Slideshow 3 Mr Richard Sasaki Room 307 Moduli. Vocabulary Check Vocabulary Check Understanding the...
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Transcript of Slideshow 3 Mr Richard Sasaki Room 307 Moduli. Vocabulary Check Vocabulary Check Understanding the...
Slideshow 3Mr Richard
SasakiRoom 307
Moduli
• Vocabulary Check• Understanding the meaning of modulus• Calculating moduli (moduli is the plural
of modulus)
Objectives
Please complete the vocabulary check. You have four minutes. Good luck!
Answers3+8=1112+4=163×5=1510−3=712÷3=4
?+5=17 , ?=1230÷3=104×4=1612+13=25
12÷2+2=83×9=274 – 3=17×2– 1=13?+?=10 ,?=5?×?=16 ,?=48×2– 2=14
?+(2×?)=24 , ?=8(3×2)2=36
We saw this on a worksheet before but didn’t explain it properly.
Natural Numbers are within the sequence…
Natural Numbers
, , , ,
So decimals, fractions and negative integers are not natural numbers.
Note: Is 0 a natural number? This is again, disputed. Some people think it is, some don’t!
Larger or more?
Which is larger, 2 or -9?-9
2
In this instance, larger is not a good word to use. -9 is further away from 0 (the neutral number) so it appears that -9 may be larger.
It has more weight (or size) than 2, just its weight is in the opposite direction.
Moduli
-9
2It’s “size” or “weight” is known as its modulus. A number’s modulus is its distance from zero.
29
Note: Modulus is also known as “absolute value”.Moduli (plural of modulus) are measurements, not regular numbers. Calculating them is easy!
ExamplesFind the modulus of each of the following…
4 4−3 3
7−6 1¿14 is a distance of 4 away from 0 so its modulus is 4. How can we write this mathematically?
The “modulus of 4” is written as… .¿ 4∨¿So in other words… , and|4|=¿4|−3|=¿3
.|7−6|=¿|1|=¿1Please try the first worksheet!
Answers - Easy
31250
5364
|−3|=3|−93 .068|=93.068
|4|+|3|=7No. For example…|−3+1|=2≠|−3|+|1|=4
−4
colder than zero|−4|−3=1−|4−3|=−1
or ()
¿ ¿¿ ¿
Answers – Hard (Q1 – 2) 15052
122−3
𝑥<4
¿ 𝑥∨¿ 4
only works for a number with a modulus less than 4. So -5 for example is not in this range.
Answers – Hard (Q3 – 9) 4
No. is always positive or zero.
Yes, they are always the same.
Yes, which is a natural number.
No, (natural or not?). Also which is not.
≥≤ ( is acceptable.)
Yes, they are always the same.