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.