TACHS Math : Operations

Study concepts, example questions & explanations for TACHS Math

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Example Questions

Example Question #1 : Tachs: Math And Ability

Subtract.

\(\displaystyle 999-82\)

Possible Answers:

\(\displaystyle 971\)

\(\displaystyle 171\)

\(\displaystyle 719\)

\(\displaystyle 711\)

\(\displaystyle 917\)

Correct answer:

\(\displaystyle 917\)

Explanation:

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

\(\displaystyle \frac{\begin{array}[b]{r}999\\ -\ 82\end{array}}{ \ \ \ \space 917}\)

Example Question #1 : Math

Square 0.44.

Possible Answers:

\(\displaystyle 0.1936\)

 \(\displaystyle 0.01936\)

\(\displaystyle 0.0028\)

\(\displaystyle 0.028\)

Correct answer:

\(\displaystyle 0.1936\)

Explanation:

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

\(\displaystyle 0.44 \times 0.44\)

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

\(\displaystyle 44 \times 44 = 1,936\)

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:

\(\displaystyle 0.{\color{Red} 44} \times 0.{\color{Red} 44} = 0.{\color{Red} 1936}\)

The square of 0.44 is 0.1936.

Example Question #11 : Math

Tiffany earns \(\displaystyle \$1500\) each week. If Mark earns \(\displaystyle 15\%\) less than Tiffany, what is the sum of their salaries each week?

Possible Answers:

\(\displaystyle 2775\)

\(\displaystyle 2875\)

\(\displaystyle 3225\)

\(\displaystyle 3025\)

Correct answer:

\(\displaystyle 2775\)

Explanation:

Start by finding out how much Mark makes. Since he makes \(\displaystyle 15\%\) less than Tiffany, we can write the following to find Mark's weekly salary:

\(\displaystyle 1500-0.15(1500)=1275\)

Mark must make \(\displaystyle \$1275\) each week. Now, add together their salaries to find the sum.

\(\displaystyle 1500+1275=2775\)

Example Question #1 : Operations

Rachel earns \(\displaystyle \$12.50\) an hour as an assistant in a science lab. How many \(\displaystyle 40\) hour work weeks will she need to work in order to pay for a car that costs \(\displaystyle \$3000\)?

Possible Answers:

\(\displaystyle 8\)

Cannot be determined

\(\displaystyle 6\)

\(\displaystyle 5\)

Correct answer:

\(\displaystyle 6\)

Explanation:

Start by figuring out how much Rachel can earn in each week by multiplying her hourly rate by the number of hours worked each week.

\(\displaystyle \text{Earning each week}=12.50\times 40=500\)

Now, divide the amount she needs to earn by the amount earned each week to find how many weeks she will need to work to earn that amount.

\(\displaystyle \frac{3000}{500}=6\)

Rachel must work for \(\displaystyle 6\) weeks in order to earn enough for the car.

Example Question #1 : Operations

Add.

\(\displaystyle 3.74+22.786\)

Possible Answers:

\(\displaystyle 27\)

\(\displaystyle 27.526\)

\(\displaystyle 32.524\)

\(\displaystyle 23.453\)

\(\displaystyle 26.526\)

Correct answer:

\(\displaystyle 26.526\)

Explanation:

In order to solve this problem we need to line up the decimal places and add.

\(\displaystyle \frac{\begin{array}[b]{r}3.740\\\ +\ 22.786\end{array}}{ \ \ \ \space 26.526}\)

Example Question #1 : Fractions

What is the value of \(\displaystyle \frac{3}{4 }+\frac{1}{2}-\frac{2}{3}\)?

Possible Answers:

\(\displaystyle \frac{1}{3}\)

\(\displaystyle \frac{5}{12}\)

\(\displaystyle \frac{3}{4}\)

\(\displaystyle \frac{7}{12}\)

Correct answer:

\(\displaystyle \frac{7}{12}\)

Explanation:

Start with finding the value of \(\displaystyle \frac{3}{4 }+\frac{1}{2}\).

In order to add fractions with different denominators, we will need to change one or both denominators first. Notice that \(\displaystyle 2\) is a factor of \(\displaystyle 4\), which means we can multiply the numerator and the denominator of \(\displaystyle \frac{1}{2}\) by \(\displaystyle 2\) to get \(\displaystyle \frac{2}{4}\).

