Math Rules For Subtraction

Subtraction, along with addition, multiplication and division, is one of the four basic operations of arithmetic. In plain English, subtracting one number from another means reducing the value of the second number by exactly the amount of the first. While in principle this is a straightforward process, in practice, subtraction problems are often a part of more complex computations, and it's helpful to know the rules in these cases to avoid getting stuck.

A few examples of math rules for subtraction:

When you subtract a positive number from a smaller positive number, the result will be a negative number:

\(8 – 11 = -3\)

Subtracting a negative number has the effect of adding the positive counterpart of that number. In other words, the negatives cancel out to create a positive:

\(7 -(-5) = 7 + 5 = 12\)

Significant figures are all of the digits shown to the right of a decimal point in any number. For example, 2.35608 has five significant digits, 12.75 has two, and 163.922 has three.

When subtracting one decimal number from another, or multiple such numbers from each other, give an answer containing the least number of significant digits of any of the numbers in the problem. For example,

\(14.15 – 2.3561 – 4.537 = 7.2569\)

but you would express this as 7.26 after rounding to adhere to the convention described above.

When subtracting fractions that have the same denominator, simply keep the denominator and subtract the numerators. Thus:

\(\frac{9}{17} – \frac{5}{17} = \frac{ 4}{17}\)

When subtracting fractions that have different denominators, first find the lowest common denominator (or, failing this, any common denominator) and proceed as before. For example, given:

\(\frac{4}{5} – \frac{1}{2}\)

Bearing in mind that 2 and 5 both divide evenly into 10, multiply the top and bottom of the left fraction by 2 and the top and bottom of the right fraction by 5 to give a version of the problem that has 10 in the denominator of both fractions. This gives:

\(\frac{8}{10} – \frac{5}{10} = \frac{3}{10}\)

When dividing two numbers including the same base and different exponents, subtraction comes into play because you subtract the exponent in the dividend by the exponent in the divisor to obtain the result. For example,

\(10^{13} ÷ 10^{-5} = 10 ^{13-(-5)} = 10^{18}\)

Here, it's helpful to keep in mind that dividing by a number raised to a negative power of 10 is tantamount to multiplying by a number raised to that same number without the negative sign. That is, dividing by, say, 10 ⁻³, or 0.001, is the same as multiplying by 10³, or 1,000.