What is the value of a in this equation?
\( \frac{\mathrm{6a} }{\mathrm{5}} -\frac{\mathrm{2a} }{\mathrm{2}}=\frac{\mathrm{1} }{\mathrm{2}}\)

250 miles/(50 miles per hour) = 5 hours

From 7:45 am today to 7:45 am tomorrow is 24 hours. From 7:45 am tomorrow to 3:15 pm tomorrow is 7 1/2 hours. Total is 31 1/2 hours

The digit in the hundredth place is 3. The digit to the right of the hundredth place is 2; therefore, the 3 remains the same. The number rounds to 1230.93.

When solving an equation with one variable, your goal is to isolate the variable on one side of the equal sign. You do this by moving all of the other numbers to the opposite of the equal sign. You move numbers by performing the opposite operation (subtraction/addition and multiplication/division), on both sides of the equation to keep it balanced.
|14x – 1⁄3| = 2
In this equation, we see the use of the absolute value symbol, | |.
The absolute value of a number is the magnitude of that number. In other words, it is the number of places it is from zero. This means that the absolute value of a negative number is simply the number of spaces it is away from zero (in either direction). For example, |- 3| = 3 because -3 is three places from zero.
When there is an absolute value within an equation, it represents the absolute value of that number, when x is known.
When we see the absolute value symbol, it alerts us that the value of the number inside can be either positive or negative.
Therefore, we must solve for both possibilities, and separate the problem into the positive answer and the negative answer and solve for both:
Situation 1: One version of the equation should represent what is inside the absolute value symbols as a positive number. Remember that it is the entire 14x – 1/3 that could be a positive number here.
14x – 1⁄3 = 2
Add 1⁄3 to each side to eliminate the (-1⁄3 ) from the left-hand side of the equation.
14x – 1⁄3 + 1⁄3 = 2 + 1⁄3
14x = 2 1⁄3
Now, you need to divide both sides of the equation by the coefficient (14) to isolate the variable completely. Convert the mixed number to an improper fraction in order to divide the fractions.
2 1⁄3 → (2 • 3) + 1 = 7 → 7⁄3
14x = 7⁄3
14x ÷ 14= 7⁄3 ÷ 14
Remember that when dividing fractions, you multiply by the reciprocal (flip the second fraction and multiply). Since 14 is a whole number, you can make it a fraction by making 14 the numerator and 1 the denominator (14⁄1). Then, flip it (1⁄14) and multiply the two fractions.
x = 7⁄3 × 1⁄14
x = 7⁄42
Reduce by finding a common factor between the two (7) and dividing both the numerator and denominator by that number.
x = 1⁄6
Situation 2:One version of the equation should represent what is inside the absolute value symbols as a positive number. Remember that it is the entire 14x – 1/3 that could be a positive number here. -(14x – 1⁄3) = 2
Distribute the negative sign to all values included in the absolute value of the original equation.
-14x + 1⁄3 = 2
Subtract ⅓ from each side of the equation in order to eliminate the ⅓ from the left-hand side of the equation.
-14x + 1⁄3– 1⁄3 = 2 – 1⁄3
-14x = 2 – 1⁄3
Determine a common denominator in order to subtract the fractions. Remember that whole numbers are written as fractions by making the whole number the numerator and 1 the denominator (2⁄1).
-14x = 2⁄1 – 1⁄3
The lowest common denominator for 1 and 3 is 3. In order to make the denominator of 2⁄1 a 3, you need to multiply both the numerator and the denominator by 3 (because 1 • 3 = 3).
-14x = 6⁄3 – 1⁄3
-14x = 5⁄3
Now, you need to divide both sides of the equation by the coefficient (14) to isolate the variable completely. Remember that when dividing fractions, you multiply by the reciprocal (flip the second fraction and multiply). Since 14 is a whole number, you can make it a fraction by making 14 the numerator and 1 the denominator (14⁄1). Then, flip it (1⁄14) and multiply the two fractions.
-14x ÷ -14= 5⁄3 ÷ –14⁄1
x = 5⁄3 × –1⁄14
x = –5⁄42

