Part 3: Multiplication

# 3.1: Multiplying integers

Notes

##### Partial-products method

To multiply two integers together, multiply each combination of digits in the two integers, taking account of place value. Then, add these “partial-products” together. For example,

**46**x**27**- = (
**4**0 +**6**) x (**2**0 +**7**)*[expand integers into tens and ones]* - = (
**7**+**2**0) x (**6**+**4**0)*[re-order to match usual layout in diagram below]* - = (
**7**x**6**) + (**7**x**4**0) + (**2**0 x**6**) + (**2**0 x**4**0)*[use the distributive property, i.e., FOIL:***F**irst,**O**uter,**I**nner,**L**ast] - = (
**7**ones x**6**ones) + (**7**ones x**4**tens) + (**2**tens x**6**ones) + (**2**tens x**4**tens) - = 42 + 280 + 120 + 800
- = 1242

##### Common method

The common method uses the same idea of partial-products, but writes the calculations more compactly. For example,

**46**x**27**- = (
**4****6**) x (**2**0 +**7**)*[expand second integer into tens and ones]* - = (
**7**+**2**0) x (**4****6**)*[re-order to match usual layout in diagram below]* - = (
**7**x**4****6**) + (**2**0 x**4****6**)*[use the distributive property]* - = 322 + 920
- = 1242

The video below works through some examples of multiplying integers.

Video Tips

Practice Exercises

Do the following exercises to practice multiplying integers.