Praxis II - 5003 - Mathematics
Composing and Decomposing Numbers - CORRECT ANSWER-"composing"
So 349 is composed of 3 hundreds, 4 tens and 9 ones, in other words:
300 + 40 + 9 ⇒ 349
"Decomposing"
Decomposing is when we break the number apart
349 ⇒ 300 + 40 + 9
"Decomposing"
Standard/Expanded Form - CORRECT ANSWER-Standard and Expanded Form
Some people call the two different forms "Standard" and "Expanded":
Whole Number Exponents - CORRECT ANSWER-10 ^ 5 = 10 x 10 x 10 x 10 x
10
Inverse Operations - CORRECT ANSWER-Additive Inverse Property - when you
add a number to its opposite, the result is always 0
2 + -2 = 0
,Multiplicative Inverse Property - when you multiply any number by its opposite,
the result is always 1
213 x 1/213 = 1
Additive Property - When you add any number to zero the number stays the
same
7+0=7
Multiplicative Property - any time you multiply a number by 1 the number does
not change
13 x 1 = 13
Rational Numbers - CORRECT ANSWER-Sometimes when dividing there is
something left over. It is called the remainder.
Example: There are 7 bones to share with 2 pups.
But 7 cannot be divided exactly into 2 groups,
so each pup gets 3 bones,
and there is 1 left over:
Or each pup gets 3.5 bones
Examples where multiplication does not result in a product greater than both
factors: - CORRECT ANSWER-Whenever you multiply a positive number by a
positive factor less than 1, the product will be smaller than the original number.
For example,
1/2 * 3/4 = 3/8
We want to buy 30 roses which are sold in bunches of 5, so we ask for "6 of the
5-rose bunches". In this way, the word times also often means of. If we try using
the word of
when times appears to have an unclear meaning, we get
11 of 8 rather than 22
, times 8.
Indeed we know what
12
of 8 means - namely 4.
(−4) × 8
= -32
1.) Multiplication of a positive number by a number greater than 1 always
increases the number.
2.) Multiplication of a positive number by a positive number between 0 and 1
always increases the number.
3.) Multiplication of a negative number by a positive number always increases the
first number.
1.) Always True
2.) Always false, as multiplication of a positive number by a number between 0
and 1 will always reduce the number. (e.g. 1 × 12 = 6, 1 × 12 = 4, etc.) 23
3.) Sometimes false and sometimes true; e.g. for the number - 8, 2 × (−8) = −16,
so the number is decreased, whereas the number increases in the example
below:
1 × (− 8) = − 4
Examples where division does not result in a quotient smaller than the dividend. -
CORRECT ANSWER-
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