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Math Cheat Sheet


Unless you’re an accountant, an engineer or a math teacher, you’ve probably forgotten some math lessons from long ago. As a reminder: middle school means algebra.

Junior high math teachers attempt to bridge the gap and make a smooth transition from the basics learned in elementary school to the theory-based lessons taught at the high school level. An awkward stage for your child in general, middle-school doesn’t need not mean additional angst over math homework.

Using this worksheet as a refresher course, you can help your child feel more comfortable with these increasingly complex math sets.

Figuring Out Fractions

A fraction is a number written in the form: N/D where N is the numerator and D is thedenominator. In the typical case, the numerator and denominator are whole numbers. However, the denominator cannot be zero.

proper fraction has a numerator that is less than the denominator:

An improper fraction has a numerator greater than or equal to the denominator:

mixed number is a whole number and a fraction.
1 ¾

The reciprocal is the inverse of a number. For a fraction, it’s obtained by “turning the fraction over.”
Fraction: 2/3
Reciprocal: 3/2

Fraction • Reciprocal = 1
2/3 • 3/2 = 1

Equality Rule: a/b = c/d if and only if a • d = b • c

When the cross products, the results of a • d and b • c, are the same values, the two fractions are equal.

Adding and Subtracting Fractions:

Like fractions have the same denominator (2/3 and 1/3 are like fractions). You can add and subtract like fractions easily—simply add or subtract the numerators and write the sum over the common denominator.
1/3 + 2/3 = 3/3
5/7 - 2/7 = 3/7

Before you can add or subtract fractions with different denominators, you must first find equivalent fractions with the same denominator, or the least common denominator (LCM). Here’s how: 
  1. Find the smallest multiple (LCM) of both numbers.
  2. Rewrite the fractions as equivalent fractions with the LCM as the denominator.
1/5 + 1/3 = 1 • 3 + 1 • 5 = (3/15) + (5/15) = 8/15

5 • 33 • 5
The same rules apply for subtracting fractions with different denominators.

Multiplying and Dividing Fractions:

Multiplication Rule: a/b • c/d = ac/bd

Multiply the two numerators over the two denominators.

1/3 • 4/5 = 1 • 4 = 4/15

3 • 5

Division Rule: Multiply the dividend by the reciprocal of the divisor.

2/5 = 2/5 • 4/3 = 8/15