Multiplying Real Numbers Algebra

Boxes of nails are stacked on top of each other on a work bench. The table shows how the height above the floor of the topmost box depends on the number of boxes. What is the rule for height? Give the rule in words and as an algebraic expression.

• The height is the product of 39 and 9 plus number of boxes, n. The rule is 39(9+n)

• The height is the sum of 39 and 9 times the number of boxes, n. The rule is 9n + 39.

• The height is the product of 9 and 39 plus the number of boxes, n. The rule is 9(n + 39)

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Select all that are true about multiplying by -1

• (-1)(345) = -345

• -1 times a number equals its opposite

• -1 times a number = the same number

• (-1)(-1) = 1

Tags

CCSS.7.NS.A.2A

CCSS.7.NS.A.2B

Which are true regarding the multiplicative inverse:

• two numbers with a product of 1

• two numbers with a negative product

• multiplicative inverse of 4/5 = 5/4

• multiplicative inverse of 4/5 = -4/5

If a = 4 and b = (-3), find ab.

• -12

• 12

• -3/4

• -4/3

Answer explanation

$ab=4\cdot\left(-3\right)=-12$

Tags

CCSS.7.NS.A.2A

CCSS.7.NS.A.2B

If b = (-3) and c = (-1/2), find bc.

• 3/2

• -3/2

• 6

• -6

Answer explanation

$bc=\left(-3\right)\cdot\left(-\frac{1}{2}\right)=\frac{3}{2}$

Tags

CCSS.7.NS.A.2A

If p is positive and n is negative, pn is

• positive

• negative

• zero

• undefined

Answer explanation

positive times negative = negative
e.g.

$2\cdot\left(-3\right)=-6$

Tags

CCSS.7.NS.A.2A

CCSS.7.NS.A.2B

If p is positive and n is negative, -(pn) is

• positive

• negative

• zero

• undefined

Answer explanation

There are two negative signs in this expression, therefore the result is positive.
E.g. $-\left(3\cdot\left(-2\right)\right)=6$

Tags

CCSS.7.NS.A.2A

CCSS.7.NS.A.2B

What is the sign of the product of an even number of factors with the same sign?

• Positive

• Negative

• It depends

Answer explanation

Pairs of numbers produce a positive product/quotient.

Tags

CCSS.7.NS.A.2A

What is the sign of the product of an odd number of negative factors?

• Positive

• Negative

• It depends

Answer explanation

$\left(-2\right)\left(-2\right)\left(-2\right)=4\left(-2\right)=-8$
Any pair of negative numbers produces a positive product. Multiplying it by another negative will produce a negative product.

Tags

CCSS.3.OA.D.9