- Convert the larger-unit part to the requested unit first. - Add only after both parts use the same unit. - Use square-unit conversion factors, not length conversion factors.

1. Since \(2\,\text{yd}^2=18\,\text{ft}^2\), adding \(3\,\text{ft}^2\) gives \(21\,\text{ft}^2\). 2. Since \(1\,\text{m}^2=10{,}000\,\text{cm}^2\), adding \(20\,\text{cm}^2\) gives \(10{,}020\,\text{cm}^2\).

a) \(21\,\text{ft}^2\) b) \(10{,}020\,\text{cm}^2\)

- Use the area conversion factor for each pair of units. - Converting to a smaller unit makes the numerical value larger. - Use \(1\,\text{yd}^2=9\,\text{ft}^2\).

1. \(12\times 10{,}000=120{,}000\,\text{cm}^2\). 2. \(0.5\times 10{,}000=5000\,\text{cm}^2\). 3. \(7\times 9=63\,\text{ft}^2\). 4. \(13.4\times 100=1340\,\text{mm}^2\).

a) \(120{,}000\,\text{cm}^2\) b) \(5000\,\text{cm}^2\) c) \(63\,\text{ft}^2\) d) \(1340\,\text{mm}^2\)

- Convert each pair to a common unit before comparing. - Use area conversion factors. - Check whether the converted numerical values are equal.

1. \(5\,\text{m}^2=50{,}000\,\text{cm}^2\), so \(5\,\text{m}^2>45{,}000\,\text{cm}^2\). 2. \(0.2\times9=1.8\,\text{ft}^2\), so the measurements are equal. 3. \(8.5\,\text{cm}^2=850\,\text{mm}^2\), so the measurements are equal. 4. \(1\,\text{ft}^2=144\,\text{in}^2\), so \(1\,\text{ft}^2<150\,\text{in}^2\).

a) \(>\) b) \(=\) c) \(=\) d) \(<\)

- Identify the area conversion factor for each part. - Converting to a larger unit requires division. - Record each result with the requested square unit.

1. \(1400\div100=14\,\text{cm}^2\). 2. \(252\div9=28\,\text{yd}^2\). 3. \(8000\div10{,}000=0.8\,\text{m}^2\). 4. \(720\div144=5\,\text{ft}^2\).

a) \(14\,\text{cm}^2\) b) \(28\,\text{yd}^2\) c) \(0.8\,\text{m}^2\) d) \(5\,\text{ft}^2\)

- Decide whether the target unit is larger or smaller. - Use \(1\,\text{ft}^2=144\,\text{in}^2\) and \(1\,\text{yd}^2=9\,\text{ft}^2\).

1. \(450\times144=64{,}800\,\text{in}^2\). 2. \(6\times9=54\,\text{ft}^2\). 3. \(288\div9=32\,\text{yd}^2\).

a) \(64{,}800\,\text{in}^2\) b) \(54\,\text{ft}^2\) c) \(32\,\text{yd}^2\)

- Identify the smaller unit in each pair. - Convert the larger-unit part to the smaller unit. - Add the two values after converting.

1. \(7\,\text{yd}^2=63\,\text{ft}^2\), so the total is \(63+2=65\,\text{ft}^2\). 2. \(12\,\text{ft}^2=12\times144=1728\,\text{in}^2\), so the total is \(1728+7=1735\,\text{in}^2\). 3. \(4\,\text{m}^2=40{,}000\,\text{cm}^2\). Adding \(9\,\text{cm}^2\) gives \(40{,}009\,\text{cm}^2\). 4. \(1\,\text{m}^2=10{,}000\,\text{cm}^2\). Adding \(1500\,\text{cm}^2\) gives \(11{,}500\,\text{cm}^2\).

a) \(65\,\text{ft}^2\) b) \(1735\,\text{in}^2\) c) \(40{,}009\,\text{cm}^2\) d) \(11{,}500\,\text{cm}^2\)

- Convert the larger unit to the smaller unit first. - Then add or subtract. - Use \(1\,\text{yd}^2=9\,\text{ft}^2\) and \(1\,\text{ft}^2=144\,\text{in}^2\).

1. \(7\,\text{yd}^2=63\,\text{ft}^2\), so \(63+15=78\,\text{ft}^2\). 2. \(12\,\text{ft}^2=1728\,\text{in}^2\), so \(1728-400=1328\,\text{in}^2\). 3. \(1\,\text{yd}^2=9\,\text{ft}^2\), so \(9+50=59\,\text{ft}^2\).

a) \(78\,\text{ft}^2\) b) \(1328\,\text{in}^2\) c) \(59\,\text{ft}^2\)

- Use \(1\,\text{yd}^2=9\,\text{ft}^2\). - Use \(1\,\text{ft}^2=144\,\text{in}^2\). - Add mixed-unit parts after converting.

