We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.More informationAgree
menu ×
Google
Custom Search
cancel
search
FacebookTwitterLinkedIn×
share
page location
×
ad

Multiplication Using a Base - Part 2 (Speed Math)

We can extend base method to multiply two numbers when both of them are close to a multiple of power of ten. (Note: speed math calculator can be used to practise problems using this method.)

Example: Calculate 397 × 392

Select $100$ as base and $400$ as working base. Subtract working base from both numbers. That is, $397 - 400 = -3$ and $392 - 400 = -8$

$397$$-3$
$392$$-8$

Find any diagonal sum, and multiply result by $4$ (because working base is $4$ times the base) to obtain left side of answer. Note that both diagonal sums will be same.

$4(392 - 3) = 1556$

Multiply differences to obtain right side of answer.

$-3 × -8 = 24$

Combine left and right sides, that is, $1556$ and $24$

Answer is $155624$

Example: Calculate 1996 × 2016

Select $1000$ as base and $2000$ as working base. Subtract working base from both numbers. That is, $1996 - 2000 = -4$ and $2016 - 2000 = 16$

$1996$$-4$
$2016$$16$

Find any diagonal sum, and multiply result by $2$ (because working base is $2$ times the base) to obtain left side of answer. Note that both diagonal sums will be same.

$2(2016 - 4) = 4024$

Multiply differences to obtain right side of answer.

$-4 × 16 = -64$

Make right side positive by borrowing $1$ from left side. This borrowed $1$ becomes $1000$ when coming to right side (because base is $1000$ and $1 × 1000 = 1000$) and therefore right side becomes $1000 - 64 = 936.$ Since we borrowed $1,$ left side becomes $4024 - 1 = 4023$

Combine left and right sides, that is, $4023$ and $936$

Answer is $4023936$

Example: Calculate 40003 × 40015

Select $10000$ as base and $40000$ as working base. Subtract working base from both numbers. That is, $40003 - 40000 = 3$ and $40015 - 40000 = 15$

$40003$$3$
$40015$$15$

Find any diagonal sum, and multiply result by $4$ (because working base is $4$ times the base) to obtain left side of answer. Note that both diagonal sums will be same.

$4(40015 + 3) = 160072$

Multiply differences to obtain right side of answer.

$3 × 15 = 45$

Since base $10000$ has four zeros, write $45$ as $0045$

Combine left and right sides, that is, $160072$ and $0045$

Answer is $1600720045$

Add Your Comment

(use Q&A for new questions)
?
Name
cancel
preview