Apply multiplication and division rules

Key notes:

1. Multiplication Rules:

  • Multiplying Integers:
    • Same sign (positive × positive or negative × negative): The product is positive.
    • Different signs (positive × negative or negative × positive): The product is negative.
    • Example:
      • 4×3=12 (positive × positive)
      • −4×3=−12 (negative × positive)
      • −4×−3=12 (negative × negative)
  • Multiplying Fractions:
    • Multiply the numerators together and multiply the denominators together.
    • Example:
      • 2/3 × 3/4 = 6/12 =1/2
  • Multiplying Decimals:
    • Ignore the decimal points, multiply the numbers as whole numbers, and then place the decimal point in the product.
    • Example:
      • 2.5×3.2=8.00

2. Division Rules:

  • Dividing Integers:
    • Same sign (positive ÷ positive or negative ÷ negative): The quotient is positive.
    • Different signs (positive ÷ negative or negative ÷ positive): The quotient is negative.
    • Example:
      • 6÷3=2 (positive ÷ positive)
      • −6÷3=−2(negative ÷ positive)
      • −6÷−3=2 (negative ÷ negative)
  • Dividing Fractions:
    • Invert the divisor (the second fraction) and multiply.

Dividing Decimals:

  • Move the decimal points in the divisor and dividend to make the divisor a whole number, then divide as if with whole numbers.
  • Example:
    • 3.75÷1.5=2.5

Learn with an example

🎈 The number line shows an unknown number, a.

Is 4a positive or negative?

  • positive
  • negative
  • Determine if a is positive or negative.
  • The unknown number a is to the left of 0. So, a is negative.
  • Determine if 4a is positive or negative.
  • In the expression 4a, 4 is positive and a is negative. The product of a positive number and a negative number is negative. So, 4a is negative.

🎈 The number line shows an unknown number, q.

Is 2q positive or negative?

  • positive
  • negative
  • Determine if q is positive or negative.
  • The unknown number q is to the right of 0. So, q is positive.
  • Determine if 2q is positive or negative.
  • In the expression 2q, 2 is positive and q is positive. The product of two positive numbers is positive. So, 2q is positive.

🎈 The number line shows an unknown number, b.

Is 3b positive or negative?

  • positive
  • negative
  • Determine if b is positive or negative.
  • The unknown number b is to the right of 0. So, b is positive.
  • Determine if 3b is positive or negative.
  • In the expression 3b, 3 is positive and b is positive. The product of two positive numbers is positive. So, 3b is positive.

Let’s practice!🖊️