1. \(8\times9+3=75\,\text{ft}^2\). 2. \(432\div144=3\,\text{ft}^2\). 3. \(2\times9+5=23\,\text{ft}^2\). 4. \(10\times9=90\,\text{ft}^2\). 5. \(6480\div144=45\,\text{ft}^2\).

a) \(75\,\text{ft}^2\) b) \(3\,\text{ft}^2\) c) \(23\,\text{ft}^2\) d) \(90\,\text{ft}^2\) e) \(45\,\text{ft}^2\)

- Write the area conversion factor for each pair of units. - A larger target unit gives a smaller numerical value. - A smaller target unit gives a larger numerical value.

1. Since \(1\,\text{cm}^2=100\,\text{mm}^2\), divide by \(100\): \(1800\div100=18\). 2. Since \(1\,\text{m}^2=10{,}000\,\text{cm}^2\), multiply by \(10{,}000\): \(0.45\times10{,}000=4500\).

a) divide by \(100\); \(18\,\text{cm}^2\) b) multiply by \(10{,}000\); \(4500\,\text{cm}^2\)

- Square the linear conversion factor from meters to centimeters. - Multiply the given area by the resulting area conversion factor.

1. Since \(1\,\text{m}=100\,\text{cm}\), \(1\,\text{m}^2=100\times 100=10{,}000\,\text{cm}^2\). 2. Multiply by \(10{,}000\): \(0.25\times 10{,}000=2500\,\text{cm}^2\).

\(2500\,\text{cm}^2\); multiply by \(10{,}000\).

- Convert each mixed measurement to square inches. - Use \(1\,\text{ft}^2=144\,\text{in}^2\). - Compare the converted values.

1. \(A=5\times144+4=724\,\text{in}^2\). 2. \(B=540\,\text{in}^2\). 3. \(C=5\times144+40=760\,\text{in}^2\). 4. Since \(760>724>540\), measurement C is greatest.

C: \(5\,\text{ft}^2\ 40\,\text{in}^2\)

- Remember that \(1\,\text{yd}=3\,\text{ft}\), so \(1\,\text{yd}^2=9\,\text{ft}^2\). - Convert both expressions to square feet before comparing. - Divide after completing the unit conversion.

1. Convert \(6\,\text{yd}^2\) to square feet. Since \(1\,\text{yd}^2=9\,\text{ft}^2\), \(6\,\text{yd}^2=54\,\text{ft}^2\). Then \(54\div8=6.75\), so Expression A is \(6.75\,\text{ft}^2\). 2. For Expression B, \(70\div10=7\), so the result is \(7\,\text{ft}^2\). 3. Since \(7>6.75\), Expression B is greater.

Expression B, \(7\,\text{ft}^2\), is greater than Expression A, \(6.75\,\text{ft}^2\).

- Find the combined area of the two sections first. - Express the combined area and the total area in the same unit. - Then write a part-to-whole fraction and simplify it.

1. Add the two sections: \(100+140=240\,\text{yd}^2\). 2. Convert the total area to square yards. Since \(1\,\text{yd}^2=9\,\text{ft}^2\), \(3600\,\text{ft}^2=400\,\text{yd}^2\). 3. Write the part-to-whole fraction and simplify: \(\frac{240}{400}=\frac{3}{5}\).

\(\frac{3}{5}\)

- Use the area conversion factor, not the linear conversion factor. - Decide whether to multiply or divide based on whether the target unit is smaller or larger. - Remember that \(1\,\text{yd}^2=9\,\text{ft}^2\).

1. Since \(1\,\text{m}^2=10{,}000\,\text{cm}^2\), \(0.8\times 10{,}000=8000\,\text{cm}^2\). 2. Since \(1\,\text{cm}^2=100\,\text{mm}^2\), \(12{,}500\div 100=125\,\text{cm}^2\). 3. Since \(1\,\text{yd}^2=9\,\text{ft}^2\), \(5\times 9=45\,\text{ft}^2\). 4. Since \(1\,\text{m}^2=10{,}000\,\text{cm}^2\), \(3400\div 10{,}000=0.34\,\text{m}^2\).

a) \(8000\,\text{cm}^2\) b) \(125\,\text{cm}^2\) c) \(45\,\text{ft}^2\) d) \(0.34\,\text{m}^2\)

- Convert all four measurements to the same unit. - Use \(1\,\text{ft}^2=144\,\text{in}^2\). - Then compare the numerical values.

