Fraction Basics

What is a fraction? Definition: A part of whole. 𝟏 𝟒 𝟏 𝟒 Numerator 𝟏 𝟒 𝟏 𝟒 Numerator Denominator

Practice Draw a diagram to represent 5 8 :

Practice Draw a diagram to represent 3 1 3 :

Finding the Abcissa A fractions point on a number line. 0 1 0 1 Find the abcissa of 5 6 on the number line. What about 2 3 ?

Equivalent fractions If fractions are equivalent than, 𝑎 𝑏 = 𝑐 𝑑 The cross product proves this: axd = cxb Try with numbers: 2 3 = 4 6 2x6=12 and 3x4=12

Equivalent fractions

Example Find a fraction having a denominator of 24 which is equivalent to 3 4 . Find the factor that turns 4 into 24. 6 does! 3 4 𝑥6 𝑥6 = 18 24

Comparing Fractions Arranging from smallest to biggest ( Increasing order). If the denominators are the same, Than the greater the numerator the greater the fraction. Example: 1 7 , 2 7 , 3 7 , 4 7

Comparing fractions Arranging from smallest to biggest ( increasing order) if they have different denominators. We need to get both fractions over a common denominator ,and compare the numerators. Example: Lets place them in order 2 3 , 3 4 , 5 12

Comparing fractions 5 12 , 8 12 , 9 12

Simplifying Fractions Reducing or simplifying a fraction requires dividing the numerator and the denominator by same factor(GCD). Example: 2 4 ÷ ÷ 2 2 = 1 2

Word Problem In a music camp, the 360 campers were divided according to their choice of instrument: 160 chose piano, 100 the violin, 45 the cello , 25 the saxophone, 18 the flute and 12 the harp. Express as an irreducible fraction the campers that chose piano.

Answer 4 9