Prealgebra: Intro to Algebra
Name: _______________________________________________ Topic B6: Simplifying Algebraic Expressions | VERSION A Apply the associative property to these expressions, and then simplify the result. Apply the distributive property to these expressions, and then simplify: 1.
−2 5ℎ = 7.
5 ℎ + 1 = 2.
14 + 19 + 𝑗 = 8.
9 𝑑 − 8 = 3.
4 10𝑧 = 9.
2 3𝑢 + 11 = 4.
9 −11𝑢 = 10. 4 𝑠 − 𝑞 = 5.
17𝑑 + 1 + 6 = 11. 5 1 + 𝑚 = 6.
15𝑘 + 3 + 1 = 12. 8 7𝑤 + 6 = www.varsitylearning.com 1 Prealgebra: Intro to Algebra
Name: _______________________________________________ Topic B6: Simplifying Algebraic Expressions | VERSION A 13. 9 2𝑏 − 𝑘 = 18. Find the area and perimeter for a rectangle if the length is 𝑙 = 15 miles and the width is 𝑤 =
24 miles. a.
The area is mi². b.
The perimeter is mi. 14. 8 9𝑥 − 𝑦 = 19. Find the area and perimeter for a rectangle if the length is 𝑙 = 130 yards and the width is 𝑤 = 190 yards. 15. 5 6 − 7𝑐 = 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 yd². b.
The perimeter is yd. 20. Find the area and perimeter for a rectangle if the length is 𝑙 = 160 yards and the width is 𝑤 = 210 yards. a.
The area is yd². b.
The perimeter is yd. 16. 77°F = °C 17. 40.1°F = °C www.varsitylearning.com 2 Prealgebra: Intro to Algebra
Name: _______________________________________________ Topic B6: Simplifying Algebraic Expressions | VERSION A Apply the associative property to these expressions, and then simplify the result. Apply the distributive property to these expressions, and then simplify: 1.
−2 5ℎ = -­‐10h 7.
5 ℎ + 1 = 5ℎ + 5 2.
14 + 19 + 𝑗 = 33 + j 8.
9 𝑑 − 8 = 9𝑑 − 72 3.
4 10𝑧 = 40𝑧 9.
2 3𝑢 + 11 = 6𝑢 + 22 4.
9 −11𝑢 = −99𝑢 10. 4 𝑠 − 𝑞 = 4𝑠 − 4𝑞 5.
17𝑑 + 1 + 6 = 17𝑑 + 7 11. 5 1 + 𝑚 = 5 + 5𝑚 6.
15𝑘 + 3 + 1 = 15𝑘 = 4 12. 8 7𝑤 + 6 = 56𝑤 + 48 www.varsitylearning.com 3 Prealgebra: Intro to Algebra
Name: _______________________________________________ Topic B6: Simplifying Algebraic Expressions | VERSION A 13. 9 2𝑏 − 𝑘 = 18𝑏 − 9𝑘 18. Find the area and perimeter for a rectangle if the length is 𝑙 = 15 miles and the width is 𝑤 =
24 miles. a.
The area is 360 mi². b.
The perimeter is 78 mi. 14. 8 9𝑥 − 𝑦 = 72𝑥 − 8𝑦 19. Find the area and perimeter for a rectangle if the length is 𝑙 = 130 yards and the width is 𝑤 = 190 yards. 15. 5 6 − 7𝑐 = 30 − 35𝑐 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 24,700 yd². b.
The perimeter is 640 yd. 20. Find the area and perimeter for a rectangle if the length is 𝑙 = 160 yards and the width is 𝑤 = 210 yards. a.
The area is 33,600 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. 77°F = 25 °C 17. 40.1°F = 4.5 °C www.varsitylearning.com 4