Question

equality
practice

1. if 6 + 2 = 8, does 6 + 2 + 3 = 8 + 3? why or why not?
2. if 8 - 1 = 7, does 8 - 1 - 2 = 7 - 3? why or why not?
3. if 4 + 6 = 10, does (4 + 6) × 3 = 10 × 3? why or why not?
4. if 5 + 4 = 9, does (5 + 4) ÷ 3 = 9 ÷ 4? why or why not?

Explanation:

Step1: Evaluate left-hand side (LHS)

$6+2+3 = 11$

Step2: Evaluate right-hand side (RHS)

$8+3 = 11$

Step3: Compare LHS and RHS

$11=11$, so equality holds due to the Addition Property of Equality (adding the same value to both sides of a true equality keeps it true).

Step4: Evaluate LHS of question 2

$8-1-2 = 5$

Step5: Evaluate RHS of question 2

$7-3 = 4$

Step6: Compare LHS and RHS

$5
eq4$, so equality fails because different values were subtracted from each side.

Step7: Evaluate LHS of question 3

$(4+6)\times3 = 10\times3 = 30$

Step8: Evaluate RHS of question 3

$10\times3 = 30$

Step9: Compare LHS and RHS

$30=30$, so equality holds due to the Multiplication Property of Equality (multiplying both sides of a true equality by the same non-zero value keeps it true).

Step10: Evaluate LHS of question 4

$(5+4)\div3 = 9\div3 = 3$

Step11: Evaluate RHS of question 4

$9\div4 = 2.25$

Step12: Compare LHS and RHS

$3
eq2.25$, so equality fails because different values were used to divide each side.

Answer:

1. Yes, because $6+2+3=11$ and $8+3=11$. Adding the same number to both sides of a true equality preserves the equality.
2. No, because $8-1-2=5$ and $7-3=4$. Different numbers were subtracted from each side, so the equality does not hold.
3. Yes, because $(4+6)\times3=30$ and $10\times3=30$. Multiplying both sides of a true equality by the same number preserves the equality.
4. No, because $(5+4)\div3=3$ and $9\div4=2.25$. Different numbers were used to divide each side, so the equality does not hold.