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Find the number that makes each equation true. Draw a diagram if it is helpful. 12/5 = 12 x ____ 12/5 = 3 x...

1. Find the number that makes each equation true. Draw a diagram if it is helpful.
12/5 = 12 x ____
12/5 = 3 x ____
12/5 = 6 x ____
12/5 = 2 x ____
12/5 = 4 x ____
12/5 = 1 x ____
2. Here are two sets of numbers:
Set A: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Set B: 1/7, 2/7, 3/7, 4/7, 5/7, 6/7, 7/7
a. Choose a number from Set A and a number from Set B to complete this equation and make it true:
6/7 x _____ x _____
b. Choose a different number from Set A and from Set B to complete the equation to make it true.
6/7 x _____ x _____
3. Explain or show how you know that the two equations you wrote are both true.

Answer

  1. 12/5 = 12 x 1/5

    12/5 = 3 x 4/5

    12/5 = 6 x 2/5

    12/5 = 2 x 6/5

    12/5 = 4 x 3/5

    12/5 = 1 x 12/5

    1. Choose 7 from Set A and 1/7 from Set B: 6/7 x 7 x 1/7 = 6/7

    2. Choose 1 from Set A and 6/7 from Set B: 6/7 x 1 x 6/7 = 36/49

  2. The first equation is true because multiplying by 7 and then by 1/7 cancels out, leaving 6/7. The second equation is true because multiplying by 1 does not change the value, and multiplying 6/7 by itself results in 36/49.

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