Lesson 6

In this lesson, students continue to develop methods for computing products of decimals, including using area diagrams. They multiply decimals by expressing them as fractions, or by interpreting each decimal as a product of a whole number and a power of 10 and \(\frac{1}{10}\). To multiply \((0.25) \boldcdot (1.6)\), for example, students may first multiply 0.25 by 100 and 1.6 by 10 to have whole numbers 25 and 16, multiply the whole numbers to get 400, and then multiply 400 by \(\frac {1}{1,000}\) to invert the initial multiplication by 1,000. They may also think of 0.25 and 1.6 as \(\frac {25}{100}\) and \(\frac {16}{10}\), multiply the fractions, and then express the fractional product as a decimal.

In earlier grades, students used the area of rectangles to represent and find products of whole numbers and fractions. Here they do the same to represent and find products of decimals. They see that a rectangle that represents \(4 \boldcdot 2\), for instance, can also be used to reason about \((0.4) \boldcdot (0.2)\), \((0.004) \boldcdot (0.002)\), or \(40 \boldcdot 20\) because they all share a common structure. In this lesson, students extend their understanding of multiplication of fractions and multiplication using area diagrams by using previous methods to multiply any pair of decimals.