Question

Y = (5 x 9) + 1 X 9) = 54

MP.8 Generalize

Pam wrote the equations below.

1. Tell how you can use repeated reasoning to find multiplication facts.

# your

on by

2. Which factors did Pam use repeatedly?

Make a generalization.

7 x 6 = (5 x 6) + (2 X 6) = 42

7 x 9 = (5 x 9) + (2 X 9) = 63

7x7 = (5 x 7) + (2 X 7) = 49

- facts.

3. Complete this equation to test whether your generalization is

true for other facts. Explain.

7 X 8=LX+LX) =

Answer 1

Explanation:

1. Given that: y = (5 x 9) + (1 x 9)

= 45 + 9

= 54

Using repeated reasoning;

y = (5 x 9) + (1 x 9)

factoring 9 in the equation, we have;

y = 9 (5 + 1)

= 9 (6)

= 54

2i. 7 x 6 = (5 x 6) + (2 x 6)

= (5 + 2)6

= 7 x 6

= 42

ii. 7 x 9 = (5 x 9) + (2 x 9)

= (5 + 2)9

= 7 x 9

= 63

iii. 7 x 7 = (5 x 7) + (2 x 7)

= (5 + 2)7

= 7 x 7

= 49

Therefore, the factors that Pam used repeatedly are 5 and 2.

3. 7 x 8 = (LX) + (LX)

= X(L + L)

Representing L and X by a number,

7 x 8 = (4 x 7) + (4 x 7)

= 7(4 + 4)

= 7(8)

= 7 x 8

= 56

Thus, the generalization is true.