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7th Grade MathematicsUnit 2: Lesson 3 Anna Taylor and Debra ConoverProperties of Multiplying Rational Numbers

Welcome to 7th grade mathematics (pause) unit 2, lesson 3 (pause) Properties of multiplying rational numbers (pause) by Anna Taylor and Debra Conover. 1Content StandardsM.7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (1)(1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then (p/q) = (p)/q = p/(q). Interpret quotients of rational numbers by describing real world contexts. Apply properties of operations as strategies to multiply and divide rational numbers. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. (CSS Math.7.NS.2)

Content Standards. M.7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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Now lets look at how we would solve the problem two fifths times three fourths.3For this problem we need to multiply the numerators and the denominators.

For this problem we are going to need to multiply the numerator and the denominators. So we are going to multiply 2 by 3 and then 5 by 4.4

So the solution to this problem is six twentieths. 5Now Simplify!Ask yourself this question: What is a common factor of 6 and 20?

6 = 1, 2, 3, 620 = 1, 2, 4, 5, 10, 20

What is the same?2

Now we are going to simplify our answer. The question you need to ask yourself is what is the common factor of 6 and 20? So the factors of 6 are 1,2,3, and 6. The factors of 20 are 1,2,4,5,10, and 20. So what is the largest number that is the same? 2 is in both factors.6

So six twentieths, the numerator and the denominator are going to be divided by 2. So 6 is divided by 2 and 20 is divided by 2. So our answer is now going to be three tenths. 7