1.5 Dividing Whole Numbers 59The quotient is 706. Check the result using multiplication.706
(^48) 33888
336
28
0
288
288
0
Caution! If a difference at any time in the long division process is greater
than or equal to the divisor, the estimate made at that point should be
increased by 1, and you should try again.
4 Perform long division (with a remainder).
Sometimes, it is not possible to separate a group of objects into a whole number of
equal-sized groups. For example, if we start with a set of 14 stars and divide them
into groups of 4 stars, we will have 3 groups of 4 stars and 2 stars left over. We call
the left over part the remainder.
There are 3 groups of 4 stars. There are 2
stars left over.
A set of 14 stars.
In the next long division example, there is a remainder. To check such a
problem, we add the remainder to the product of the quotient and divisor. The result
should equal the dividend.
Recall that the operation within the
parentheses must be performed
first.
(Quotientdivisor)remainderdividend
EXAMPLE (^4) Divide: Check the result.
StrategyWe will follow a four-step process:estimate, multiply, subtract,and
bring down.
WHYThis is how long division is performed.
Solution
Since 23 will not divide 8, we divide 83 by 23.
Ask: “How many times will 23 divide 83?” Since 23 is about 20, we can
the answer to that question by thinking is 4, and we write
the 4 in the tens column of the quotient.
4 and 23, and write their product, 92, under the 83. Because 92
is greater than 83, the estimate of 4 for the tens column of the quotient
is too large.We will erase the 4 and decrease the estimate of the quotient
by 1 and try again.
Multiply
4
23 832
92
estimate 8 24
(^23) 832
(^23) 832.
Self Check 4
Divide: Check the
result.
Now TryProblem 39
(^34) 792.
Change the from 5 to 6 in the ones column of the quotient.
6 and 48, and their product, 288, from 288 to
get 0. Your solution should look like this.
Multiply subtract
estimate