Math Lab
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Integer Multiplication and Division

Integers · Class VII

Slide two signed integers and watch their product and quotient.

-4
type a value
-1212
3
type a value
-1212
Live values
  • Product-12
  • Quotient-1.3333
  • Sign of product-1
xy
  • y = a * x

Formulas in this lab

  • Product
    a⋅ba \cdot b
  • Quotient
    ab\dfrac{a}{b}
  • Sign of product
    sign(a b)\text{sign}(a\,b)
Tip: Multiplying by a is a straight line through the origin with slope a , negative a tilts it the other way.

Frequently asked questions

▶What is the sign rule for multiplying integers?

Same signs give plus, different signs give minus. So 4 * 3 = 12 and (-4) * (-3) = 12, but 4 * (-3) = -12 and (-4) * 3 = -12. The lab slides a and b through positive and negative values to make this pattern stick.

▶How do I use the integer multiplication lab?

Slide a and b between -12 and 12. The lab shows product a*b and quotient a/b. Try a = -6 and b = 2 to see product -12 and quotient -3, then flip b to -2 and watch both answers turn positive.

▶Why does dividing by zero show an error?

Division by zero is not defined in mathematics. If b = 0, the lab shows NaN (Not a Number) for the quotient because 6/0 has no answer. Many calculators and bank apps in India simply refuse to give an answer for this reason.

▶Negative times negative: why is it positive?

Think of it as cancelling two debts. If you owe Rs 5 to four people (4 * -5 = -20), removing four such debts is -4 * -5 = +20, a gain of Rs 20. The lab confirms this pattern: every minus paired with another minus turns positive.