Now, add the two fractions together as they have the same denominator.

\(\displaystyle \frac{3}{4}+\frac{1}{2}=\frac{3}{4}+\frac{2}{4}=\frac{5}{4}\)

Next, solve \(\displaystyle \frac{5}{4}-\frac{2}{3}\).

The least common multiple of \(\displaystyle 3\) and \(\displaystyle 4\) is \(\displaystyle 12\).

Thus, \(\displaystyle \frac{5}{4}-\frac{2}{3}=\frac{15}{12}-\frac{8}{12}=\frac{7}{12}\)

Example Question #1 : Operations

Janice's car can travel \(\displaystyle 30\) miles on one gallon of gas. Her car can normally hold \(\displaystyle 15\) gallons of gas, but it is only \(\displaystyle \frac{2}{3}\) full. How many miles can Janice travel before the tank is empty?

Possible Answers:

\(\displaystyle 450\)

\(\displaystyle 300\)

\(\displaystyle 270\)

\(\displaystyle 360\)

Correct answer:

\(\displaystyle 300\)

Explanation:

Start by finding out how many gallons is currently in Janice's tank.

Since it is only \(\displaystyle \frac{2}{3}\) full, 

\(\displaystyle \frac{2}{3}\times 15=10\).

The tank only has \(\displaystyle 10\) gallons in it right now. Multiply this by the number of miles traveled per gallon to find how far Janice can travel before the tank is empty.

\(\displaystyle 10 \times 30 = 300\)

Example Question #11 : Tachs: Math And Ability

What is the product of \(\displaystyle \frac{5}{6}\) and \(\displaystyle \frac{3}{8}\)?

Possible Answers:

\(\displaystyle \frac{7}{16}\)

\(\displaystyle \frac{5}{16}\)

\(\displaystyle \frac{3}{8}\)

\(\displaystyle \frac{1}{8}\)

Correct answer:

\(\displaystyle \frac{5}{16}\)

Explanation:

Since the question asks for the product, you will need to multiply the two fractions. Recall that in multiplying two fractions, you will multiply the numerators together and then multiply the denominators together.

\(\displaystyle \frac{5}{6}\times \frac{3}{8}=\frac{15}{48}\)

Next, reduce the fraction.

\(\displaystyle \frac{15}{48}=\frac{5}{16}\)

Example Question #3 : Operations

What is the difference between \(\displaystyle \frac{11}{12}\) and \(\displaystyle \frac{3}{4}\)?

Possible Answers:

\(\displaystyle \frac{1}{4}\)

\(\displaystyle \frac{1}{5}\)

\(\displaystyle \frac{1}{6}\)

\(\displaystyle \frac{1}{8}\)

Correct answer:

\(\displaystyle \frac{1}{6}\)

Explanation:

Since the question asks you to find the difference, you will need to subtract the two fractions:

\(\displaystyle \frac{11}{12}-\frac{3}{4}\)

Start by making both denominators the same. Multiply the numerator and denominator of \(\displaystyle \frac{3}{4}\) by \(\displaystyle 3\) to get \(\displaystyle \frac{9}{12}\).

Now, subtract.

\(\displaystyle \frac{11}{12}-\frac{3}{4}=\frac{11}{12}-\frac{9}{12}=\frac{2}{12}\)

Make sure to simplify the answer.

\(\displaystyle \frac{2}{12}=\frac{1}{6}\)

Example Question #13 : Tachs: Math And Ability

Paul can type \(\displaystyle 60\) words per minute. If Josie can type \(\displaystyle 15\%\) faster than Paul can, how many words can Josie type in \(\displaystyle 15\) minutes?

Possible Answers:

\(\displaystyle 1035\)

Cannot be determined

\(\displaystyle 897\)

\(\displaystyle 1173\)

Correct answer:

\(\displaystyle 1035\)

Explanation:

Start by finding out Josie's typing rate.

Since she types \(\displaystyle 15\%\) faster, we can find her rate with the following equation:

\(\displaystyle 60+0.15(60)=69\)

Since Josie types at \(\displaystyle 69\) words per minute, we can multiply by the total number of given minutes to find out how many words she can type in the given time frame.

\(\displaystyle 69 \times 15=1035\)

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