Multiplying Fractions

CCSS.Math.Content.5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. CCSS.Math.Content.5.NF.B.4 CCSS.Math.Content.5.NF.B.4.a Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) CCSS.Math.Content.5.NF.B.4.a

NUMBER LINES

5/4 IS MADE UP OF FIVE ¼’S 5/4 = 1/4 + ¼ + ¼ + ¼ + ¼ It represents 5 parts in the number line!

EQUIVALENCE – NUMBER LINE

Equivalence Fraction Bars ars.html ars.html Fraction strips hapes/fractionStrip.htm hapes/fractionStrip.htm

EQUIVALENT FRACTIONS Area Models: Creating Multiplying the Numerator and Denominator by the same number.

CONNECTING WHOLE NUMBER MULTIPLICATIONS WITH MULTIPLICATION OF A FRACTION 3 X 7 = X 1/3= 1/3 + 1/3 +1/3 7/5 = 7 X 1/5

1/3 X 1/2 What is 1/3 of ½? Use a fraction strip to figure it out? How would you solve it with a number line? How would you solve it using an area model? Write a context problem

Learn a Zillion Video Multiply whole number by a fraction Multiply a fraction by a fraction Multiply fraction by mixed numbers

CCSS.Math.Content.5.NF.B.5 Interpret multiplication as scaling (resizing), by: CCSS.Math.Content.5.NF.B.5 CCSS.Math.Content.5.NF.B.5.a Comparing 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. CCSS.Math.Content.5.NF.B.5.a CCSS.Math.Content.5.NF.B.5.b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. CCSS.Math.Content.5.NF.B.5.b

Multiplication as Scaling understand-multiplication-by-a-fraction-less- than-one understand-multiplication-by-a-fraction-less- than-one