Transcript Mental calculations using rounding

Estimation
Estimation
 Estimation should only be used:
 when an exact answer is difficult
to get mentally
 or an exact answer is not
necessary.
 For example, there is no point estimating the
answer to 32 + 45 when it is just as easy to get
the exact answer.
About…
1 million
For estimation to be
efficient, it needs
to be performed
mentally,
quickly
& easily.
Rounding
Numbers are usually rounded to:
 the nearest 10 when working with 2-digit numbers
 the nearest 100 when working with 3-digit numbers
 the nearest 1 000 when working with 4-digit numbers.
 Rounding up or down depends on which makes the
number easier to work with mentally.
Rounding for addition
Example:
 Rounding for addition
695 + 224
 Rounding for subtraction
541 – 287
 Rounding for multiplication
18 x 3
 Rounding for division
3 ÷ 81
Rounding
 Numbers are rounded mentally
to 700 and 200, giving an
approximate answer of 900.
 Numbers are rounded mentally
to 500 and 300, giving an
approximate answer of 200.
 The larger number is rounded
mentally to 20 which is easily
multiplied by 3 to give an
approximate answer of 60.
 The larger number is rounded
mentally to 90 which is easily
divided by 3, giving an
approximate answer of 30.
Front Ending
Using the first digit in a number to estimate
an answer.
 Front ending is using the first digit/s of a number to
estimate an answer and is more effective and more
accurate when using larger numbers.
 Simply round the number to the value of the highest place
(the front end).
For example, 4 005 and 4 905 would both be rounded to
4 000 giving an approximate answer of 8000.
 We can then adjust the answer for a more accurate
answer by looking at the numbers in the second highest
place to see if there is enough room to adjust up.
Front Ending for Addition
1372
+6885
7000
1372
+6885
8000
• Make the first estimate using the digits on the
left (thousands).1 000 + 6 000 = 7 000.
• To get a closer estimate, look at the digits in
the next place (hundreds) to see if there are
enough to increase the first estimate. In this
case, there are. So the estimate can be
increased to 8 000.
Front Ending for Subtraction
8748
–2435
6000
8748
–2435
6300
Make the first estimate using the digits
on the left (thousands).
8 000 - 2 000 = 6 000.
Compare the digits in the next place
(hundreds). 700 - 400 = 300.
Second estimate, 6 300
Multiplication & Division
Use rounding for estimation of 2-digit
multiplication or division.
Use front ending for multiplication or division
estimates of 3-digit or larger numbers.