Units - HiSet: High School Equivalency Test: Math

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Question

Rewrite the sum of 16 gallons and pints as a number of quarts.

Answer

One gallon is equivalent to 4 quarts, so 16 gallons can be converted to quarts by multiplying by conversion factor 4:

$16 \textup{ gal } \times 4\textup{ qt/gal} = 64 \textup{ qt }$

One quart is equivalent to 2 pints, so pints can be converted to quarts by dividing by conversion factor 2:

$y \textup{ pt } \div 2 \textup{ pt/qt} = \frac{y}{2} \textup{ qt}$

Added together:

$64 \textup{ qt }+ \frac{y}{2} \textup{ qt}$

$= \frac{128}{2} \textup{ qt }+ \frac{y}{2} \textup{ qt}$

$= \frac{y+128}{2} \textup{ qt }$ ,

the correct response.

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Question

Rewrite the sum of gallons and 10 pints as a number of quarts.

Answer

One gallon is equivalent to 4 quarts, so gallons can be converted to quarts by multiplying by conversion factor 4:

$x \textup{ gal } \times 4\textup{ qt/gal} = 4x \textup{ qt }$

One quart is equivalent to 2 pints, so 10 pints can be converted to quarts by dividing by conversion factor 2:

$10 \textup{ pt } \div 2 \textup{ pt/qt} = 5 \textup{ qt}$

Added together:

$4x \textup{ qt }+ 5 \textup{ qt } = 4x+5 \textup{ qt }$ ,

the correct response.

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Question

Rewrite the sum of meters and 50 millimeters as a number of centimeters.

Answer

One meter is equivalent to 100 centimeters, so meters can be converted to centimeters by multiplying by conversion factor 100:

$x \textup{ m} \times 100 \textup{ cm/m} = 100x \textup{ cm}$

One centimeter is equivalent to 10 millimeters, so 50 millimeters can be converted to centimeters by dividing by conversion factor 10:

$50 \textup{ mm} \div 10 \textup{ mm/cm} = 5 \textup{ cm}$

Add these quantities:

$100x \textup{ cm} + 5 c= 100x + 5 \textup{ cm}$ ,

the correct response.

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Question

Rewrite the sum of 2 meters and millimeters as a number of centimeters.

Answer

One meter is equivalent to 100 centimeters, so 2 meters can be converted to centimeters by multiplying by conversion factor 100:

$2 \textup{ m} \times 100 \textup{ cm/m} = 200 \textup{ cm}$

One centimeter is equivalent to 10 millimeters, so millimeters can be converted to centimeters by dividing by conversion factor 10:

$y \textup{ mm} \div 10 \textup{ mm/cm} = \frac{y}{10} \textup{ cm}$

Add these quantities:

$200 \textup{ cm}+ \frac{y}{10} \textup{ cm}$

$=200 + \frac{y}{10} \textup{ cm}$

$=\frac{2,000}{10} + \frac{y}{10} \textup{ cm}$

$= \frac{y+2,000}{10} \textup{ cm}$ ,

the correct answer.

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Question

Rewrite the sum of feet and 18 inches as a number of yards.

Answer

One yard is equivalent to 3 feet, so feet can be converted to yards by dividing by the conversion factor 3:

$x \textup{ ft} \div 3\textup{ yd/ft} = \frac{x}{3} \textup{ yd}$

Also, one yard is equal to 36 inches, so 18 inches can be converted to yards by dividing by the conversion factor 36;

$18 \textup{ in} \div 36\textup{ in /yd} = \frac{18}{36} \textup{ yd} = \frac{1}{2} \textup{ yd}$

Add these quantities:

$\frac{x}{3} + \frac{1}{2} \textup{ yd}$

Rewriting with the least common denominator, which is 6:

$= \frac{x \times 2}{3\times 2} + \frac{1\times 3}{2\times 3} \textup{ yd}$

$= \frac{2x }{6} + \frac{ 3}{6} \textup{ yd}$

$= \frac{2x+3}{6} \textup{ yd}$ ,

the correct choice.

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Question

Rewrite the sum of 2 feet and inches as a number of yards.

Answer

One yard is equivalent to 3 feet, so 2 feet can be converted to yards by dividing by the conversion factor 3:

$2\textup{ ft} \div 3\textup{ yd/ft} = \frac{2}{3} \textup{ yd}$

Also, one yard is equal to 36 inches, so inches can be converted to yards by dividing by the conversion factor 36;

$y\textup{ in} \div 36\textup{ in /yd} = \frac{y}{36} \textup{ yd}$

Add these quantities:

$\frac{2}{3} \textup{ yd} + \frac{y}{36} \textup{ yd}$

$\frac{2}{3} + \frac{y}{36} \textup{ yd}$

Rewriting with the least common denominator, which is 36:

$=\frac{2 \times 12 }{3 \times 12} + \frac{y}{36} \textup{ yd}$

$=\frac{24}{36} + \frac{y}{36} \textup{ yd}$

$=\frac{y+24}{36} \textup{ yd}$ ,

the correct choice.

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Question

Rewrite the sum of milligrams and centigrams in terms of grams.