1. Convert the square-foot measurements to square inches using \(1\,\text{ft}^2=144\,\text{in}^2\). 2. \(30\times 144=4320\,\text{in}^2\), and \(31\times 144=4464\,\text{in}^2\). 3. Compare: \(4320<4400<4464<4500\).

\(30\,\text{ft}^2<4400\,\text{in}^2<31\,\text{ft}^2<4500\,\text{in}^2\)

- Identify the conversion factor for each pair of area units. - Square units use squared conversion factors. - Check whether the missing value should be larger or smaller than the given value.

1. Since \(1\,\text{m}^2=10{,}000\,\text{cm}^2\), \(0.75\,\text{m}^2=7500\,\text{cm}^2\). 2. Since \(1\,\text{yd}^2=9\,\text{ft}^2\), \(252\div 9=28\,\text{yd}^2\). 3. Since \(1\,\text{cm}^2=100\,\text{mm}^2\), \(12\,\text{cm}^2=1200\,\text{mm}^2\). 4. Since \(1\,\text{ft}^2=144\,\text{in}^2\), \(5\times 144=720\,\text{in}^2\).

a) \(\text{cm}^2\) b) \(28\) c) \(\text{mm}^2\) d) \(720\)

- Check each statement against the conversion relationship supplied for that pair of area units. - Be alert to using a linear conversion factor where an area conversion factor is required. - For the acre statement, think about what multiplying by one-half does to the full conversion amount.

1. Statement a is false. Since \(1\,\text{cm}^2=100\,\text{mm}^2\), \(2.4\times100=240\), so \(2.4\,\text{cm}^2=240\,\text{mm}^2\). 2. Statement b is correct because \(7\times100=700\). 3. Statement c is false. Since \(1\,\text{yd}^2=9\,\text{ft}^2\), \(6\times9=54\), so \(6\,\text{yd}^2=54\,\text{ft}^2\). 4. Statement d is correct because half of \(43{,}560\) is \(21{,}780\).

a) False; \(2.4\,\text{cm}^2=240\,\text{mm}^2\). b) Correct. c) False; \(6\,\text{yd}^2=54\,\text{ft}^2\). d) Correct.

- Find each rectangle's area in its labeled unit first. - Convert the two areas to the same square unit before comparing them. - A smaller numerical measurement can represent the same physical length or area when the unit is larger.

1. Rectangle A has area \(30\,\text{cm}\times20\,\text{cm}=600\,\text{cm}^2\). 2. Rectangle B has area \(3\,\text{dm}\times2\,\text{dm}=6\,\text{dm}^2\). 3. Convert the second area: \(6\times100=600\), so \(6\,\text{dm}^2=600\,\text{cm}^2\). 4. The rectangles have equal area, so Diego's claim is not correct. The numerical side lengths cannot be compared without considering their units.

No. Rectangle A has area \(600\,\text{cm}^2\), and rectangle B also has area \(600\,\text{cm}^2\).

- Use \(1\,\text{ft}^2=144\,\text{in}^2\). - Use \(1\,\text{yd}^2=9\,\text{ft}^2\). - Consider which unit is commonly used for room size.

1. Since \(1\,\text{ft}^2=144\,\text{in}^2\), \(12{,}960\div144=90\,\text{ft}^2\). Since \(1\,\text{yd}^2=9\,\text{ft}^2\), \(90\div9=10\,\text{yd}^2\). 2. Square feet is the best unit because room sizes in US real-estate listings are commonly described in square feet, and \(90\) is easy to interpret.

1. \(90\,\text{ft}^2\) and \(10\,\text{yd}^2\) 2. Square feet is the most appropriate unit.

- Use the rectangle area formula. - Use \(1\,\text{yd}^2=9\,\text{ft}^2\). - Compare the square-foot area with \(43{,}560\,\text{ft}^2\) per acre.

1. The area is \(330\times 132=43{,}560\,\text{ft}^2\). 2. Since \(1\,\text{yd}^2=9\,\text{ft}^2\), \(43{,}560\div 9=4840\,\text{yd}^2\). 3. Since \(1\) acre is \(43{,}560\,\text{ft}^2\), the field is exactly \(1\) acre. Acres is reasonable when comparing the field with larger land areas, although square feet or square yards is more direct for one field.

1. \(43{,}560\,\text{ft}^2\) 2. \(4840\,\text{yd}^2\) 3. \(1\) acre; yes, acres is useful for comparison with larger properties.

- Multiply the number of sticky notes by the area of one note. - Use \(1\,\text{ft}^2=144\,\text{in}^2\) to convert.

1. The estimated area is \(40\times9=360\,\text{in}^2\). 2. Since \(1\,\text{ft}^2=144\,\text{in}^2\), \(360\div144=2.5\,\text{ft}^2\).

Approximately \(360\,\text{in}^2\), or \(2.5\,\text{ft}^2\)

- Convert the larger unit to the requested smaller unit first. - Add only after both parts use the same unit. - Remember that area units are squared, so use the area-unit conversion rather than the length-unit conversion.

1. \(6\,\text{yd}^2=6\times9=54\,\text{ft}^2\). Adding \(3\,\text{ft}^2\) gives \(57\,\text{ft}^2\). 2. \(9\,\text{ft}^2=9\times144=1296\,\text{in}^2\). Adding \(4\,\text{in}^2\) gives \(1300\,\text{in}^2\). 3. \(14\,\text{m}^2=14\times10{,}000=140{,}000\,\text{cm}^2\). Adding \(50\,\text{cm}^2\) gives \(140{,}050\,\text{cm}^2\).

a) \(57\,\text{ft}^2\) b) \(1300\,\text{in}^2\) c) \(140{,}050\,\text{cm}^2\)

- Square the length conversion factor when converting area units. - Compare the converted area with \(64\,\text{m}^2\). - A large numerical value can result from using a small square unit.

1. Since \(1\,\text{m}=100\,\text{cm}\), one square meter contains \(100\times100=10{,}000\,\text{cm}^2\). 2. Convert the area: \(650{,}000\div10{,}000=65\). Therefore, \(650{,}000\,\text{cm}^2=65\,\text{m}^2\). 3. Since \(65\,\text{m}^2\) is close to \(64\,\text{m}^2\), the measurement is close to the stated classroom size.

\(650{,}000\,\text{cm}^2=65\,\text{m}^2\). Yes, it is close to \(64\,\text{m}^2\).

- Convert both areas to square centimeters. - Remember that area conversion factors are squared. - Compare each converted result with the stated range.

1. Since \(1\,\text{cm}^2=100\,\text{mm}^2\), \(12{,}500\div100=125\). Mateo's measurement is \(125\,\text{cm}^2\), which is in the stated reasonable range. 2. Since \(1\,\text{m}^2=10{,}000\,\text{cm}^2\), \(1.5\times10{,}000=15{,}000\). Julia's measurement is \(15{,}000\,\text{cm}^2\). 3. Julia's value is far outside the stated range, so she made the major error.

Julia is incorrect. Mateo's value is \(125\,\text{cm}^2\), while Julia's value is \(15{,}000\,\text{cm}^2\).

- Recalculate each conversion independently. - Use area conversion factors, not linear conversion factors. - Decide whether the numerical value should increase or decrease.

1. Statement a is incorrect. Since \(1\,\text{cm}^2=100\,\text{mm}^2\), \(300\div 100=3\,\text{cm}^2\). 2. Statement b is incorrect. Since \(1\,\text{yd}^2=9\,\text{ft}^2\), \(15\times 9=135\,\text{ft}^2\). 3. Statement c is correct because \(2000\div 10{,}000=0.2\,\text{m}^2\).

a) Incorrect; \(300\,\text{mm}^2=3\,\text{cm}^2\) b) Incorrect; \(15\,\text{yd}^2=135\,\text{ft}^2\) c) Correct

- Write the conversion factors for each requested unit. - Use multiplication for smaller target units and division for larger target units. - Convert in two steps when helpful.

1. \(810\div9=90\,\text{yd}^2\), and \(810\times144=116{,}640\,\text{in}^2\). 2. \(15{,}000\div10{,}000=1.5\,\text{m}^2\), and \(15{,}000\times100=1{,}500{,}000\,\text{mm}^2\). 3. \(400\times9=3600\,\text{ft}^2\), and \(3600\times144=518{,}400\,\text{in}^2\). 4. \(20{,}736\div144=144\,\text{ft}^2\), and \(144\div9=16\,\text{yd}^2\).

a) \(90\,\text{yd}^2\) and \(116{,}640\,\text{in}^2\) b) \(1.5\,\text{m}^2\) and \(1{,}500{,}000\,\text{mm}^2\) c) \(3600\,\text{ft}^2\) and \(518{,}400\,\text{in}^2\) d) \(144\,\text{ft}^2\) and \(16\,\text{yd}^2\)

- Convert every measurement to square inches. - Use \(1\,\text{ft}^2=144\,\text{in}^2\) and \(1\,\text{yd}^2=1296\,\text{in}^2\). - Then order the numerical values.

1. \(3\,\text{yd}^2=3\times1296=3888\,\text{in}^2\). 2. \(2800\,\text{in}^2\) is already in the target unit. 3. \(31\,\text{ft}^2=31\times144=4464\,\text{in}^2\). 4. \(2\,\text{yd}^2\ 90\,\text{in}^2=2\times1296+90=2682\,\text{in}^2\). 5. Therefore, \(2682<2800<3888<4464\).

\(2\,\text{yd}^2\ 90\,\text{in}^2<2800\,\text{in}^2<3\,\text{yd}^2<31\,\text{ft}^2\)

- Express each square-foot area as a multiple of \(43{,}560\,\text{ft}^2\). - Use \(1\) acre \(=43{,}560\,\text{ft}^2\). - Add the converted areas.

1. Since \(1\) acre is \(43{,}560\,\text{ft}^2\) and \(43{,}560\times 5=217{,}800\), the second field is \(5\) acres. 2. Since \(43{,}560\times 10=435{,}600\), the third field is \(10\) acres. 3. The total area is \(15+5+10=30\) acres.

\(30\) acres

- Convert the known larger-unit measurement to the unit on the right. - Then find the missing difference or addend.

1. \(5\,\text{ft}^2=720\,\text{in}^2\). Therefore, \(720-420=300\), so the missing number is \(300\). 2. \(2\,\text{yd}^2=18\,\text{ft}^2\). Therefore, \(26-18=8\), so the missing number is \(8\).

a) \(300\) b) \(8\)

- Convert the entire left side to the unit used on the right. - Calculate first, then compare.

1. \(4\,\text{ft}^2+9\,\text{in}^2=576\,\text{in}^2+9\,\text{in}^2=585\,\text{in}^2\), and \(585>490\). 2. \(10\,\text{yd}^2-10\,\text{ft}^2=90\,\text{ft}^2-10\,\text{ft}^2=80\,\text{ft}^2\), so the values are equal.

a) \(>\) b) \(=\)

- Convert every measurement to square feet. - Use \(1\,\text{ft}^2=144\,\text{in}^2\) and look for multiples of \(144\). - Match values with equal numerical results.

1. Convert all measurements to square feet. 2. \(A=2\times9+4=22\,\text{ft}^2\). 3. \(B=24\,\text{ft}^2\). 4. Since \(20\times144=2880\) and \(2\times144=288\), \(C=3168\,\text{in}^2=22\,\text{ft}^2\). 5. \(D=2\times9+6=24\,\text{ft}^2\). 6. \(E=240\,\text{ft}^2\). 7. Since \(24\times144=3456\), \(240\times144=34{,}560\), so \(F=240\,\text{ft}^2\).

A and C B and D E and F

- Find the greatest whole-number multiple of the conversion factor that does not exceed the given area. - Express the remainder in the original smaller unit. - Use \(144\), \(9\), or \(10{,}000\) as appropriate.

1. Since \(20\times144=2880\) and \(7\times144=1008\), \(27\times144=3888\). The remainder is \(4005-3888=117\), so \(4005\,\text{in}^2=27\,\text{ft}^2\ 117\,\text{in}^2\). 2. Since \(7\times144=1008\), \(70\times144=10{,}080\). The remainder is \(10{,}200-10{,}080=120\), so \(10{,}200\,\text{in}^2=70\,\text{ft}^2\ 120\,\text{in}^2\). 3. \(807\div9=89\) remainder \(6\), so \(807\,\text{ft}^2=89\,\text{yd}^2\ 6\,\text{ft}^2\). 4. \(30{,}050\div10{,}000=3\) remainder \(50\), so \(30{,}050\,\text{cm}^2=3\,\text{m}^2\ 50\,\text{cm}^2\).

a) \(27\,\text{ft}^2\ 117\,\text{in}^2\) b) \(70\,\text{ft}^2\ 120\,\text{in}^2\) c) \(89\,\text{yd}^2\ 6\,\text{ft}^2\) d) \(3\,\text{m}^2\ 50\,\text{cm}^2\)

- Divide by \(9\) to convert square feet to square yards with a remainder. - For part b, first remove one acre, or \(43{,}560\,\text{ft}^2\). - Convert the remaining square feet to square yards.

