Operations

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TACHS Math › Operations

Questions 1 - 10

What is the difference between $\frac{11}{12}$ and $\frac{3}{4}$ ?

$\frac{1}{6}$

$\frac{1}{8}$

$\frac{1}{5}$

$\frac{1}{4}$

Explanation

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

$\frac{11}{12}-\frac{3}{4}$

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

Now, subtract.

$\frac{11}{12}-\frac{3}{4}=\frac{11}{12}-\frac{9}{12}=\frac{2}{12}$

Make sure to simplify the answer.

$\frac{2}{12}=\frac{1}{6}$

What is the difference between $\frac{11}{12}$ and $\frac{3}{4}$ ?

$\frac{1}{6}$

$\frac{1}{8}$

$\frac{1}{5}$

$\frac{1}{4}$

Explanation

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

$\frac{11}{12}-\frac{3}{4}$

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

Now, subtract.

$\frac{11}{12}-\frac{3}{4}=\frac{11}{12}-\frac{9}{12}=\frac{2}{12}$

Make sure to simplify the answer.

$\frac{2}{12}=\frac{1}{6}$

Which of the following is the most reduced form of ?

$2 \frac{2}{5}$

$2 \frac{4}{10}$

$\frac{24}{10}$

$\frac{22}{5}$

Explanation

Start by converting into a fraction.

$\frac{2.4}{1} \times \frac{10}{10}=\frac{24}{10}$

We multiply both numerator and denominator by to get rid of the decimal.

Now, convert $\frac{24}{10}$ into a mixed number.

$\frac{24}{10}=2\frac{4}{10}=2\frac{2}{5}$

Which of the following is the most reduced form of ?

$2 \frac{2}{5}$

$2 \frac{4}{10}$

$\frac{24}{10}$

$\frac{22}{5}$

Explanation

Start by converting into a fraction.

$\frac{2.4}{1} \times \frac{10}{10}=\frac{24}{10}$

We multiply both numerator and denominator by to get rid of the decimal.

Now, convert $\frac{24}{10}$ into a mixed number.

$\frac{24}{10}=2\frac{4}{10}=2\frac{2}{5}$

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

Cannot be determined

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.

$\text{Earning each week}=12.50\times 40=500$

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.

$\frac{3000}{500}=6$

Rachel must work for weeks in order to earn enough for the car.

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

Cannot be determined

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.

$\text{Earning each week}=12.50\times 40=500$

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.

$\frac{3000}{500}=6$

Rachel must work for weeks in order to earn enough for the car.

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

Explanation

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

Since it is only $\frac{2}{3}$ full,

$\frac{2}{3}\times 15=10$ .

The tank only has 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.

$10 \times 30 = 300$

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

Explanation

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

Since it is only $\frac{2}{3}$ full,

$\frac{2}{3}\times 15=10$ .

The tank only has 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.

$10 \times 30 = 300$

What is the product of $\frac{5}{6}$ and $\frac{3}{8}$ ?

$\frac{5}{16}$

$\frac{3}{8}$

$\frac{7}{16}$

$\frac{1}{8}$

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.

$\frac{5}{6}\times \frac{3}{8}=\frac{15}{48}$