your answer in mixed units.

Every day last week, Pedro recorded the amount of time he spent reading. He read for $50 , 25 , 83 , 45 , 32 , 60 , \text{and} 135$ minutes. How much time, in hours and minutes, did Pedro spend reading?

Solve, and state your answer in mixed units.

Dalila wants to make pillow covers. Each cover takes $30$ inches of fabric. How many yards and inches of fabric does she need for $4$ pillow covers?

Convert between metric units.

Mount Everest is $8,850$ meters tall. Convert the height to kilometers.

Convert between metric units.

One cup of yogurt contains $13$ grams of protein. Convert this to milligrams.

Convert between metric units.

A bottle of water contained $650$ milliliters. Convert this to liters.

Solve.

Selma had a $\text{1}-\text{liter}$ bottle of water. If she drank $145$ milliliters, how much water, in milliliters, was left in the bottle?

Solve.

One ounce of tofu provides $2$ grams of protein. How many milligrams of protein are provided by $5$ ounces of tofu?

Convert between U.S. and metric units. Round to the nearest tenth.

A college basketball court is $84$ feet long. Convert this length to meters.

Convert between U.S. and metric units. Round to the nearest tenth.

Lucas weighs $78$ kilograms. Convert his weight to pounds.

Convert between U.S. and metric units. Round to the nearest tenth.

A box of books weighs $25$ pounds. Convert this weight to kilograms.

Convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.

$23 °\text{F}$

Convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.

$64 °\text{F}$

Convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

$−5 °\text{C}$

Convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.

$24 °\text{C}$

Is $\sqrt{144}$ rational or irrational?

Rewrite using the commutative property: $x \cdot 14 = _________$

Rewrite the expression using the associative property: $\left(8 \cdot 2\right) \cdot 5 = ___________$

For the number $\frac{2}{5}$ find the ⓐ additive inverse ⓑ multiplicative inverse.

Simplify the given expression.

$−3 + 15 y + 3$

Simplify the given expression.

$\left(\frac{8}{15} + \frac{2}{9}\right) + \frac{7}{9}$

Simplify the given expression.

$14 y + \left(−6 z\right) + 16 y + 2 z$

Simplify the given expression.

$6 \left(5 x - 4\right)$

Simplify the given expression.

$\frac{1}{4} \left(8 a + 12\right)$

Simplify the given expression.

$8 \left(6 p - 1\right) + 2 \left(9 p + 3\right)$

Simplify the given expression.

$\frac{0}{8}$

Simplify the given expression.

$0 \div \left(\frac{2}{3}\right)$

Solve using the appropriate unit conversions.

One cup of milk contains $276$ milligrams of calcium. Convert this to grams. $(\text{1 milligram} = \text{0}.\text{001 gram})$

Solve using the appropriate unit conversions.

Janice ran $15$ kilometers. Convert this distance to miles. Round to the nearest hundredth of a mile. $(\text{1 mile} = \text{1}.\text{61 kilometers})$

Solve using the appropriate unit conversions.

Use the formula $F = \frac{9}{5} C + 32$ to convert $35 °\text{C}$ to degrees $\text{F}$