Number Sense - TACHS Math

Proportions are ratios that are equal to one another. We can solve for the missing variable by using cross multiplication to develop an equation.

Simplify.

Divide both sides of the equation by .

Solve.

Start by listing out the factors of .

Next, list out the factors of .

Now, find the largest factor that the two numbers share. In this case, the greatest common factor is .

Recall that when a number is raised to an exponent, that means we will need to multiply the number the number of times that is equal to the exponent.

Thus, with , this means we will need to multiply by itself four times:

To form the sequence, begin with the term 8. Each subsequent term is equal to 9 added to the previous term, as follows:

,

the missing term.

Proportions are ratios that are equal to one another. We can solve for the missing variable by using cross multiplication to develop an equation.

Simplify.

Divide both sides of the equation by .

Solve.

Recall that when a number is raised to an exponent, that means we will need to multiply the number the number of times that is equal to the exponent.

Thus, with , this means we will need to multiply by itself four times:

Start by listing out the factors of .

Next, list out the factors of .

Now, find the largest factor that the two numbers share. In this case, the greatest common factor is .

Start by listing out multiples of :

Next, list out multiples of :

Now, find the smallest number that is found in both lists. In this case, the least common multiple must be .

Start by listing out the factors of .

Next, list out the factors of .

Now, find the largest factor that the two numbers share. In this case, the greatest common factor is .

After the decimal point, the place values of the digits are, in order:

...

The "6" is in the fourth place after the decimal point, so its place value is one ten-thousandth.

"Six thousand seven ten-thousandths" in fraction form is . To write this in decimal form, put the "7" in the ten-thousandths place, which is the fourth place after the decimal point. This number is "0.6007."

To form the sequence, begin with the term 8. Each subsequent term is equal to 9 added to the previous term, as follows:

,

the missing term.

Proportions are ratios that are equal to one another. We can solve for the missing variable by using cross multiplication to develop an equation.

Simplify.

Divide both sides of the equation by .

Solve.

Start by listing out multiples of :

Next, list out multiples of :

Now, find the smallest number that is found in both lists. In this case, the least common multiple must be .

"Six thousand seven ten-thousandths" in fraction form is . To write this in decimal form, put the "7" in the ten-thousandths place, which is the fourth place after the decimal point. This number is "0.6007."

After the decimal point, the place values of the digits are, in order:

...

The "6" is in the fourth place after the decimal point, so its place value is one ten-thousandth.

Start by listing out multiples of :

Next, list out multiples of :

Now, find the smallest number that is found in both lists. In this case, the least common multiple must be .

Recall that when a number is raised to an exponent, that means we will need to multiply the number the number of times that is equal to the exponent.

Thus, with , this means we will need to multiply by itself four times:

The lines on either side of the negative integer represent that we need to find its absolute value. The absolute value of a number is its real distance from zero on a number line; therefore, we need to calculate how many spaces the number is tot he left of zero on a number line. This number is a distance from zero and will not be negative. All absolute values are positive.

Therefore, the absolute value—or distance from zero—is the following: