By order of operations, subtractions are carried out in left-to-right order, so subtract 4.70 (adding the placeholder zero) from 7.82, aligning the decimal points:

\(\displaystyle 7.82\)

\(\displaystyle \underline{4.70}\)

\(\displaystyle 3.12\)

Now subtract 2.56 from this difference, again aligning vertically by decimal point:

\(\displaystyle 3.12\)

\(\displaystyle \underline{2.56}\)

\(\displaystyle 0.56\)

Rewrite this difference as a sum. The sum of two numbers of unlike sign is the difference of their absolute values, with the sign of the "dominant" number (the negative number here) affixed:

\(\displaystyle 6.54 - 9 = 6.54 + (-9) = -(9-6.54)\)

Subtract vertically by aligning the decimal points, making sure you append the 9 with a decimal point and two placeholder zeroes:

\(\displaystyle 9.00\)

\(\displaystyle \underline{6.54}\)

\(\displaystyle 2.46\)

Since the answer is negative, append a negative symbol in front. The answer is \(\displaystyle -2.46\).

Since you are subtracting a larger number from a smaller, reverse them, and affix a negative symbol:

\(\displaystyle 0.005 - 0.15 = - \left (0.15 - 0.005 \right )\)

Rewrite vertically, lining up the decimal digits. Subtract as you would two integers. (Note that you are appending a zero to the 0.15.)

\(\displaystyle \begin{matrix} \; \; \; 0.150\\ -\underline{0.005}\\\; \; \; 0.145\end{matrix}\)

Affix the negative symbol to obtain the difference of \(\displaystyle -0.145\).

Subtract the first two fractions first. This is best done by writing vertically, and subtracting integer and fraction parts.

   \(\displaystyle 6 \frac{9}{11}\)

\(\displaystyle \underline{- 2 \frac{3}{11}}\)

   \(\displaystyle 4 \frac{6}{11}\)

Now add this to the third fraction similarly, adjusting as shown for the improper fraction:

   \(\displaystyle 4 \frac{6}{11}\)

\(\displaystyle \underline{+ 4 \frac{7}{11}}\)

   \(\displaystyle 8 \frac{13}{11} = 8 +1 + \frac{2}{11} = 9 \frac{2}{11}\)

Subtract vertically, making sure the decimal points in all three numbers line up (note that a zero has been appended to the first number):

\(\displaystyle \begin{matrix} \; \; \; 8.10\\ \underline{-5.67}\\ \; \; \;2.43 \end{matrix}\)

Rewrite the first fraction in eighths, as \(\displaystyle LCD (4,8) = 8\).

\(\displaystyle 8\frac{1}{4} = 8\frac{1\times 2}{4\times 2} = 8\frac{2}{8}\)

Now write vertically:

   \(\displaystyle 8\frac{2}{8}\)

\(\displaystyle -\underline{5\frac{7}{8}}\)

"Borrow" in the first expression, then subtract integer and fractional parts separately:

  \(\displaystyle 7\frac{10}{8}\)

\(\displaystyle -\underline{5\frac{7}{8}}\)

   \(\displaystyle 2\frac{3}{8}\)

Subtract the numerators:

\(\displaystyle \frac{7}{15}-\frac{6}{15}=\frac{1}{15}\)

Answer: \(\displaystyle \frac{1}{15}\)

Rewrite \(\displaystyle 7 \frac{3}{4}\)  as a decimal:

\(\displaystyle 3 \div 4 = 0.75\), so \(\displaystyle 7 \frac{3}{4} = 7.75\)

Now subtract:

 \(\displaystyle 15.00\)

\(\displaystyle \underline{-7.75}\)

   \(\displaystyle 7.25\)

Subtract vertically, making sure the decimal points line up.

   \(\displaystyle 4.0\)

\(\displaystyle \underline{-2.8}\)

   \(\displaystyle 1.2\)

This is twelve tenths; write this as a fraction and simplify:

\(\displaystyle \frac{12}{10} = \frac{12\div 2}{10\div 2} = \frac{6}{5}\)

In order to subtract fractions we need to have a common denominator (the number on the bottom of each fractions). In this case we do have common denominators.

We need to then subtract the numerators, in this case \(\displaystyle 12-8=4\).

After subtracting the numerators we keep the denonimator the same.

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

This is known as an improper fraction because the numerator is greater than the denominator. So we need to rewrite into a mixed number. Fractions can also be read as division, meaning 4 divided by 3 is????

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