Answer

One gram is equivalent to 1,000 milligrams, so milligrams can be converted to grams by dividing by conversion factor 1,000:

$x \textup{ mg} \div 1,000 \textup{ mg/g} = \frac{x}{1,000}\textup{ g }$

One gram is also equivalent to 100 centigrams, so centigrams can be converted to grams by dividing by conversion factor 100:

$y \textup{ cg} \div 100 \textup{ cg/g} = \frac{y}{100}\textup{ g }$

Add:

$\frac{x}{1,000}\textup{ g } + \frac{y}{100}\textup{ g }$

$=\frac{x}{1,000} + \frac{y}{100}\textup{ g }$

Rewrite in terms of lowest common denominator 1,000:

$=\frac{x}{1,000} + \frac{y \cdot 10 }{100 \cdot 10 }\textup{ g }$

$=\frac{x}{1,000} + \frac{10y }{1,000 }\textup{ g }$

$=\frac{x+10y }{1,000 }\textup{ g }$ ,

the correct response.

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Question

A rectangular plot of land measures one-half of a mile by one-tenth of a mile.

Give its area in acres.

Answer

The measure of a rectangular plot of land is equal to the product of its dimensions, so the given plot has area

$\frac{1}{2} \textup{ mi} \times \frac{1}{10} \textup{ mi}$

$= \frac{1}{2} \times \frac{1}{10} \textup{ mi}^{2}$

$= \frac{1\times 1}{2 \times 10} \textup{ mi}^{2}$

$= \frac{1 }{2 0} \textup{ mi}^{2}$

One square mile is equivalent to 640 acres, so multiply this by conversion factor 640:

$\frac{1 }{2 0} \textup{ mi}^{2} \times 640 \textup{ acres / mi }^{2}$

$= \frac{1 }{2 0} \times \frac{640}{1} \textup{ acres }$

$= 32 \textup{ acres }$ ,

the correct response.

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Question

A rectangular plot of land measures 72 acres in area. The north-to-south length of the plot is one fourth of a mile. Give the east-to-west length of the plot.

Answer

One square mile is equivalent to 640 acres. Therefore, the area of the plot, 72 acres, can be converted to square miles by dividing by conversion factor 640:

$\frac{72 \textup{ acres}}{640 \textup{ acres/mi}^{2}} = \frac{9}{80} \textup{ mi}^{2}$

If we let and be the north-south and east-west lengths in miles of the rectangular land plot, respectively, then

$xy = \frac{9}{80}$

Substitute $\frac{1}{4}$ for :

$\frac{1}{4}y = \frac{9}{80}$

Solve for by multiplying both sides by 4:

$4 \cdot \frac{1}{4}y = 4 \cdot \frac{9}{80}$

$y = \frac{36}{80} = \frac{9}{20}$

The east-west length of the plot is $\frac{9}{20}$ mile.

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Question

One cup of water is poured out of a pitcher containing one gallon of water. How many cups are left in the pitcher?

Answer

One gallon is equivalent to 4 quarts.

One quart is equivalent to 2 pints.

One pint is equivalent to 2 cups.

Therefore, one gallon is equivalent to $4 \times 2 \times 2 = 16$ cups.

Pouring out one cup leaves 15 cups, the correct response.

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Question

Give the area, in acres, of a square plot of land with sidelength 528 yards.

Answer

528 yards, the sidelength of the square plot, can be converted to square miles as follows:

1,760 yards are equivalent to one mile. Therefore, 528 can be divided by conversion factor 1,760:

$\frac{528\textup{ yd} }{1,760 \textup{ yd/mi}} = 0.3\textup{ mi}$

The area of the plot is equal to the square of this, or

$0.3 \textup{ mi} \times 0.3\textup{ mi}$

$=0.09 \textup{ mi}^{2}$

One square mile is equivalent to 640 acres, so multiply by conversion factor 640:

$=0.09\textup{ mi}^{2} \times 640 \textup{ acres/mi} ^{2}$

$=0.09\times 640 \textup{ acres}$

$= 57.6 \textup{ acres}$ ,

the correct response.

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Question

One meter is equal to about 39.37 inches. Convert 30 inches to centimeters. (Nearest tenth)

Answer

This problem can be solved using a proportion statement.

One meter is equal to 100 centimeters, which in turn is equal to 39.37 inches. Letting be the centimeter equivalent of 30 inches, the proportion statement that relates centimeters and inches can be written

$\frac{x}{30 \textup{ in}}=\frac{100\textup{ cm}}{39.37 \textup{ in}}$

Multiply both sides by 30:

$\frac{x}{30 \textup{ in}} \times 30 \textup{ in} =\frac{100\textup{ cm}}{39.37 \textup{ in}} \times 30 \textup{ in}$

$x =\frac{3,000\textup{ cm}}{39.37 }$

$x \approx 76.2\textup{ cm}$

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Question

In acres, give the area of a square plot of land three and one half miles in sidelength.

Answer

A square plot of land has as its area the square of the length of a side, so the land in question has area

$3 \frac{1}{2} \times 3 \frac{1}{2} = \frac{7}{2} \times \frac{7}{2} = \frac{49}{4} = 12\frac{1}{4}$ square miles.

One square mile is equal to 640 acres, so multiply this by the conversion factor 640:

$12\frac{1}{4} \textup{ mi}^{2} \times 640 \textup{ acres / }\textup{mi}^{2} = 7,840 \textup{ acres }$

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