6.4 Introduction to representations of multiplying and dividing fractions

Introduction Boxes can be split into all kinds of sections Introduction Boxes can be split into all kinds of sections. Can you tell what fraction is shaded in each box?

To multiply, put together like this To multiply, put together like this! Vertical is first, Horizontal is last! Order does not matter with multiplication, but it sure does with division! So we are going to always do it like this. 2/3 x 1/2 Tada! The product is 2/6 or 1/3! The denominator is all the sections and the numerator is the overlap! Now Watch!

We can check this! ¼ x 3/5 is 1 x 3= 3 4 x 5= 20 The product is 3/20 Try these! ¼ x 3/5 We can check this! ¼ x 3/5 is 1 x 3= 3 4 x 5= 20 The product is 3/20

Do you think you can? 5/6 x 1/4 5 x 1 = 5 6 x 4 = 24 The product is 5/24

Try another? 5/8 x 7/12 Check! 5 x 7 = 35 8 x 12 = 96 The product is 35/96

Try another? 1/4 x 1/2 Check! 1 x 1 = 1 4 x 2 = 8 The product is 1/8

Now for DIVISION!

When using division models, order matters. The first bar is the dividend and the second bar is the divisor. This means how many will fit into 2 5 11 12 11 12 2 5 11 12 ÷ Same Change Flip 11 12 x 5 2 = 55 24 =2 7 24 2 5

Now it’s time to set up our notebook and practice! 6.4 The student will demonstrate multiple representations of multiplication and division of fractions

6.4 Directions Multiplication Pg 13 6.4 Directions Multiplication First fraction square is vertical. Overlap the second fraction square horizontally. Multiplication- count all the sections once squares are overlapped. This is the denominator. Count the sections where the colors or patterns combine. This is the numerator. Example- ½ x ¼ 1 section overlaps 8 sections total Product is 1/8 Check- ½ x ¼ =1/8 Vocabulary 6.4 pg. 14 mixed number SOL 6.4/6.6 A numerical value that combines a whole number and a fraction EX- 2 ¾ addition The act or process of combining numerical values, so as to find their sum simplest form A fraction is in simplest form when the greatest common factor of the numerator and denominator is 1. sum An amount obtained as a result of adding numbers EX 2+2=4 4 is the sum simplify To reduce the numerator and the denominator in a fraction to the smallest form possible. To divide the numerator and denominator by the GCF is simplifying a fraction. subtraction The arithmetic operation of finding the difference between two quantities or numbers LCD difference The least common multiple of the denominators of two or more fractions. Example: 6 is the least common denominator of 2/3 and 1/6. An amount obtained as a result of subtracting numbers EX 5-3=2 2 is the difference reciprocal estimate Any two numbers whose product is 1. To make an approximate or rough calculation, often based on rounding Example: ½ and 2 are reciprocals because ½ X 2 = 1product An amount obtained as a result of multiplying numbers division The operation of determining how many times one quantity is contained in another; the inverse of multiplication. quotient An amount obtained as a result of dividing numbers EX-12 ÷ 2= 6 six is the quotient numerator The expression written above the line in a fraction EX- ½ One is the numerator denominator The expression written below the line in a fraction that indicates the number of parts into which one whole is divided. EX- ½ 2 is the denominator improper fraction A fraction in which the numerator is larger than or equal to the denominator. The value of an improper fraction is greater than or equal to one. EX- 14/5

Dividend- first fraction bar Divisor- second fraction bar Pg __ 6.4 Directions for division . Example- ½ ÷ ¼ same change flip 1 2 x 4 1 = 4 2 = 2 Dividend- first fraction bar Divisor- second fraction bar Quotient- the answer FLIP is the reciprocal Pg __ Practice Multiplication Draw a box. When you shade use stripes. Split vertically into 3 sections. Shade 1 section. Split horizontally into 2 sections. Shade one. This is 1/3 x ½ = 1/6 Practice Division------------------------- ___ ÷ ___   ___ x ___ = ___