# Carpentry & Building Construction

## Math Activities :

### Fractions

Fractions express parts of a whole number. A fraction is made up of a numerator and a denominator. The numerator is the number above the line and tells how many parts. The denominator is below the line and tells how many parts are in the whole.

Three types of fractions are proper fractions, improper fractions, and mixed numbers. In a proper fraction, such as 3/4, the numerator is smaller that the denominator. In an improper fraction, such as 2/2 or 7/2, the numerator is the same or larger than the denominator. A mixed number has a whole number and any type of fraction. An example is 3 1/2.

Carpenters measure and lay out materials using all of these fractions. Carpenters use fractions in rough carpentry and finish work. They measure rough openings for doors and windows. Also, carpenters may measure molding using fractions so pieces fit together well.

 Terms, Symbols, & Abbreviationsfraction - a portion of the wholenumerator - top number in a fractiondenominator - bottom number in a fractionproper fraction - numerator is less than denominatorimproper fraction - numerator equals the denominator, or numerator is greater than denominatormixed number - whole number and fraction

Practice Exercise 1
 Convert the improper fraction 5/4 to a mixed number. Step 1 Divide the numerator by the denominator. 5 ÷ 4 = 1, with 1/4 remainder Step 2 The answer is 1 1/4.

Practice Exercise 2
 Convert the mixed number 3 1/2 to an improper fraction. Step 1 Multiply the whole number (3) by the denominator in the fraction (2). 3 × 2 = 6 Step 2 Add the numerator (1) to the result (6). 1 + 6 = 7 Step 3 Place this number (7) over the denominator (2).

The improper fraction is 7/2.

Problem Exercises

 1 The improper fraction 9/2 is the same as A) 2/9 B) 4 C) 4 1/2 D) 9 1/2 2 11/4 is the same as A) 11 1/4 B) 2 3/4 C) 2/4 D) 2 3 30/8 is the same as A) 3 B) 2 3/4 C) 3 1/4 D) 3 3/4 4 The mixed number 2 3/4 is the same as A) 6/4 B) 11/4 C) 8/3 D) 11/3 5 The mixed number 5 3/8 is the same as A) 43/8 B) 53/8 C) 40/8 D) 15/8