 MATH CHEAT SHEET (6TH – 8TH GRADE)
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 theorybased lessons taught at the high school level. An awkward stage for your child in general, middleschool 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.
A proper fraction has a numerator that is less than the denominator: 4/9 An improper fraction has a numerator greater than or equal to the denominator: 9/4 A 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: 2/3Reciprocal: 3/2 Fraction • Reciprocal = 12/3 • 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 = 3/35/7  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:
 Find the smallest multiple (LCM) of both numbers.
 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 • 3  3 • 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 

 3/4

