Free Algebra Tutorials!

 Home Exponential Functions Powers Linera Equations Simple Trinomials as Products of Binomials Laws of Exponents and Dividing Monomials Solving Equations Multiplying Polynomials Multiplying and Dividing Rational Expressions Solving Systems of Linear Inequalities Mixed-Number Notation Linear Equations and Inequalities in One Variable The Quadratic Formula Fractions and Decimals Graphing Logarithmic Functions Multiplication by 111 Fractions Solving Systems of Equations - Two Lines Solving Nonlinear Equations by Factoring Solving Linear Systems of Equations by Elimination Rationalizing the Denominator Simplifying Complex Fractions Factoring Trinomials Linear Relations and Functions Polynomials Axis of Symmetry and Vertices Equations Quadratic in Form The Appearance of a Polynomial Equation Subtracting Reverses Non-Linear Equations Exponents and Order of Operations Factoring Trinomials by Grouping Factoring Trinomials of the Type ax 2 + bx + c The Distance Formula Invariants Under Rotation Multiplying and Dividing Monomials Solving a System of Three Linear Equations by Elimination Multiplication by 25 Powers of i Solving Quadratic and Polynomial Equations Slope-intercept Form for the Equation of a Line Equations of Lines Square Roots Integral Exponents Product Rule for Radicals Solving Compound Linear Inequalities Axis of Symmetry and Vertices Multiplying Rational Expressions Reducing Rational Expressions Properties of Negative Exponents Fractions Numbers, Factors, and Reducing Fractions to Lowest Terms Solving Quadratic Equations Factoring Completely General Quadratic Trinomials Solving a Formula for a Given Variable Factoring Polynomials Decimal Numbers and Fractions Multiplication Properties of Exponents Multiplying Fractions Multiplication by 50

What's a reverse? A reverse is a number written backwards from another number. So, 256 is the reverse of 652. There is a neat little trick dealing with the subtraction of reverses.

## 1 Method with Nines

When you subtract two three-digit reverses, a pattern emerges with the difference. The difference is usually a three-digit answer, except in one case, where it is the number 99.

• The first digit of the difference is the difference in the hundreds places, minus 1.
• The center digit is 9.
• The last digit is the number you need to add to the first digit of the difference to get 9.

Example:

764 - 467 =

The first digit is the difference in the hundreds place, minus 1: 7 - 4 - 1 = 2.

The center digit is 9.

The last digit is the number you add to the first digit to get 9, or 9 - 2 = 7.

Therefore, 764 - 467 = 297.

Example

423 - 324 =

The first digit is the difference in the hundreds place, minus 1: 4 - 3 - 1 = 0. Since it's 0, you don't write anything.

The center digit is 9.

The last digit is 9 - 0 = 9.

Thus, 423 - 324 = 99.

Also, watch out for problems where you are subtracting a smaller number minus a larger number. The process is the same, using the bigger number as your starting point. Don't forget to put a negative sign on the answer.

Example:

357 - 753 =

You have to think of this one backwards. You still subtract the hundreds places, minus 1: 7 - 3 - 1 = 3.

The center number is 9.

9 - 3 = 6.

Therefore, 357 - 753 = -396. Don't forget the negative.