Factors, Multiples, Fractions, and Mixed Numbers Study Guide for McGraw-Hill's ASVAB
Factors are whole numbers that are multiplied together to create another number.
2 × 4 = 8 (2 and 4 are factors of 8.)
1 × 8 = 8 (1 and 8 are factors of 8.)
So 1, 2, 4, and 8 are all factors of 8.
1 × 32 = 32 (1 and 32 are factors of 32.)
2 × 16 = 32 (2 and 16 are factors of 32.)
8 × 4 = 32 (8 and 4 are factors of 32.)
So 1, 2, 4, 8, 16, and 32 are all factors of 32.
Types of Factors Knowing about factors will be very useful when solving equations.
Common Factors Common factors are factors that are shared by two or more numbers. As shown above, 8 and 32 share the common factors 1, 2, 4, and 8.
Multiples of a number are found by multiplying the number by 1, 2, 3, 4, 5, 6, 7, 8, and so on. So multiples of 5 are 10, 15, 20, 25, 30, 35, 40, and so on.
Common Multiples Common multiples are multiples that are shared by two or more numbers.
Least Common Multiple The least common multiple is the smallest multiple that two numbers share. For example, 6, 12 and 18 are all common multiples of 2 and 3 because they are all evenly divisible by both 2 and 3. 6 is the least common multiple because it is the smallest number that 2 and 3 both divide evenly.
Fractions have two numbers, a numerator and a denominator.
The denominator tells how many parts something is divided into. The numerator tells how many of those parts you have. The fraction as a whole tells the proportion of the parts you have to the parts there are in all.
So if a pie is divided into 8 pieces and you take 2 of them, the fraction telling the proportion of the pie you have is . The denominator (8) tells how many pieces of pie there are in all. The numerator (2) tells how many of those pieces you have.
- or a proportion of 2 to 8.
Fractions can be positive or negative. A negative fraction is written like this:
Types of Fractions For the ASVAB, you'll need to know about proper fractions, improper fractions, and mixed numbers.
Proper Fractions Fractions representing amounts smaller than 1 are called proper fractions. Fractions smaller than 1 have numerators that are smaller than the denominators.
Improper Fractions Improper fractions are greater than 1. The numerator is larger than the denominator.
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