In the final array picture, the original whole is divided into fifteenths (15 equal size parts). The light green overlapping region is the product (answer). Two of those fifths are shaded green to show 2/ 5. In the third step, the whole is divided into fifths to form an array of three by five.
In the second step, this whole is divided into thirds and two of those thirds are shaded yellow to show 2/ 3. The sequence of pictures below shows the steps to find the answer to 2/ 3 by 2/ 5. Multiplying when both factors are fractions The answer here is 15/ 4 when expressed as an improper fraction, or 3 3/ 4 when expressed as a mixed number. By counting the number of fourths that have been shaded suggests that the final answer is found by multiplying the numerator (3) by the whole number (5). The answer (product) is 5/ 4.īelow is a similar example using the non-unit fraction 3/ 4.
The answer can be found by counting the number of one-fourths, or by rearranging the fourths to cover one whole plus an extra fourth, as shown below. In this example, one-fourth of each whole has been shaded. The example below is an area illustration of 1/ 4 by 5. Multiplying when one factor is a fraction When multiplying fractions using the array model, there are two basic forms: one factor is a fraction or both factors are fractions. In particular, it is best to use the area form of the array, as shown on the right, for the whole number example 4 by 6. However, the most universal visual representation is the array. It is possible to use the set, length or number line models for some situations involving multiplication or division of fractions.
The examples below illustrate a uniform teaching approach across both multiplication and division, as well as situations within each operation. For example, the approach used for a unit fraction should be the same as a multiple fraction and for a mixed whole number or fraction.
There are too many components within computational thinking to discuss in this blog, but an analysis of the writing related to the topic 1 suggests that good code must apply to all instances of the situation. This teaching enables students to be competent at writing computer code and these codes become digital algorithms.
The importance of knowing how to do the operations might have diminished, but there is a greater need to develop the understanding behind the skills.Ĭomputational thinking is one of the expressions used to describe teaching that helps students think and solve problems in ways a computer would process and solve a problem. The usual comment is something like, “Why is it important to know how to multiply or divide with fractions?” The obvious real-world applications of multiplying and dividing fractions involve percentage (discount, commission, and interest rates), but there are myriad unseen instances where digital algorithms work with operations involving fractions. And yet, this writer often sees a failure to employ these visual models due to the lack of pressing need to teach multiplication and division of fractions. In the move to use visual models to provide understanding of mathematical ideas and skills, there seems to be an overload of suggestions that can be applied across all possible situations involving multiplication and division of fractions. For multiplication, adults usually recall the rule, “Multiply the top numbers and multiply the bottom numbers.” For division, they often remember the rhyme, “There’s no need to wonder why, just invert and multiply.” This blog explains the reasoning behind the rules for multiplying and dividing fractions and why understanding is important. Two of these relate to multiplying and dividing fractions. There are a few statements from elementary school mathematics that seem to be universally imprinted in the minds of adults. We can see that one of the numbers is a whole number while the other is a fraction.Employing Computational Thinking when teaching multiplication and division of fractions. We know that a fraction is a number that is in the form of $\frac$ by 22 It provides limitless multiplying fraction questions including with whole numbers and with mixed numbers. Have a look at the fraction worksheet generator.
Multiplying fractions is relatively straightforward. Multiplying Fractions Worksheet Generators.Common error when multiplying fractions by a whole number.Representing multiplication of fractions in pictorial form.Multiplication of a Fraction by a Whole Number.General Steps Involved in multiplying two or more Fractions.Reducing a Fraction to its Simplest Form.