### All TACHS Math Resources

## Example Questions

### Example Question #1 : Greatest Common Factor

What is the greatest common factor of and ?

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #1 : Tachs: Math And Ability

What is the least common multiple of and ?

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #3 : Tachs: Math And Ability

Solve:

**Possible Answers:**

**Correct answer:**

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:

### Example Question #1 : Tachs: Math And Ability

Which of the following is equal to six thousand seven ten-thousandths?

**Possible Answers:**

**Correct answer:**

"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."

### Example Question #1 : Number Sense

Examine the decimal

What is the place value of the position occupied by the "6"?

**Possible Answers:**

Tenths

Thousandths

Hundredths

Hundredths

**Correct answer:**

Hundredths

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

...

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

### Example Question #1 : Tachs: Math And Ability

Which of the following is equivalent to ?

**Possible Answers:**

**Correct answer:**

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:

### Example Question #1 : Tachs: Math And Ability

Solve for the missing variable in the following proportion:

**Possible Answers:**

**Correct answer:**

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.

### Example Question #1 : Number Sequences

Give the next number in the sequence:

**Possible Answers:**

**Correct answer:**

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.

### Example Question #9 : Tachs: Math And Ability

Subtract.

**Possible Answers:**

**Correct answer:**

In order to solve this problem we must subtract the second number from the first number.

### Example Question #1 : Decimals

Square 0.44.

**Possible Answers:**

**Correct answer:**

To square a number means to multiply it by itself, so we seek to compute

To multiply two decimal fractions, first multiply, ignoring the decimal points:

Move the (implied) decimal point the number of spaces right equal to the total number of digits right of the decimal points in the factors; this can be seen to be four:

The square of 0.44 is 0.1936.

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