1. Since \(1\,\text{yd}^2=9\,\text{ft}^2\), \(56{,}343\div 9=6260\) remainder \(3\). Therefore, the area is \(6260\,\text{yd}^2\ 3\,\text{ft}^2\). 2. One acre is \(43{,}560\,\text{ft}^2\). The remaining area is \(56{,}343-43{,}560=12{,}783\,\text{ft}^2\). 3. \(12{,}783\div 9=1420\) remainder \(3\), so the complete mixed-unit form is \(1\) acre \(1420\,\text{yd}^2\ 3\,\text{ft}^2\).

a) \(6260\,\text{yd}^2\ 3\,\text{ft}^2\) b) \(1\) acre \(1420\,\text{yd}^2\ 3\,\text{ft}^2\)

- Express each target and starting area in the same unit. - Think about what amount completes the starting area to the target. - Check that adding your result to the starting area gives the target.

1. \(1\,\text{yd}^2=9\,\text{ft}^2\), so \(9-5=4\,\text{ft}^2\). 2. \(1\,\text{ft}^2=144\,\text{in}^2\), so \(144-62=82\,\text{in}^2\). 3. \(0.05\,\text{m}^2=500\,\text{cm}^2\), so \(500-450=50\,\text{cm}^2\). 4. \(0.01\,\text{m}^2=100\,\text{cm}^2\), so \(100-8.5=91.5\,\text{cm}^2\).

a) \(4\,\text{ft}^2\) b) \(82\,\text{in}^2\) c) \(50\,\text{cm}^2\) d) \(91.5\,\text{cm}^2\)

- Convert the dividend to one unit. - What happens to the units when one area is divided by another area in the same unit? - Check your quotient by multiplying it by \(3\,\text{ft}^2\). You should get back the total area.

1. Convert the mixed area to square feet: \(6\,\text{yd}^2=54\,\text{ft}^2\), so the total is \(54+6=60\,\text{ft}^2\). 2. Divide: \(60\,\text{ft}^2\div3\,\text{ft}^2=20\). The area units cancel.

\(20\)

- Evaluate the expression inside the grouping symbols first. - Convert the mixed area to square feet. - Then multiply and subtract in order.

1. Convert the mixed area: \(5\,\text{yd}^2\ 2\,\text{ft}^2=45\,\text{ft}^2+2\,\text{ft}^2=47\,\text{ft}^2\). 2. Evaluate inside the grouping symbols: \(18\,\text{ft}^2\div 2=9\,\text{ft}^2\), and \(9\,\text{ft}^2+3\,\text{ft}^2=12\,\text{ft}^2\). 3. Multiply: \(12\,\text{ft}^2\times 2=24\,\text{ft}^2\). 4. Subtract: \(47\,\text{ft}^2-24\,\text{ft}^2=23\,\text{ft}^2\).

\(23\,\text{ft}^2\), or \(2\,\text{yd}^2\ 5\,\text{ft}^2\)

- Compare the square-inch parts before subtracting. - Regroup \(1\,\text{ft}^2\) as \(144\,\text{in}^2\) when needed. - Subtract the square inches and square feet separately.

1. Since \(20\,\text{in}^2\) is less than \(50\,\text{in}^2\), regroup \(1\,\text{ft}^2\) as \(144\,\text{in}^2\). The total area becomes \(179\,\text{ft}^2\ 164\,\text{in}^2\). 2. Subtract the square inches: \(164-50=114\,\text{in}^2\). 3. Subtract the square feet: \(179-90=89\,\text{ft}^2\). Therefore, the remaining area is \(89\,\text{ft}^2\ 114\,\text{in}^2\).

\(89\,\text{ft}^2\ 114\,\text{in}^2\)

- Convert the entire field to square feet. - Use \(1\) acre \(=43{,}560\,\text{ft}^2\). - Divide the total by \(6\).

1. Convert the acres to square feet: \(4\times 43{,}560=174{,}240\,\text{ft}^2\). 2. Add the remaining area: \(174{,}240+21{,}780=196{,}020\,\text{ft}^2\). 3. Divide equally: \(196{,}020\div 6=32{,}670\,\text{ft}^2\).

\(32{,}670\,\text{ft}^2\) per paddock

- Make the wall area and the poster area use the same unit. - Think about how square yards relate to square feet before combining the two parts of the wall area. - Once the units match, ask how many poster-sized areas fit in the wall area.

1. Convert the wall area to square feet: \(6\times9+6=60\,\text{ft}^2\). 2. Divide by the area of one poster: \(60\,\text{ft}^2\div5\,\text{ft}^2=12\).

\(12\) posters

- Convert before rounding. - Use the correct area conversion factor. - Look at the decimal part or use benchmark values to round to the nearest whole unit.

