![]() The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include: A sound understanding of multiplication of fractions is therefore a prerequisite for multiplying decimals with a sense of the size of the product. Expressing both multiplications as fractions gives 6/10 x 4/10= 24/100 and 3/10 x 8/100 = 24/1000, so the products are 0.24 and 0.024 respectively. Knowing 1/10 x 1/10 = 1/100 and 1/10 x 1/100 = 1/1000, etc., makes it possible to know the size of the products for factors like 0.6 x 0.4 and 0.3 x 0.08. Estimation of the size of products requires understanding of the multiplication of decimal fractions. Deci is the prefix meaning one tenth, to indicate that decimal fractions are powers of one tenth, or negative powers of ten, e.g. The multiplier is applied to the rate resulting in a measure, for example, 3 kilograms of meat at $12.50 per kilogram costs $37.50.ĭecimals might more correctly be termed decimal fractions. A rate is a relationship between two measures, such as 60 kilometres per hour (speed), 456 kilograms per cubic metre (density), or 30 people per square kilometre (also density). For example, 3.9 ÷ 10 = 0.39, 3.9 ÷ 100 = 0.039, 3.9 ÷ 1000 = 0.0039.Īpplying multiplication to measurement situations often involves a multiplier and a rate. The effect of division by ten is to make each unit one tenth of its previous size, represented as a shift of the digits one place to the right. ![]() Therefore, understanding the effect of multiplying and dividing a decimal amount by ten, one hundred, and one thousand is foundational to estimating the products of decimals. are the result of division by ten of the previous larger unit. The prefixes deci (tenth), centi (hundredth) and milli (thousandth) are applied to base units, such as metres and litres, to obtain a necessary degree of precision. Common situations where tenths, hundredths, thousandths, etc. The decimal system includes a restricted set of equivalent fractions for situations where whole units are inadequate for purpose. Making sensible estimates for the products of decimals requires a flexible connection of place number understanding with whole numbers, the meaning of multiplication, and multiplication with fractions. In this unit, students will develop number sense related to multiplying decimals.
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