Units and Unit Conversions - GED Math

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

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$\small 1\ year=365\ days$

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$

How many cups are in 3 gallons?

$\small 1\ gallon=4\ quarts$

$\small 1\ quart=4\ cups$

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

Express 6 yards in inches.

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A yard comprises 36 inches, so multiply by 36:

$36 \times 6 = 216$

One yard is equal to 216 inches.

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

1 cup = 8 ounces

1 ounce - .125 cups

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

Convert 47 inches to feet.

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$1\ ft=12\ in$

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$

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?

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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.

$45 \times 6 = 270\ miles$

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.

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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 $72 ^{ \circ }\textrm{ F}$ .

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 ?

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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 .

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.

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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 .

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 ?

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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 .

Convert 10 yards to inches.

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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:

Convert 2.5 yards to inches.

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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: $90 \textup{ inches}$

Convert 6 inches to yards.

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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: $\frac{1}{6}$

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

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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 }$

$=78\textrm{ in}$

Convert 6 feet to inches.

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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: $72 \textup{ in}$

Convert 10 inches to yards.

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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: $\frac{5}{18}$

Convert yards feet inches into inches.

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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.

Convert hours minutes and seconds into seconds.

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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.

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:

$\large 16 oz= 1lb$

$\large 1kg\approx2.2lbs$

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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.

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?

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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.