Multiply & Divide Fractions

ESSENTIAL UNDERSTANDING:

• The denominator describes what number of equal parts a whole has been divided into.

• The denominator describes what number of equal parts a whole has been divided into.

• The numerator describes how many of the parts are considered.

• The numerator is a multiplier, eg., 4/5 = 4 x 1/5

• A fraction represents division 

  • The denominator is the dividend

  • The numerator is the dividend

• Equal shares means each sharer gets the same sized part & no parts are discarded

• The solution to an equal sharing problem can be shown with a fraction representing the relationship of the sharers and the amount

• When adding or subtracting unlike fractions, all fractions must be represented with equal sized parts of the same whole. 

• The idea of the numerator as a multiplier can be used when a fraction is being multiplied by a whole number, e.g., Just as 5/8 = 5 x 1/8 5 groups of 3/8 equals 5 x 3/8 = (5x3) x 1/8 which equals 15/8

• Arrays, number lines, fraction strips, or sets can be used to find the solution to multiplying a whole number by a fraction. 

• The relationship between multiplication and division is applied to fractions just as it is applied to whole numbers.

• The area of a rectangle with fractional side lengths an be computed. 

• Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

• Explore & explain the value for the solutions when multiplying the following:

  • • a given number by a fraction greater than one

    • a given number by a fraction less than one

• When a number is multiplied by a number greater than one, the product will be greater than the original number, e.g. 3 x 5/4 will be greater than 3. 

• When a number is multiplied by a fraction less than one the product is smaller than the original number, e.g., 5 x 3/4 will be less than 5. 

• When two fractions less than one are multiplied, the product is smaller than both of the original fractions. 

• Represent & create real-world problems with visual models & a corresponding equation, justifying the solution:

  • • fractions by whole numbers

    • fractions by unit fractions

    • two fractions

    • fractions & mixed numbers 

• A whole number can be divided by a non-zero fraction

• A fraction can be divided by a non-zero whole number

Student I Can Statements:

• I can explain how a fraction represents the division of the numerator by the denominator.

• I can solve word problems involving division of whole numbers where the quotient is a fraction or mixed number by using visual models or equations. 

• I can multiply fractions

• I can explain how a fraction times a whole number is dividing the whole into parts & taking a certain number of them.

• I an find the area of a rectangle with fractional sides by tiling it with fractional unit squares.

• I can find the area of a rectangle with fractional sides by multiplying the side lengths. 

• I can explain scaling

• I can explain how to multiply a given number and make it smaller.

• I can explain how to multiply a given number and make it larger

• I can generate equivalent fractions by multiplying by various versions of one (2/2 3/3, . . . n/n)

• I can multiply fractions & mixed numbers using fraction models & or equations

• I can solve real world problems involving multiplication of fractions & mixed numbers. 

• I can explain the meaning & process of dividing a unit fraction by a non-zero whole number. 

• I can explain the meaning & process of dividing a whole number by a unit fraction

• I can solve real world problems involving division of unit fractions by non-zero whole numbers.

• I can solve real world problems involving division of whole numbers by unit fractions.