Apply multiplication and division rules

Key notes:

Multiplication Rules

Product of Positive and Negative Numbers

  • (+) × (+) = (+)
  • (-) × (-) = (+)
  • (+) × (-) = (-)
  • (-) × (+) = (-)

Multiplication of Fractions

  • Multiply numerators and multiply denominators.
  • Simplify the fraction if needed.

Multiplication of Decimals

  • Multiply as whole numbers.
  • Count total decimal places in both numbers and place the decimal in the product accordingly.

Multiplication of Exponents (Same Base)

  • am × an = am+n

Division Rules

Quotient of Positive and Negative Numbers

  • (+) ÷ (+) = (+)
  • (-) ÷ (-) = (+)
  • (+) ÷ (-) = (-)
  • (-) ÷ (+) = (-)

Division of Fractions

  • Flip the divisor (reciprocal) and multiply.
  • Simplify if necessary.

Division of Decimals

  • Move the decimal in the divisor to make it a whole number.
  • Move the decimal in the dividend the same number of places.
  • Divide as usual and place the decimal in the quotient.

Division of Exponents (Same Base)

  • am ÷ an = am−n

Order of Operations (PEMDAS/BODMAS)

  • Always follow the correct order when applying multiplication and division:

Parentheses, Exponents, Multiplication/Division (from left to right), Addition/Subtraction (from left to right).

Word Problems

  • Identify whether to multiply or divide based on context.
  • Use units and estimation to check answers.

Learn with an example

🔥The number line shows an unknown number, b.

Is 3b positive or negative?

Determine if b is positive or negative.

The unknown number b is to the left of 0. So, b is negative.

Determine if 3b is positive or negative.

In the expression 3b, 3 is positive and b is negative. The product of a positive number and a negative number is negative. So, 3b is negative.

🔥The number line shows an unknown number, v.

Is 5v positive or negative?

Determine if v is positive or negative.

The unknown number v is to the right of 0. So, v is positive.

Determine if 5v is positive or negative.

In the expression 5v, 5 is positive and v is positive. The product of two positive numbers is positive. So, 5v is positive.

The number line shows an unknown number, z.

Is 3z positive or negative?

  • positive
  • negative

Determine if z is positive or negative.

The unknown number z is to the left of 0. So, z is negative.

Determine if 3z is positive or negative.

In the expression 3z, 3 is positive and z is negative. The product of a positive number and a negative number is negative. So, 3z is negative.

Let’s practice!🖊️