\(\frac{\mathrm{240} }{\mathrm{6}}\) = 40, \(\frac{\mathrm{6} }{\mathrm{2}}\)=3, (40 pcks of pens x $2.35 ea.) + (3 pcks of staplers x $12.95 ea.) =$132.85

500mg Ca – 325 mg Ca = 175 mg Ca

First, you must calculate how many hours the nurse works each week. Three 8-hour shifts plus one 12-hour shift equals 36 hours per week.
Beginning Salary = 36 × 17.81=641.16
Deductions = \$102.80 + \$24.58 + $18.13 + \$52.15 = \$197.66
Take-Home Pay = \$641.16 − \$197.66 = \$443.50

Step 1: Read the Decimal Out Loud
A few reminders:
a. We read everything to the left of the decimal by itself.
b. The decimal says the word “and”.
c. We then read everything to the right of the decimal.
d. We end it by saying the place value of the last number.
Therefore, 0.932 is said as:
Nine Hundred Thirty-two Thousandths
Step 2: Write the Fraction You Read Out Loud
Zero came before the decimal, so there is no whole number.
We also said nine hundred thirty-two thousandths out loud. Nine hundred thirty-two would be our numerator and one thousand would be our denominator.
\(\frac{\mathrm{932} }{\mathrm{1000}}\)
Let’s check and see if the fraction can be simplified.
932 and 1000 have a factor of 4 in common so we can simplify the fraction by dividing both the numerator and denominator by a common factor, 4.
932/1000 ÷ 4/4 = 932÷4/1000÷4
= \(\frac{\mathrm{233} }{\mathrm{250}}\)
Let’s check and see if the fraction can be further simplified.
Because the only factor that 233 and 250 have in common is 1, the fraction is completely simplified.
0.932 is \(\frac{\mathrm{233} }{\mathrm{250}}\) when written as a fraction.

His profit will be his income minus his expenses. He will earn $40 for each lawn, or 40m. He pays $35 in expenses each week, or 35x.
profit = 40m − 35x

\(\frac{\mathrm{4} }{\mathrm{5}}\) –\(\frac{\mathrm{1} }{\mathrm{3}}\), find common denominator, \(\frac{\mathrm{12} }{\mathrm{15}}\) - \(\frac{\mathrm{5} }{\mathrm{15}}\) = \(\frac{\mathrm{7} }{\mathrm{15}}\) cups

Step 1: Remember Addition Rules for Odd/Even Numbers
Firstly, we can look at the odd and even rules involving addition.
Odd Number + Odd Number = Even Number
Even Number + Even Number = Even Number
Odd Number + Even Number = Odd Number
Step 2: Try an Example Problem Or Interpret The Situation
The situation above says we are adding two even numbers to an odd number and then multiplying the result by an odd number. Let’s take this step by step.
Even Integer + Even Integer = Even Integer (New Sum 1)
Since two even integers added together got us an even integer, we can add this new even integer to the odd number.
Even Integer (New Sum 1) + Odd Integer = Odd Integer(New Sum 2)
Step 3: Multiply the Result from Step 2 by an Odd Number
We can look at the odd and even rules involving multiplication.
Odd Number × Odd Number = Odd Number
Even Number × Even Number = Even Number
Odd Number × Even Number = Even Number
Odd Integer(New Sum 2) × Odd Integer = Odd Integer
We expect the result to be an odd integer
Step 4: Interpret the Information
Since we know that our answer has to be an odd integer, which means a whole number ending in a 1, 3, 5, 7, or 9, the only answer choice that could potentially be the answer to this problem would be 175.

The smallest number is the greatest negative value:
\(-\frac{1}{4}\left(\right.-0.25\left.\right)\)
The next smallest is:
\(-0.2\)
The largest value is:
\(\pi\left(\right.3.14\left.\right)\)

Substitute the values of x and y into the given equation and evaluate:
= \(3^4\) − (20)
= 3×3×3×3 − (20)
= 81 − 20
= 61

1 yard = 3 feet
44 yards = 132 feet
Perimeter = 2 × (length) + 2 × (width)
132 = 2(36) + 2 × width
Width = \(\frac{132-72}{2}\) = 30 feet