Units and Unit Conversions - GED Math

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Question

Convert 2.5 years to days. Assume that the years in question are not leap years. Round to the nearest day.

Answer

$\small 1\ year=365\ days$

Make sure that your units cross out properly.

$\small \frac{2.5\ years}{1}\times \frac{365\ days}{1\ year}=912.5\ days= 913\ days$

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Question

How many cups are in 3 gallons?

$\small 1\ gallon=4\ quarts$

$\small 1\ quart=4\ cups$

Answer

$\small \frac{3\ gallons}{1}\times \frac{4\ quarts}{1\ gallon}\times \frac{4\ cups}{1\ quart}=48\ cups$

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Question

Express 6 yards in inches.

Answer

A yard comprises 36 inches, so multiply by 36:

$36 \times 6 = 216$

One yard is equal to 216 inches.

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Question

How many ounces are in cups? If necessary, round to the nearest tenth.

1 cup = 8 ounces

1 ounce - .125 cups

Answer

Convert cups to ounces by creating a ratio (see below). In the second fraction, the cups unit is on the denominator so "cups" cancels out.

$\frac{3.5\textup{ cups}}{1}=\frac{8\textup{ ounces}}{1\textup{ cup}}=28\textup{ ounces}$

$\frac{3.5\textup{ cups}}{1}= \textup{this is what we are being asked to convert}$

$\frac{8\textup{ ounces}}{1\textup{ cup}}=\textup{8 ounces = 1 cup}$

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Question

Convert 47 inches to feet.

Answer

$1\ ft=12\ in$

Multiply 47 inches by the conversion ratio to get the equivalent measure in feet:

$\frac{47\ in}{1}\times \frac{1\ ft}{12\ in}=3.9\ ft$

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Question

A scale on a map states that every represents . If cities are apart on the scaled map, how many miles are between the two cities?

Answer

If each 1/3 of an inch on the scaled map = 15 miles; then 1 inch would represent

$3 \times 15$ or $45\ miles$ per inch.

The measured distance is 6 inches.

$45 \times 6 = 270\ miles$

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Question

Fahrenheit temperature can be converted to its Celsius equivalent using the formula

$C = \frac{5}{9} (F-32)$ .

Celsius temperature can be converted to its Fahrenheit equivalent using the formula

$F = \frac{9}{5} C + 32$ .

Wesley, an American visiting London, is confused by a weather report that says that the temperature today is to reach a peak of 22 degrees. This being a British weather report, that temperature is expressed in degrees Celsius, but being American, Wesley is used to the Fahrenheit temperature scale. To the nearest degree, convert the predicted peak temperature to Fahrenheit.

Answer

We are converting Celsius to Fahrenheit , so we use the formula

$F = \frac{9}{5} C + 32$ .

Substitute 22 for to calculate the value of :

$F = \frac{9}{5} \cdot 22 + 32 = 39.6 + 32 = 71.6$ ,

which rounds to $72 ^{ \circ }\textrm{ F}$ .

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Question

Fahrenheit temperature can be converted to its Celsius equivalent using the formula

$C = \frac{5}{9} (F-32)$ .

Celsius temperature can be converted to its Fahrenheit equivalent using the formula

$F = \frac{9}{5} C + 32$ .

Which of the following Fahrenheit temperatures comes closest to $150^{\circ } \textrm{C}$ ?

Answer

We are converting Celsius to Fahrenheit , so we use the formula

$F = \frac{9}{5} C + 32$ .

Substitute 150 for to calculate the value of :

$F = \frac{9}{5} \cdot 150 + 32 = 270 + 32 = 302$

The equivalent Fahrenheit temperature is $302^{\circ }\textrm{F}$ .

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Question

Fahrenheit temperature can be converted to its Celsius equivalent using the formula

$C = \frac{5}{9} (F-32)$ .

Celsius temperature can be converted to its Fahrenheit equivalent using the formula

$F = \frac{9}{5} C + 32$ .

Anja, a German woman visiting St. Louis, is confused by a weather report that says that the temperature today is to reach a peak of 58 degrees. This being an American weather report, that temperature is expressed in degrees Fahrenheit, but being German, Anja is used to the Celsius temperature scale. To the nearest degree, convert the predicted peak temperature to Celsius.

Answer

We are converting Fahrenheit to Celsius, so we use the formula

$C = \frac{5}{9} (F-32)$ .

Substitute to calculate the value of :

$C = \frac{5}{9} (58-32) = \frac{5}{9} \cdot 26 = 14.444...$

The temperature, expressed in degrees Celsius, is $14^{\circ }\textrm{C}$ .

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Question

Fahrenheit temperature can be converted to its Celsius equivalent using the formula

$C = \frac{5}{9} (F-32)$ .

Celsius temperature can be converted to its Fahrenheit equivalent using the formula

$F = \frac{9}{5} C + 32$ .

Which of the following Celsius temperatures comes closest to $150^{\circ } \textrm{F}$ ?

Answer

We are converting Fahrenheit to Celsius, so we use the formula

$C = \frac{5}{9} (F-32)$ .

Substitute 150 for to calculate the value of :

$C = \frac{5}{9} (150-32) = \frac{5}{9} \cdot 118 \approx 66$

The temperature, expressed in degrees Celsius, is $66^{\circ }\textrm{C}$ .

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Question

Convert 2.5 yards to inches.

Answer

For every yard, there are 3 feet.

$1 \textup{ yard} = 3 \textup{ ft}$

For every feet, there are 12 inches.

$1\textup{ ft} = 12 \textup{ inches}$

Write the dimensional analysis.

$2.5 \textup{ yds} (\frac{3 \textup{ ft}}{1\textup{ yard}})(\frac{12 \textup{ inches}}{1\textup{ ft}})$

Multiply the numbers. The unit which remains is in inches.

The answer is: $90 \textup{ inches}$

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Question

Convert 6 inches to yards.

Answer

One yard is equivalent to 3 feet.

One foot is equivalent to 12 inches.

Set up the dimensional analysis.

$6 \textup{ in}(\frac{1 \textup{ ft}}{12 \textup{ in}})(\frac{1 \textup{ yd}}{3 \textup{ ft}}) = \frac{6}{36} = \frac{1}{6} \textup{ yd}$

The answer is: $\frac{1}{6}$

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Question

Express $6\frac{1}{2}$ feet in inches.

Answer

One foot is equivalent to 12 inches, so multiply the number of feet by 12 inches per foot in order to convert:

$6\frac{1}{2} \textrm{ ft } \times 12 \textrm{ in / ft}$

Rewrite the numbers as improper fractions:

$= \frac{6 \times 2+ 1}{2} \times \frac{12 }{1 }\textrm{ in }$

$=\frac{12+ 1}{2} \times \frac{12 }{1 }\textrm{ in }$

$=\frac{13}{2} \times \frac{12 }{1 }\textrm{ in }$

Cross-cancel, then multiply across:

$=\frac{13}{1} \times \frac{6}{1 }\textrm{ in }$

$=78\textrm{ in}$

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Question

Convert 6 feet to inches.

Answer

There are 12 inches in a foot. Set up the dimensional analysis to solve.

$6 \textup{ ft} (\frac{12 \textup{ in}}{1\textup{ ft}}) = 72 \textup{ in}$

The answer is: $72 \textup{ in}$

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Question

Convert 10 inches to yards.

Answer

One yard is equal to 3 feet.

One foot is equal to 12 inches.

Set up the dimensional analysis.

$10 \textup{ in} (\frac{1 \textup{ ft}}{12 \textup{ in} })(\frac{1 \textup{ yd}}{3 \textup{ ft}}) = \frac{10}{36} \textup{ yd}$

Reduce the fraction.

The answer is: $\frac{5}{18}$

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Question

Convert 10 yards to inches.

Answer

There are 3 feet in a yard, and 12 inches to a foot.

Write the dimensional analysis.

$10 \textup{ yds} (\frac{3 \textup{ ft}}{1 \textup{ yds}}) (\frac{12 \textup{ in}}{1 \textup{ ft}})$

The answer is:

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Question

Convert yards feet inches into inches.

Answer

Start by converting the yards into inches. Recall that there are feet in a yard, and inches in a foot.

$14\text{ yards }(3)=42 \text{ feet}(12)=504 \text{ inches}$

Next, convert feet into inches.

$6(12)=72\text{ inches}$

Now add up all the inches.

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Question

Convert hours minutes and seconds into seconds.

Answer

Start by converting the hours into seconds. Recall that there are minutes in an hour and seconds in a minute.

Thus, there are seconds in hours.

Next, convert the minutes into seconds.

There are seconds in minutes.

Now, add together all of the seconds.

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Question

You have 34oz of ground beef which you plan on making into hambrugers to grill with your friends. One of your friends is from Europe, and she is used to the metric system. She claims that burgers made with a $\large \frac{1}{4}kg$ of beef are the best. If you decide to make burgers of this size, how many can you make? Round to the nearest whole burger.

Note:

$\large 16 oz= 1lb$

$\large 1kg\approx2.2lbs$

Answer

You have 34oz of ground beef which you plan on making into hambrugers to grill with your friends. One of your friends is from Europe, and she is used to the metric system. She claims that burgers made with a $\large \frac{1}{4}kg$ of beef are the best. If you decide to make burgers of this size, how many can you make? Round to the nearest whole burger.

Note:

$\large 16 oz= 1lb$

$\large 1kg\approx2.2lbs$

Let's begin by running through what we need to do.

Convert 34 oz to pounds

Convert the answer to 2) to kilograms

Divide the answer to 3) by $\large \frac{1}{4}kg$

Okay, to find the number of pounds we have, do the following:

$\large 34oz\frac{1lb}{16oz}=2.125lb$

So, we have 2.125lbs of ground beef

Let's find what 2.125lbs is in kg

$\large 2.125lbs\frac{1kg}{2.2lb}\approx0.966kg$

So, we have 0.966kg of beef.

Finally, let's see how many burgers we can make.

$\large 0.966kg*\frac{1 burger}{0.25kg}=3.863burgers$

Now, we need to round to the nearest burger, so we can make about 4 burgers.

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Question

If you need 256 inches of cloth, and the store from which you want to buy it only sells it in two-foot increments, how much will you have to buy?

Answer

One foot is equal to 12 inches, so divide 256 inches by the conversion factor 12 inches/foot to obtain the equivalent in feet:

$256 \textup{ in } \div 12 \textup{ in/ft } = 21 \textup{ ft } \textup{ R }4 \textup{ in}$ .

The next highest even number of feet is 22 feet, the correct choice.

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