Math - Number Theory | Practice Hub

Without using a calculator, which of the following is the best estimate for $\sqrt{90}$ ?

Explanation

We know that and .

$\sqrt{81}<\sqrt{90}<\sqrt{100}$

$9<\sqrt{90}<10$

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.

Without using a calculator, which of the following is the best estimate for $\sqrt{90}$ ?

Explanation

We know that and .

$\sqrt{81}<\sqrt{90}<\sqrt{100}$

$9<\sqrt{90}<10$

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.

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?

$\frac{4}{13}$

$\frac{2}{13}$

$\frac{17}{52}$

$\frac{5}{52}$

$\frac{7}{52}$

Explanation

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

$\frac{16}{52}$ $=\frac{4}{13}$

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?

$\frac{4}{13}$

$\frac{2}{13}$

$\frac{17}{52}$

$\frac{5}{52}$

$\frac{7}{52}$

Explanation

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

$\frac{16}{52}$ $=\frac{4}{13}$

What number is of ?

Explanation

For percent problems there are verbal cues:

"IS" means equals and "OF" means multiplication.

Then the equation to solve becomes:

$n=0.20\cdot 15=3$

What number is of ?

Explanation

For percent problems there are verbal cues:

"IS" means equals and "OF" means multiplication.

Then the equation to solve becomes:

$n=0.20\cdot 15=3$

Place in order from smallest to largest:

$\frac{3}{4},; ; \frac{1}{8},; ; \frac{5}{8},; ; \frac{1}{6},; ; \frac{1}{2},; ; \frac{1}{5},; ; \frac{1}{3}$

$\frac{1}{8},; ; \frac{1}{6},; ; \frac{1}{5},; ; \frac{1}{3},; ; \frac{1}{2},; ; \frac{5}{8},; ; \frac{3}{4}$

$\frac{1}{2},; ; \frac{1}{3},; ; \frac{3}{4},; ; \frac{1}{5},; ; \frac{1}{6},; ; \frac{1}{8},; ; \frac{5}{8}$

$\frac{1}{5},; ; \frac{3}{4},; ; \frac{1}{3},; ; \frac{1}{2},; ; \frac{5}{8},; ; \frac{1}{8},; ; \frac{1}{6}$

$\frac{1}{8},; ; \frac{1}{5},; ; \frac{1}{2},; ; \frac{3}{4},; ; \frac{1}{6},; ; \frac{1}{3},; ; \frac{5}{8}$

$\frac{1}{2},; ; \frac{3}{4},; ; \frac{1}{6},; ; \frac{5}{8},; ; \frac{1}{3},; ; \frac{1}{5},; ; \frac{1}{8}$

Explanation

To place in order, first we must find a common denominator and convert all fractions to that denominator.

have a common denominator of .

Therefore we can use common denominators to make all of the fractions look similar. Then the ordering becomes trivial.

$\frac{1}{8}=\frac{15}{120},; ; \frac{1}{6}=\frac{20}{120},; ; \frac{1}{5}=\frac{24}{120}$

$\frac{1}{3}=\frac{40}{120},; ; \frac{1}{2}=\frac{60}{120}$

$\frac{5}{8}=\frac{75}{120},; ; \frac{3}{4}=\frac{90}{120}$

Place in order from smallest to largest:

$\frac{3}{4},; ; \frac{1}{8},; ; \frac{5}{8},; ; \frac{1}{6},; ; \frac{1}{2},; ; \frac{1}{5},; ; \frac{1}{3}$

$\frac{1}{8},; ; \frac{1}{6},; ; \frac{1}{5},; ; \frac{1}{3},; ; \frac{1}{2},; ; \frac{5}{8},; ; \frac{3}{4}$

$\frac{1}{2},; ; \frac{1}{3},; ; \frac{3}{4},; ; \frac{1}{5},; ; \frac{1}{6},; ; \frac{1}{8},; ; \frac{5}{8}$

$\frac{1}{5},; ; \frac{3}{4},; ; \frac{1}{3},; ; \frac{1}{2},; ; \frac{5}{8},; ; \frac{1}{8},; ; \frac{1}{6}$

$\frac{1}{8},; ; \frac{1}{5},; ; \frac{1}{2},; ; \frac{3}{4},; ; \frac{1}{6},; ; \frac{1}{3},; ; \frac{5}{8}$

$\frac{1}{2},; ; \frac{3}{4},; ; \frac{1}{6},; ; \frac{5}{8},; ; \frac{1}{3},; ; \frac{1}{5},; ; \frac{1}{8}$

Explanation

To place in order, first we must find a common denominator and convert all fractions to that denominator.

have a common denominator of .

Therefore we can use common denominators to make all of the fractions look similar. Then the ordering becomes trivial.

$\frac{1}{8}=\frac{15}{120},; ; \frac{1}{6}=\frac{20}{120},; ; \frac{1}{5}=\frac{24}{120}$

$\frac{1}{3}=\frac{40}{120},; ; \frac{1}{2}=\frac{60}{120}$

$\frac{5}{8}=\frac{75}{120},; ; \frac{3}{4}=\frac{90}{120}$

Find the distance between and on a number line.

Explanation

To find the distance on a number line:

$d=x_{2}-x{{_1}}$

Find the distance between and on a number line.

Explanation

To find the distance on a number line:

$d=x_{2}-x{{_1}}$

Number Theory

Help Questions

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation