These are dynamically generated statements for the following real number properties for equality. These statements will be unique every time you visit the page. The correct options will be from;
Reflexive Property
Symmetric Property
Transitive Property
Additive Property
Multiplicative Property
Cancellation Property w.r.t. Addition and Multiplication
Enter the property name and click submit. See the explanation for why a given answer is correct. Best of luck.
Name the property used in the following equation
b=h⇒h=b
Your answer:
Correct answer:Symmetric Property
❌ Incorrect. Give it another look!
This demonstrates the Symmetric Property, which states that if one number is equal to another, then the second is equal to the first.
That is, if a=b, then b=a.
The formal statement is: For all a,b∈R,if a=b then b=a.
Name the property used in the following equation
w=−2⇒w×118=−2×118
Your answer:
Correct answer:Multiplicative Property
❌ Incorrect. Give it another look!
This demonstrates the Multiplicative Property of Equality: multiplying both sides of an equation by the same number preserves equality.
That is, if a=b, then a×c=b×c.
The formal statement is: For all a,b,c∈R,a=b⇒a×c=b×c.
Name the property used in the following equation
a=g∧g=−1413⇒a=−1413
Your answer:
Correct answer:Transitive Property
❌ Incorrect. Give it another look!
This demonstrates the Transitive Property of Equality: if one quantity equals a second, and the second equals a third, then the first equals the third.
That is, if a=b∧b=c, then a=c.
The formal statement is: For all a,b,c∈R,a=b∧b=c⇒a=c.
Name the property used in the following equation
v=5⇒v+(−10)=5+(−10)
Your answer:
Correct answer:Additive Property
❌ Incorrect. Give it another look!
This demonstrates the Additive Property of Equality: adding the same value to both sides of an equation preserves equality.
That is, if a=b, then a+c=b+c.
The formal statement is: For all a,b,c∈R,a=b⇒a+c=b+c.
Name the property used in the following equation
11=y⇒y=11
Your answer:
Correct answer:Symmetric Property
❌ Incorrect. Give it another look!
This demonstrates the Symmetric Property, which states that if one number is equal to another, then the second is equal to the first.
That is, if a=b, then b=a.
The formal statement is: For all a,b∈R,if a=b then b=a.
Name the property used in the following equation
s=9⇒s×(−1313)=9×(−1313)
Your answer:
Correct answer:Multiplicative Property
❌ Incorrect. Give it another look!
This demonstrates the Multiplicative Property of Equality: multiplying both sides of an equation by the same number preserves equality.
That is, if a=b, then a×c=b×c.
The formal statement is: For all a,b,c∈R,a=b⇒a×c=b×c.
Name the property used in the following equation
z=−15⇒z+(−13)=−15+(−13)
Your answer:
Correct answer:Additive Property
❌ Incorrect. Give it another look!
This demonstrates the Additive Property of Equality: adding the same value to both sides of an equation preserves equality.
That is, if a=b, then a+c=b+c.
The formal statement is: For all a,b,c∈R,a=b⇒a+c=b+c.
Name the property used in the following equation
−9=−9
Your answer:
Correct answer:Reflexive Property
❌ Incorrect. Give it another look!
This demonstrates the Reflexive Property, which states that any real number is equal to itself.
That is, a=a.
The full mathematical statement is: For all a∈R,a=a.
Name the property used in the following equation
−6=−6
Your answer:
Correct answer:Reflexive Property
❌ Incorrect. Give it another look!
This demonstrates the Reflexive Property, which states that any real number is equal to itself.
That is, a=a.
The full mathematical statement is: For all a∈R,a=a.
Name the property used in the following equation
z=11⇒z+7=11+7
Your answer:
Correct answer:Additive Property
❌ Incorrect. Give it another look!
This demonstrates the Additive Property of Equality: adding the same value to both sides of an equation preserves equality.
That is, if a=b, then a+c=b+c.
The formal statement is: For all a,b,c∈R,a=b⇒a+c=b+c.
This demonstrates the Cancellation Property w.r.t. Multiplication: if the same value is multiplied on both sides of an equation, it can be removed (canceled) without affecting the equality.
That is, if a×c=b×c then a=b.
Formally: For all a,b,c∈R,a∘c=b∘c⇒a=b where ∘ is ×.
Name the property used in the following equation
s=−4⇒s×(−3)=−4×(−3)
Your answer:
Correct answer:Multiplicative Property
❌ Incorrect. Give it another look!
This demonstrates the Multiplicative Property of Equality: multiplying both sides of an equation by the same number preserves equality.
That is, if a=b, then a×c=b×c.
The formal statement is: For all a,b,c∈R,a=b⇒a×c=b×c.
Name the property used in the following equation
y=w∧w=5⇒y=5
Your answer:
Correct answer:Transitive Property
❌ Incorrect. Give it another look!
This demonstrates the Transitive Property of Equality: if one quantity equals a second, and the second equals a third, then the first equals the third.
That is, if a=b∧b=c, then a=c.
The formal statement is: For all a,b,c∈R,a=b∧b=c⇒a=c.
Name the property used in the following equation
s=b∧b=x⇒s=x
Your answer:
Correct answer:Transitive Property
❌ Incorrect. Give it another look!
This demonstrates the Transitive Property of Equality: if one quantity equals a second, and the second equals a third, then the first equals the third.
That is, if a=b∧b=c, then a=c.
The formal statement is: For all a,b,c∈R,a=b∧b=c⇒a=c.
This demonstrates the Cancellation Property w.r.t. Addition: if the same value is added to both sides of an equation, it can be removed (canceled) without affecting the equality.
That is, if a+c=b+c then a=b.
Formally: For all a,b,c∈R,a∘c=b∘c⇒a=b where ∘ is +.
Identify Properties of Equality – Interactive Exercise | Fazeel