1. Algebra Readiness Chapter 2 Section 2

2. 2.2 Mixed Numbers and Improper Fractions A fraction is a proper fraction if its numerator is less than its denominator. A fraction is an improper fraction if its numerator is greater than or equal to its denominator. A mixed number is the sum of a whole number and a proper fraction.

3. To write a mixed number as an improper fraction, multiply the whole number part and the denominator (bottom), then add the numerator (top), and write the sum over the denominator (bottom stays the same). To write an improper fraction as a mixed number, divide the numerator (top number goes inside the box) by the denominator (bottom) and write the remainder as a fraction.

4. Example 1: A) Write 4 3/5 as an improper fraction. 4 3/5 = 5 · 4 + 3 5 = 23/5 B) Write 27/7 as a mixed number. 3 r. 6 7 27 - 21 6 27/7 = 3 6/7 Multiply the bottom (denominator) and the whole number, then add the top (numerator). The sum is the new top (numerator), the bottom (denominator) stays the same. Divide the numerator (top) by the denominator (bottom). The top number goes inside the box. However many times the denominator goes into the numerator, is the whole number. The remainder makes the new numerator (top) and the denominator stays the same.

5. You Try on Your White Board Write the number as an improper fraction. 1) 5 8/9 2) 63) 2 1/8 Write the number as a mixed number. 4) 15/45) 21/86) 19/6 53/86/1 17/8 3 3/42 5/83 1/6

6. Example 2: Comparing Mixed Numbers and Fractions Compare 23/14 and 1 7/8 Rewrite 1 7/8 as an improper fraction. 1 7/8 = 15/8 Now, you can cross multiply to compare the numerators. 23/14 and 15/8 23 x 8 and 14 x 15 184 and 210 184 < 210 so, 23/14 < 15/8

7. You try on Your White Board 7) 39/13 and 3 ½ 39/13 and 7/2 78 and 91 39/13 < 3 1/2 8) 4 and 32/7 4/1 and 32/7 28 and 32 4 < 32/7 9) 5 1/3 and 37/7 16/3 and 37/7 112 and 111 5 1/3 > 37/7