Math 6 H Periods 1, 6 & 7 (Wednesday)

Equivalent Fractions 6-2

Fractions can be pictured on the number line.

If you multiply the numerator and the denominator of a fraction but the same nonzero number the resulting fraction is equivalent to the original fraction

1/2 (3/3) = 3/6

Properties

For any whole numbers a, b, and c, with b≠ 0 and c≠ 0

a/b = a(c)/b(c) and a/b = (a÷c) / (b÷c)

A fraction is in lowest terms if its numerator and denominator are relatively prime If their Greatest Common Factor (GCF) is 1



Fractions and Mixed Numbers 6-3

You know that ½ + ½ + ½ = 3/2
A fraction such as 3/2 (whose numerator is greater than or equal to its denominator) is called an improper fraction. Every improper fraction is greater than or equal to 1. A proper fraction is a fraction whose numerator is less than its denominator.

Proper fractions
1/4 2/3 5/9 10/12

Improper fractions
5/2, 8/3. 11/9 , 18/15

You can express any improper fractions as the sum of a whole number and a proper fraction

3/2 = 1 + ½ or 1½

A number such as 1½ (that is expressed as the sum of a whole number and a fraction) is called a mixed number.

If the fractional part of a mixed number is a proper fraction in lowest terms, the mixed number is said to be in simplest form.

To change an improper fraction to a mixed number in simple form, we divide the numerator by the denominator and express the remainder as a fraction

14/3 = 14 ÷ 3 = 4 2/3

30/4 = 30 ÷ 4 = 7 2/4 = 7 ½

To change a mixed number to an improper fraction, rewrite the whole number part as a fraction with the same denominator as the fractional part

1 3/8 = 8/8 + 3/8 = 11/8