The classic way to teach fraction division is like this. To work out, say,<\/p>\n
<\/p>\n
we ‘turn the second fraction upside-down’, to get<\/p>\n
<\/p>\n
and then the division question becomes a multiplication question.<\/p>\n
I’ve been watching my son do a whole bunch of fractions questions lately, and a couple of thoughts crossed my mind. First of all, this method will confuse some students. Secondly, there’s another way to do fraction division.<\/p>\n
With fraction arithmetic, we give the students procedures for working out various sums. For addition and subtraction, ‘put the fractions over a common denominator’. For multiplication, ‘multiply the top and bottom’. For division, ‘convert it to a multiplication problem’. Ideally, kids would know these methods and the reasons why they work. However, faced with the limited time available in a lower school classroom (and the limited attention span of a typical lower school pupil), I guess a teacher can consider him\/herself lucky if an average student just learns the procedures.<\/p>\n
In any case, it’s easier to test if a student can solve fractions problems than to test if they understand fractions.<\/p>\n
If we teach<\/p>\n
then<\/p>\n
At least the idea of putting things over a common denominator can make sense without too much trouble, as well the way you need to combine the fractions afterwards. For example<\/p>\n
<\/p>\n<\/div>\n
Subtraction is similar –<\/p>\n
<\/p>\n<\/div>\n
Is there any reason not to use the same approach for division?<\/p>\n
<\/p>\n<\/div>\n
You can easily check that the standard method gives the same answer.<\/p>\n
In full detail, this method for dividing fractions looks like this :<\/p>\n
I’ll illustrate this with the original example I gave above.<\/p>\n
<\/p>\n
If this were the standard method kids were taught to divide fractions, we would teach<\/p>\n
then it’s possible that fraction arithmetic would be easier to grasp all round.<\/p>\n
Or it might not. For every student who struggles with the ‘standard method’ of fraction division, there will probably be five who are greatly relieved that it doesn’t involve common denominators. Nor would I particularly recommend teaching both<\/em> methods to an entire class and letting them pick for themselves. Although it’s worth knowing that many mathematical problems will bow to several different methods, there’s also the danger that different methods, shakily memorized, will combine confusedly in the pupil’s mind and completely mess up their ability to work with fractions.<\/p>\n Instead, I’d recommend<\/p>\n The classic way to teach fraction division is like this. To work out, say, we ‘turn the second fraction upside-down’, to get and then the division question becomes a multiplication question.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[8,196,195,51,197],"_links":{"self":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts\/309"}],"collection":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/comments?post=309"}],"version-history":[{"count":1,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts\/309\/revisions"}],"predecessor-version":[{"id":1401,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts\/309\/revisions\/1401"}],"wp:attachment":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/media?parent=309"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/categories?post=309"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/tags?post=309"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n