1. \(548\div9\approx60.89\,\text{yd}^2\), which rounds to \(61\,\text{yd}^2\). 2. \(12{,}750\div100=127.5\,\text{cm}^2\), which rounds to \(128\,\text{cm}^2\). 3. Since \(1\,\text{ft}^2=144\,\text{in}^2\), \(142.8\,\text{in}^2\) is slightly less than \(1\,\text{ft}^2\) and greater than \(0.5\,\text{ft}^2\). Therefore, it rounds to \(1\,\text{ft}^2\).

a) \(61\,\text{yd}^2\) b) \(128\,\text{cm}^2\) c) \(1\,\text{ft}^2\)

- Convert before rounding. - Use \(1\,\text{yd}^2=9\,\text{ft}^2\). - For acres, compare the area with nearby whole-number multiples of \(4840\,\text{yd}^2\).

1. \(7420\div 9\approx 824.44\,\text{yd}^2\), which rounds to \(824\,\text{yd}^2\). 2. Since \(1\) acre is \(4840\,\text{yd}^2\), \(5\) acres is \(24{,}200\,\text{yd}^2\) and \(6\) acres is \(29{,}040\,\text{yd}^2\). The given area is \(4290\,\text{yd}^2\) above \(5\) acres but only \(550\,\text{yd}^2\) below \(6\) acres, so it rounds to \(6\) acres.

a) \(824\,\text{yd}^2\) b) \(6\) acres

- Convert each square-foot value before rounding. - Use \(1\,\text{yd}^2=9\,\text{ft}^2\) and \(1\) acre \(=43{,}560\,\text{ft}^2\). - Compare with nearby whole-number acre values.

1. For \(184{,}300\,\text{ft}^2\), \(184{,}300\div9\approx20{,}477.78\,\text{yd}^2\), which rounds to \(20{,}478\,\text{yd}^2\). Four acres is \(174{,}240\,\text{ft}^2\), and five acres is \(217{,}800\,\text{ft}^2\). The given area is closer to four acres, so it rounds to \(4\) acres. 2. For \(75{,}550\,\text{ft}^2\), \(75{,}550\div9\approx8394.44\,\text{yd}^2\), which rounds to \(8394\,\text{yd}^2\). One acre is \(43{,}560\,\text{ft}^2\), and two acres is \(87{,}120\,\text{ft}^2\). The given area is closer to two acres, so it rounds to \(2\) acres.

<table> <tr> <th>Area</th> <th>Nearest square yard</th> <th>Nearest acre</th> </tr> <tr> <td>\(184{,}300\,\text{ft}^2\)</td> <td>\(20{,}478\,\text{yd}^2\)</td> <td>\(4\) acres</td> </tr> <tr> <td>\(75{,}550\,\text{ft}^2\)</td> <td>\(8394\,\text{yd}^2\)</td> <td>\(2\) acres</td> </tr> </table>

- Convert to the smallest unit before calculating. - Use the appropriate area conversion factor. - When equal area units are divided, the units cancel.

1. \(5\,\text{yd}^2=45\,\text{ft}^2\), so \(45+35=80\,\text{ft}^2\). 2. \(2\,\text{yd}^2\ 5\,\text{ft}^2=18+5=23\,\text{ft}^2\). Then \(23\times4=92\,\text{ft}^2\). 3. \(1\) acre is \(43{,}560\,\text{ft}^2\), so \(43{,}560-40{,}000=3560\,\text{ft}^2\). 4. \(12\,\text{ft}^2=1728\,\text{in}^2\), so \(1728\div48=36\). The units cancel.

a) \(80\,\text{ft}^2\) b) \(92\,\text{ft}^2\) c) \(3560\,\text{ft}^2\) d) \(36\)

- Convert mixed areas to one unit before calculating. - Use \(1\,\text{yd}^2=9\,\text{ft}^2\), \(1\,\text{ft}^2=144\,\text{in}^2\), and \(1\,\text{acre}=43{,}560\,\text{ft}^2\). - Decide whether the final result should retain an area unit.

1. \(3\,\text{yd}^2\ 5\,\text{ft}^2=27+5=32\,\text{ft}^2\). Then \(32-12=20\,\text{ft}^2\). 2. \(1\,\text{acre}=43{,}560\,\text{ft}^2\), so the result is \(43{,}559\,\text{ft}^2\). 3. \(4\,\text{ft}^2\ 4\,\text{in}^2=4\times144+4=580\,\text{in}^2\). Then \(580\div5=116\). 4. \(2\,\text{ft}^2\ 50\,\text{in}^2=338\,\text{in}^2\). Then \(12\times338=4056\,\text{in}^2\). Since \(28\times144=4032\), the remainder is \(24\,\text{in}^2\), so the mixed-unit result is \(28\,\text{ft}^2\ 24\,\text{in}^2\).

a) \(20\,\text{ft}^2\) b) \(43{,}559\,\text{ft}^2\) c) \(116\) d) \(4056\,\text{in}^2\), or \(28\,\text{ft}^2\ 24\,\text{in}^2\)

- Convert all land areas to square feet. - Subtract the corn area from the total. - Divide the remainder by \(4\).

