Both numbers are divisible by \(\displaystyle 5\).

Rewrite the numbers by their common factors.

\(\displaystyle \frac{75}{45} = \frac{5\times 5\times 3}{5\times 3 \times 3}\)

The common terms that can be cancelled are three and five.

Reduce the fraction.

The answer is: \(\displaystyle \frac{5}{3}\)

Rewrite the expression as a fraction.

\(\displaystyle \frac{1080}{320}\)

Cancel out the zeros on the ones place.  This is the same as dividing both numbers by ten.

The result is:  \(\displaystyle \frac{108}{32}\)

Both numbers are divisible by two.   Write the fractions in terms of their common factors.

\(\displaystyle \frac{108}{32} = \frac{2\times 54}{2\times 16} = \frac{2\times 2\times 27}{2\times 2\times 8}\)

The common twos can be cancelled on the numerator and denominator.

The answer is:  \(\displaystyle \frac{27}{8}\)

Write the fraction using common factors.  Both are divisible by five.

\(\displaystyle \frac{175}{35} = \frac{5\times 35}{5\times 7}\)

Simplify the fraction.

\(\displaystyle \frac{35}{7} = 5\)

This fraction reduces to a whole number.

The answer is:  \(\displaystyle 5\)

Rewrite this expression as a fraction.

\(\displaystyle \frac{250}{15}\)

Rewrite the numerator and denominator using common factors.

\(\displaystyle \frac{250}{15} = \frac{5\times 50}{5 \times 3}\)

Notice that we can now cancel the five in the numerator and denominator.

The answer is:  \(\displaystyle \frac{50}{3}\)

Write the problem statement with an expression as a fraction.

\(\displaystyle \frac{84}{16}\)

Rewrite the numerator and denominator by common factors.  Both numbers are divisible by four.

\(\displaystyle \frac{84}{16} = \frac{4\times 21}{4\times 4}\)

Notice that we can cancel the common fours on the top and bottom.

The answer is:  \(\displaystyle \frac{21}{4}\)

Write the expression for this problem.

\(\displaystyle \frac{86}{32}\)

Rewrite the fraction using common factors.  Both the numerator and denominator are divisible by two.

\(\displaystyle \frac{86}{32} =\frac{2\times 43}{2\times 16} = \frac{43}{16}\)

This fraction is no longer reducible.

The answer is:  \(\displaystyle \frac{43}{16}\)

To divide these numbers, we can rewrite this as a fraction to avoid long division.

\(\displaystyle \frac{125}{45}\)

Both numbers can be seen divisible by five.  Rewrite these numbers using common factors.

\(\displaystyle \frac{125}{45} =\frac{5 \times 25}{5\times 9}\)

Cancel the fives.

The answer is:  \(\displaystyle \frac{25}{9}\)

When subtracting integers, it is important to remember to add the inverse of the second number. In this case 4 – (–3), turns into 4 + (+3), which is 7. 

4 – (–3)

4 + 3

7

When you subtract integers, it is the same thing as adding the inverse of the second integer. You can consider the following:

\(\displaystyle -4 -6\)

\(\displaystyle -4 + (-6) = -10\)

You can also consider the problem as asking for six less than negative four. This will also get you to the answer of \(\displaystyle -10\). 

When you subtract integers, it is the same thing as adding the inverse of the second integer. You can consider the following:

\(\displaystyle -5-(-4)\)

\(\displaystyle -5 + 4 = -1\)