# 4th Grade - Many Meanings Of Fractions

 Grade Level: 4th Skill: Fractions and Probability Topic: Many Meanings of Fractions Goal: Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers, explain equivalence of fractions. Skill Description: Understand part of a whole number (3 parts out of 7 total parts) and part of a set (2 squares out of 8 squares are red 1/8 are red). Know fractions that are equal.

### Sample Problems

 (1) There are a total of eight kites: ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ Which fraction represents the number of kites that are yellow: 2/6 2/8 2/2 (b) (2) There are four sets of kites: ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ Which fraction represents the set of kites that are red: 1/4 2/8 2/6 (a) (3) Find the equivalent fraction by changing to its simplest form: 10 ÷ ⁪ = 25 ÷ ⁪ = Which fraction represents its simplest form: 1/5 2/5 5/25 (b) (4) Which factor is multiplied by the numerator and denominator to make an equivalent fraction: 3 = 18 8 48 18 9 6 (c) (5) Find the mixed number for the improper fraction: 13 5 2 3/5 5/13 5 2/3 (a)

### Learning Tips

 (1) Understand math vocabulary: Numerator = part Denominator =whole Equivalent -equal/same Simplest form-a fraction with a numerator and denominator that can only be divided by one. Improper fraction- a fraction that has a numerator greater than the denominator. Mixed number- a whole number and a fraction Greatest Common Factor- the largest number that can be divided into two or more numbers evenly. (2) Use illustrations (number line, fraction bars, or pictures) in order to visually show students how parts are equivalent. It may be smaller or larger parts, but in comparison to the whole it is equivalent (3) Color code parts and whole (shade the parts with a crayon) (4) Dividing food gives children a clear understanding of fractions and how it relates to their daily life (pie, pizza, candy, etc.) (5) Steps to finding the simplest form of a number: Find the greatest common factor for the numerator and denominator (i.e.) 18 21 -what are the factors for 18: 1,2,3,6,9,18 -what are the factors of 21: 1,3,7,21 -What factors do the numbers have in common 1 & 3, but 3 is the greatest common factor. Divide 18 and 21 by 3; 18 ÷3 = 6 21÷3 = 7 Does 6 or 7 have a factor greater than 1? No, so the fraction is in simplest form. (6) Algorithm for finding the mixed number for an improper fraction: Divide the numerator by the denominator i.e.) 17 9 17÷9 = 1 r8 Mixed number becomes 1 8 9

### Extra Help Problems

 (1) Find the equivalent fraction by changing to its simplest form: 15 ÷ ⁪ = 30 ÷ ⁪ = (1/2) (2) Find the equivalent fraction by changing to its simplest form: 9 ÷ ⁪ = 21÷ ⁪ = (3/7) (3) Find the equivalent fraction by changing to its simplest form: 12 ÷ ⁪ = 48 ÷ ⁪ = (1/4) (4) Find the equivalent fraction by changing to its simplest form: 36 ÷ ⁪ = 54 ÷ ⁪ = (4/6) (5) Find the equivalent fraction by changing to its simplest form: 12 ÷ ⁪ = 18 ÷ ⁪ = (2/3) (6) Which factor is multiplied by the numerator and denominator to make the equivalent fraction: 2 = 12 3 18 (6) (7) Which factor is multiplied by the numerator and denominator to make the equivalent fraction: 3 = 36 4 48 (8) Which factor is multiplied by the numerator and denominator to make the equivalent fraction: 3 = 12 8 42 (6) (9) Which factor is multiplied by the numerator and denominator to make the equivalent fraction: 1 = 15 3 45 (15) (10) Which factor is multiplied by the numerator and denominator to make an equivalent fraction: 2 = 14 5 35 (7) (11) Find the mixed number for the improper fraction: 13 4 (3 ¼) (12) Find the mixed number for the improper fraction: 5 2 (2 ½) (13) Find the mixed number for the improper fraction: 22 7 (3 1/7) (14) Find the mixed number for the improper fraction: 19 3 (6 1/3) (15) Find the mixed number for the improper fraction: 26 6 (4 2/6 or 4/1/3) (16) Find the greatest common factor for the following numbers: 8: ___ ___ ___ ___ 12: ___ ___ ___ ___ ___ (GCF =4) (17) Find the greatest common factor for the following numbers: 18: ___ ___ ___ ___ ___ ___ 24: ___ ___ ___ ___ ___ ___ ___ ___ (GCF = 6) (18) Find the greatest common factor for the following numbers: 16: ___ ___ ___ ___ ___ ___ 20: ___ ___ ___ ___ ___ ___ (GCF = 4) (19) Find the greatest common factor for the following numbers: 9: ___ ___ ___ ___ 12: ___ ___ ___ ___ ___ (GCF = 3) (20) Find the greatest common factor for the following numbers: 10: ___ ___ ___ ___ ___ 30 : ___ ___ ___ ___ ___ (GCF = 10) (21) Find the pattern and fill in the missing fractions: 2 4 6 8 15 20 25 30 ___ ___ ___ (10/35; 12/40; 14/45) (22) Multiply and find three equivalent fractions for the fraction below: 2 5 (4/10; 6/15; 8/20—answers may vary) (23) Multiply and find three equivalent fractions for the fraction below: 4 9 (8/18; 12/27; 14; 36—answers may vary) (24) Multiply and find three equivalent fractions for the fraction below: 5 12 (10/24; 15/36; 20/48—answers may vary) (25) Multiply and find three equivalent fractions for the fraction below: 7 8 (14/16; 21/24; 28/32—answers may vary)