Assessment questions for the four properties of equality

📚 Quick Study Guide

• 🔢 The Addition Property of Equality: If $a = b$, then $a + c = b + c$. Adding the same value to both sides maintains equality.
• ➖ The Subtraction Property of Equality: If $a = b$, then $a - c = b - c$. Subtracting the same value from both sides maintains equality.
• ✖️ The Multiplication Property of Equality: If $a = b$, then $a \* c = b \* c$. Multiplying both sides by the same value maintains equality.
• ➗ The Division Property of Equality: If $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$. Dividing both sides by the same non-zero value maintains equality.

✍️ Practice Quiz

1. What property of equality is demonstrated by the following: If $x = y$, then $x + 5 = y + 5$?
1. Addition Property
2. Subtraction Property
3. Multiplication Property
4. Division Property
2. What property of equality is demonstrated by the following: If $a = b$, then $a - 3 = b - 3$?
1. Addition Property
2. Subtraction Property
3. Multiplication Property
4. Division Property
3. What property of equality is demonstrated by the following: If $m = n$, then $4m = 4n$?
1. Addition Property
2. Subtraction Property
3. Multiplication Property
4. Division Property
4. What property of equality is demonstrated by the following: If $p = q$, then $\frac{p}{2} = \frac{q}{2}$?
1. Addition Property
2. Subtraction Property
3. Multiplication Property
4. Division Property
5. Using the properties of equality, solve for $x$: $x + 7 = 12$
1. $x = 19$
2. $x = 5$
3. $x = -5$
4. $x = -19$
6. Using the properties of equality, solve for $y$: $y - 4 = 8$
1. $y = 4$
2. $y = -4$
3. $y = 12$
4. $y = -12$
7. Using the properties of equality, solve for $z$: $3z = 15$
1. $z = 45$
2. $z = -5$
3. $z = 5$
4. $z = -45$