1. The total land area is \(4\times 43{,}560+21{,}780=196{,}020\,\text{ft}^2\). 2. The corn area is \(43{,}560\,\text{ft}^2\). 3. The remaining area is \(196{,}020-43{,}560=152{,}460\,\text{ft}^2\). 4. Each vegetable plot has area \(152{,}460\div 4=38{,}115\,\text{ft}^2\).

\(38{,}115\,\text{ft}^2\)

- Check each statement with a complete conversion. - Remember that linear conversion factors must be squared for area units.

1. Statement a is true because \(2\times144=288\,\text{in}^2\). 2. Statement b is false. First convert square yards to square feet by multiplying by \(9\), then convert square feet to square inches by multiplying by \(144\), not \(12\). Therefore, \(3\times9\times144=3888\,\text{in}^2\).

a) True b) False; multiply by \(9\) and then by \(144\). The result is \(3888\,\text{in}^2\).

- Recall the relationship between square yards and square feet. - Convert each mixed area to square feet. - Add only after all three measurements use the same unit.

1. Convert the first mixed area: \(5\,\text{yd}^2\ 3\,\text{ft}^2=5\times9+3=48\,\text{ft}^2\). 2. The second addend is already \(88\,\text{ft}^2\). 3. Convert the third mixed area: \(2\,\text{yd}^2\ 5\,\text{ft}^2=2\times9+5=23\,\text{ft}^2\). 4. Add: \(48+88+23=159\,\text{ft}^2\).

\(159\,\text{ft}^2\)

- Convert each mixed area completely to its smaller unit first. - Multiply or divide the numerical value. - Convert the result back to mixed units.

1. For a), convert to square feet: \(5\,\text{yd}^2\ 3\,\text{ft}^2=5\times9+3=48\,\text{ft}^2\). Then \(48\times8=384\,\text{ft}^2\). Since \(384=42\times9+6\), the result is \(42\,\text{yd}^2\ 6\,\text{ft}^2\). 2. For b), convert to square inches: \(24\,\text{ft}^2\ 48\,\text{in}^2=24\times144+48=3504\,\text{in}^2\). Then \(3504\div6=584\,\text{in}^2\). Since \(584=4\times144+8\), the result is \(4\,\text{ft}^2\ 8\,\text{in}^2\).

a) \(42\,\text{yd}^2\ 6\,\text{ft}^2\) b) \(4\,\text{ft}^2\ 8\,\text{in}^2\)

- Convert every given area to square inches. - Use \(1\,\text{ft}^2=144\,\text{in}^2\). - Subtract each converted area from \(144\,\text{in}^2\).

1. The target area is \(1\,\text{ft}^2=144\,\text{in}^2\). 2. For a), \(144-75=69\,\text{in}^2\). 3. For b), \(0.5\times144=72\,\text{in}^2\), so \(144-72=72\,\text{in}^2\). 4. For c), \(0.25\times144=36\,\text{in}^2\). The given area is \(30+36=66\,\text{in}^2\), so \(144-66=78\,\text{in}^2\).

a) \(69\,\text{in}^2\) b) \(72\,\text{in}^2\) c) \(78\,\text{in}^2\)

- Use the labeled length and width to find the area in square feet. - Then compare the square-foot area with the given number of square feet in one acre. - Check whether the field's area is an exact multiple of one acre.

1. Find the area: \(660\,\text{ft}\times330\,\text{ft}=217{,}800\,\text{ft}^2\). 2. Since \(43{,}560\times5=217{,}800\), the field has an area of \(5\) acres.

\(5\) acres

- Square the conversion factor from kilometers to meters. - Multiply \(0.04\) by the number of square meters in one square kilometer. - Divide the actual area by the reported area to find the scale factor.

1. Since \(1\,\text{km}=1000\,\text{m}\), \(1\,\text{km}^2=1{,}000{,}000\,\text{m}^2\). 2. Convert the official area: \(0.04\times 1{,}000{,}000=40{,}000\). Therefore, the park covers \(40{,}000\,\text{m}^2\). 3. Compare the areas: \(40{,}000\div 400=100\). The actual park is \(100\) times as large as the area stated in the article.

The article is incorrect. \(0.04\,\text{km}^2=40{,}000\,\text{m}^2\), so the actual park is \(100\) times as large as the reported \(400\,\text{m}^2\).