Depth · one concept from first principles · step 2 of 4
A hundreds digit is worth 100 each and a tens digit 10 each, so the number is
This is how 347 means 300+40+7.
7.EE.A.2Convert To Algebra100x and 10y are already multiples of 5. Only the 7 is not, so split it as 5+2.
Peel off the part that 5 goes into evenly.
7.EE.A.2Identify SubproblemsTake 5 out of every term of the first group.
This is the distributive property run backwards.
7.EE.A.1Convert To AlgebraSo the number is 5(20x+2y+1)+2. The leftover 2 is less than 5, so it is the remainder, and the quotient is 20x+2y+1.
Dividend = divisor × quotient + remainder, with remainder smaller than the divisor.
7.EE.A.2Identify SubproblemsSince the number equals and the leftover is less than , the quotient is .
The number is , because each digit counts bundles of its own place.
is groups of , groups of and groups of , which together are groups of .
A leftover smaller than cannot make another group of , so the count of whole groups is the quotient and the leftover is the remainder.
Write a number by its place values, peel off a multiple of the divisor, and the quotient appears.
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