Number Theory - High School Math
Card 0 of 7
Find the distance between 
and 
on a number line.
Find the distance between
To find the distance on a number line:
To find the distance on a number line:
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If a card is drawn randomly from a regular shuffled 52 card deck, what is the probability that the card is either a spade or a 3?
If a card is drawn randomly from a regular shuffled 52 card deck, what is the probability that the card is either a spade or a 3?
How many cards in the deck are either a spade or a 3?
There are thirteen spades, including a 3 of spades.
There are four 3's, including a 3 of spades.
Since we are counting the same card (3 of spades) twice, there are actually
distinct cards that fit the criteria of being either a spade or a 3.
Since any of the 52 cards is equally likely to be drawn, the probability that it is a spade or a 3, is
How many cards in the deck are either a spade or a 3?
There are thirteen spades, including a 3 of spades.
There are four 3's, including a 3 of spades.
Since we are counting the same card (3 of spades) twice, there are actually
Since any of the 52 cards is equally likely to be drawn, the probability that it is a spade or a 3, is
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Without using a calculator, which of the following is the best estimate for 
?
Without using a calculator, which of the following is the best estimate for
We know that 
and 
.
Because 90 falls is approximately halfway between 81 and 100, the square root of 90 is approximately halfway between 9 and 10, or 9.5.
We know that
Because 90 falls is approximately halfway between 81 and 100, the square root of 90 is approximately halfway between 9 and 10, or 9.5.
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Which of the following are considered real numbers?
Which of the following are considered real numbers?
Real numbers can be found anywhere on a continuous number line ranging from negative infinity to positive infinity; therefore, all of the numbers are real numbers.
Real numbers can be found anywhere on a continuous number line ranging from negative infinity to positive infinity; therefore, all of the numbers are real numbers.
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Place in order from smallest to largest:
Place in order from smallest to largest:
To place in order, first we must find a common denominator and convert all fractions to that denominator.
have a common denominator of 
.
have a common denominator of 
.
have a common denominator of 
.
Therefore we can use common denominators to make all of the fractions look similar. Then the ordering becomes trivial.
To place in order, first we must find a common denominator and convert all fractions to that denominator.
Therefore we can use common denominators to make all of the fractions look similar. Then the ordering becomes trivial.
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What number is 
of 
?
What number is
For percent problems there are verbal cues:
"IS" means equals and "OF" means multiplication.
Then the equation to solve becomes:
For percent problems there are verbal cues:
"IS" means equals and "OF" means multiplication.
Then the equation to solve becomes:
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Which of the following is NOT a real number?
Which of the following is NOT a real number?
We are looking for a number that is not real.
, 
, and 
are irrational numbers, but they are still real.
Then, 
is equivalent to 
by the rules of complex numbers. Thus, it is also real.
That leaves us with: 
which in fact is imaginary (since no real number multiplied by itself yields a negative number) and simplifies to 
.
We are looking for a number that is not real.
Then,
That leaves us with:
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