Prealgebra: Intro to Algebra
Name: _______________________________________________ Topic B6: Simplifying Algebraic Expressions | VERSION B Apply the associative property to these expressions, and then simplify the result. Apply the distributive property to these expressions, and then simplify: 1.
−3 9𝑞 = 7.
9 𝑏 + 5 = 2.
13 + 14 + 𝑏 = 8.
2 𝑘 − 8 = 3.
4 12𝑐 = 9.
4 2𝑞 + 9 = 4.
6 −8𝑐 = 10. 3 𝑞 − 𝑠 = 5.
4𝑛 + 3 + 6 = 11. 3 9 + 𝑐 = 6.
13𝑦 + 1 + 2 = 12. 3 2𝑣 + 1 = www.varsitylearning.com 1 Prealgebra: Intro to Algebra
Name: _______________________________________________ Topic B6: Simplifying Algebraic Expressions | VERSION B 13. 3 7𝑏 − 3𝑠 = 18. Find the area and perimeter for a rectangle if the length is 𝑙 = 2,500 kilometers and the width is 𝑤 = 20 kilometers. a.
The area is km². b.
The perimeter is km. 14. 3 9𝑥 − 𝑦 = 19. Find the area and perimeter for a rectangle if the length is 𝑙 = 180 mm and the width is 𝑤 = 150 mm. 15. 2 5 − 7𝑗 = In the metric system, the scale we use to measure temperature is the Celsius scale. On this scale, water boils at 100 degrees and freezes at 0 degrees. When we write 100 degrees measured on the Celsius scale, we use the notation 100°C, which is read “100 degrees Celsius.” If we know the temperature in degrees Fahrenheit, we can convert to degrees Celsius by using the formula 5 𝐹 − 32
𝐶=
9
where 𝐹 is the tempreature in degrees Fahrenheit. Use the formula to find the temperature in degrees Celsius: a.
The area is mm². b.
The perimeter is mm. 20. Find the area and perimeter for a rectangle if the length is 𝑙 = 140 yards and the width is 𝑤 = 230 yards. a.
The area is yd². b.
The perimeter is yd. 16. 23°F = °C 17. 65.3°F = °C www.varsitylearning.com 2 Prealgebra: Intro to Algebra
Name: _______________________________________________ Topic B6: Simplifying Algebraic Expressions | VERSION B Apply the associative property to these expressions, and then simplify the result. Apply the distributive property to these expressions, and then simplify: 1.
−3 9𝑞 = −27𝑞 7.
9 𝑏 + 5 = 9𝑏 + 45 2.
13 + 14 + 𝑏 = 27 + 𝑏 8.
2 𝑘 − 8 = 2𝑘 − 16 3.
4 12𝑐 = 48𝑐 9.
4 2𝑞 + 9 = 8𝑞 + 36 4.
6 −8𝑐 = −48𝑐 10. 3 𝑞 − 𝑠 = 3𝑞 − 3𝑠 5.
4𝑛 + 3 + 6 = 4𝑛 + 9 11. 3 9 + 𝑐 = 27 + 3𝑐 6.
13𝑦 + 1 + 2 = 13𝑦 + 3 12. 3 2𝑣 + 1 = 6𝑣 + 3 www.varsitylearning.com 3 Prealgebra: Intro to Algebra
Name: _______________________________________________ Topic B6: Simplifying Algebraic Expressions | VERSION B 13. 3 7𝑏 − 3𝑠 = 21𝑏 − 9𝑠 18. Find the area and perimeter for a rectangle if the length is 𝑙 = 2,500 kilometers and the width is 𝑤 = 20 kilometers. a.
The area is 50,000 km². b.
The perimeter is 5,040 km. 14. 3 9𝑥 − 𝑦 = 27𝑥 − 3𝑦 19. Find the area and perimeter for a rectangle if the length is 𝑙 = 180 mm and the width is 𝑤 = 250 mm. 15. 2 5 − 7𝑗 = 10 − 14𝑗 In the metric system, the scale we use to measure temperature is the Celsius scale. On this scale, water boils at 100 degrees and freezes at 0 degrees. When we write 100 degrees measured on the Celsius scale, we use the notation 100°C, which is read “100 degrees Celsius.” If we know the temperature in degrees Fahrenheit, we can convert to degrees Celsius by using the formula 5 𝐹 − 32
𝐶=
9
a.
The area is 45,000 mm². b.
The perimeter is 860 mm. 20. Find the area and perimeter for a rectangle if the length is 𝑙 = 140 yards and the width is 𝑤 = 230 yards. a.
The area is 32,200 yd². b.
The perimeter is 740 yd. where 𝐹 is the tempreature in degrees Fahrenheit. Use the formula to find the temperature in degrees Celsius: 16. 23°F = −5 °C 17. 65.3°F = 18.5 °C www.varsitylearning.com 4