6.N.4.3 Multiply and divide fractions and decimals using efficient and generalizable procedures.
In a Nutshell
A solid understanding of the multiplication and division models of fractions, decimals, and mixed numbers from 6.N.4.2 is key in solving problems involving rational numbers. With this foundation students will be able to understand and use efficient and generalizable procedures such as the invertandmultiply algorithm for dividing fractions or finding the correct placement of the decimal in the product of decimals.
Student Actions

Teacher Actions



Key Understandings

Misconceptions


The product for realworld and mathematical problems involving multiplication of fractions, decimals and mixed numbers can be smaller than the numbers being multiplied. For example, 0.75 0.4 = 0.3.

The quotient for realworld and mathematical problems involving division of fractions, decimals and mixed numbers can be larger than the dividend and the divisor. For example, 2 ÷ ¼ = 8.

That a product of fractions can be found by multiplying the numerators together and then the denominators.
 How to multiply mixed numbers by changing mixed numbers into improper fractions before multiplying or using partial products. For example, 3 2/3 2 1/4 is equivalent to (3 + 2/3)(2 + 1/4) which means the product can be found using the distributive property, (3 2) + (3 1/4) + (2/3 2) + (2/3 1/4).

How to use different algorithms for dividing fractions and mixed numbers including the commondenominator algorithm and invertandmultiply algorithm.

That the placement of the decimal in the product of decimals is determined by the combined number of decimals place in the decimals being multiplied together.


Have trouble understanding that when you multiply numbers the product can be smaller than the numbers being multiplied.

Have trouble understanding that the quotient of two numbers can be larger than the dividend and the divisor.

Forget that a whole number can be written as a fraction with a denominator of 1.

Think the product of mixed numbers is determined by multiplying the whole numbers and then multiplying the fractions.
 Misapply the invertand multiply algorithm for fraction division by inverting the first fraction instead of the second fraction or inverting both fractions.

Determine the number of decimals places in a problem involving multiplication of decimals by counting the decimal places to the left of the decimal instead of the right. For example, students may believe that 18.6 x 5.9 = 10.974.
 Move the decimal in both the divisor and dividend to make both numbers whole numbers when dividing a decimal by another decimal. For example, a student may think 4.567 0.25 is equivalent to 4567 25.

OKMath Framework Introduction
6th Grade Introduction
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