Question

For each equation, write two more equations using the same numbers that express the same relationship in a different way. a. 3 * 2 = 6 b. 2 + 3 = 5 c. 6 - 3 = 3 d. 2 / 1 = 2

Answer 1

Two equivalent equations can be formed for each given equation by rearranging the numbers or using inverse operations. These demonstrate the properties of addition, multiplication, and their respective inverse operations, subtraction and division.

Step-by-step explanation:

For each equation, two more equivalent equations using the same numbers can be written by rearranging the numbers or applying the commutative property of addition and multiplication. This understanding can help in solving equations and understanding the properties of numbers.

• For the equation 3 * 2 = 6, two more equivalent equations are:
• 2 * 3 = 6 (Commutative property of multiplication)
• 6 / 3 = 2 (Inverse operation of multiplication)

• For the equation 2 + 3 = 5, two more equivalent equations are:
• 3 + 2 = 5 (Commutative property of addition)
• 5 - 2 = 3 (Inverse operation of addition)

• For the equation 6 - 3 = 3, two more equivalent equations are:
• 3 + 3 = 6 (Inverse operation showing the additive relationship)
• 9 - 6 = 3 (Subtraction property of equality)

• For the equation 2 / 1 = 2, two more equivalent equations are:
• 2 * 1 = 2 (Inverse operation of division)
• 2 / 2 = 1 (Division by the resultant instead of the divisor)

Through these examples, one can see that understanding the relationships between operations, such as the inverse relationship between multiplication and division, or addition and subtraction, is crucial in forming equivalent equations.