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

$\frac{y+128}{2}$ quarts

CORRECT

$\frac{y+64}{2}$ quarts

$\frac{y+64}{4}$ quarts

$\frac{y+128}{4}$ quarts

None of the other choices gives the correct response.

Explanation

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.

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

quarts

CORRECT

$\frac{4x+ 5}{2}$ quarts

quarts

$\frac{2x+ 5}{2}$ quarts

quarts

Explanation

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.

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

centimeters

CORRECT

centimeters

$100x + \frac{1}{2}$ centimeters

Explanation

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.

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

$\frac{y+2,000}{10}$ centimeters

CORRECT

centimeters

$\frac{y+2}{10}$ centimeters

centimeters

Explanation

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.

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

$\frac{y+24}{36}$ yards

CORRECT

$\frac{y+12}{36}$ yards

$\frac{36y+2}{3}$ yards

$\frac{108y+2}{3}$ yards

yards

Explanation

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.

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

$\frac{2x+3}{6}$ yards

CORRECT

$\frac{3x+2}{6}$ yards

$\frac{2x+1}{6}$ yards

$\frac{x+2}{6}$ yards

$\frac{3x+1}{6}$

Explanation

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.

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

7,840 acres

CORRECT

3,920 acres

15,680 acres

4,480 acres

2,240 acres

Explanation

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:

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

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

57.6 acres

CORRECT

19.2 acres

38.4 acres

52.8 acres

19.2 acres

Explanation

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.

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.

$\frac{9}{20}$ mile.

CORRECT

$\frac{9}{80}$ mile

$1\frac{4}{5}$ miles

$2\frac{2}{9}$ miles

$\frac{2}{9}$ mile

Explanation

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:

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