MATT: Welcome to the Maths Show, with me MattParker. Today we鈥檙e doing fractions, decimalsand percentages. We鈥檙e going to troubleshootsome of the more common mistakes peoplemake. Because while fractions and percentagesmay seem a bit daunting, they鈥檙e justmathematical operations, like all of Ed Sheeran鈥檚album titles鈥
MATT: Plus, his follow up Multiply 鈥 or as I call it, of 鈥揳nd Divide. We鈥檝e also just heard that his nextalbum is going to be called 鈥榓lways show yourworking out鈥.
MATT: Ha, so, first up Fractions鈥
MATT: People often get stuck when they havesomething like a half, times five. One way to dothis is to just remember that multiply is 鈥榦f鈥.We鈥檙e asking for a half of five, which is 2.5.
MATT: Or you can look at the fraction as a division, onedivided by two. And because when you鈥檙emultiplying things the order doesn鈥檛 matter.
MATT: Three times seven is the same as seven timesthree鈥
MATT: we can rearrange this to be five times one, whichis just five. Divided by two, 2.5, that鈥檚 the correctanswer.
MATT: Next up, the advantage of converting a decimalinto a percentage.
MATT: Lets say you鈥檙e asked to turn 0.85 into a fraction,go via a percentage!
MATT: 0.85 is 85%. Percent is out of 100, so we can put85/100. Now we simplify it down to get ourfraction of 17 out of 20.
MATT: We can also use percentages if we have tomultiply a decimal by a whole number.
MATT: Lets say when I release my album from my bandA2B2. We鈥檙e a tribute band that plays simplifiedversions of Abba songs鈥
MATT: and I managed to sell 10 copies at 拢30 each.That鈥檚 拢300 of which I get 0.85. I could use acalculator to work out 0.85 times 300,
MATT: or I remember that 0.85 as a percentage is 85%.
MATT: I split 300 into it鈥檚 sections. 50%, 10%, 5%. I add150, three 10鈥檚 and a 5, to get the total of 拢255.
MATT: A final word about calculators, if you鈥檙e in anexam where you鈥檙e allowed calculators, youdefinitely should be using them. They wouldhave written the questions assuming you have acalculator.
MATT: Even in every day life, they reduce the risk of youproducing a silly numerical error. In things likecompound interest, they help with doing all thecalculations.
MATT: You鈥檒l come across compound interest in thingslike savings and investments. I鈥檝e actually gotquite a good retirement investment fund goingon, let鈥檚 just check in on how it鈥檚 doing鈥︹ 7moths and two buttons! Alright.
MATT: Now if I鈥檓 getting 8% interest on my moths andbuttons, I can calculate the compound interest ofwhat I will have in ten years time. So if I get 8% a year, and I get to keep the originalamount, at the end of the year I have 108% ofwhat I started with. I can just put this straightinto a calculator.
MATT: 7 moths, times 108, and then I just hit thepercent key鈥 equals, and I get an answer of 7.56moths after a year.
MATT: I could keep hitting enter to keep multiplying by108%, but if I want to do all 10 years at once Ican just do 7 times 108%, and now I raise that tothe power of 10. So I鈥檓 multiplying by that 10times鈥 I get an answer of
MATT: 15.11鈥 that鈥檚 over 15 moths! Alright.
MATT: I鈥檓 going to be pretty set when I retire and I sellthose on the open moth market鈥
CREW MEMBER: Um, Matt? Moths aren鈥檛 worth anything, it鈥檚butterflies.
MATT: Oh no I put all my money in moths. Well thankgoodness I diversified into buttons鈥
Video summary
A guide to converting fractions, decimals and percentages, applied to real-world problems for students struggling to achieve grade 4 pass in GCSE maths.
Looking at key errors highlighted in examiners鈥 reports, the topic of fractions, decimals and percentages is presented for revision of these key skills looking at calculator and non-calculator approaches.
Matt Parker take students through some of the basics of handling fractions and decimals and percentages, converting between different representations and examining real life applications
This short film is from the 成人快手 series, The Maths Show.
Teacher Notes
Before watching
Ensure students are comfortable with the basic approaches to fractions of an amount and non-calculator questions of percentages of an amount. Explore the difference of simple interest and compound interest.
During watching
Ensure students have a scientific calculator.
Pause the video at key moments and see if your students can work out the calculation which will be explained by Matt. When pausing the video, can students think of other mental or written methods that they prefer? Compare strategies.
Pause at the introduction to compound interest. You may wish to pause and explain in more detail what this term means.
Explore the methods that Matt has shown using the calculator - would students use that method? Some students may use a different approach, elicit confidence in what they % key on the calculator is doing if students use the method shown in the video. Which method links well to non calculator methods?
After watching
Explore different conversions between fractions, decimals and percentages. Students could use a number line, either using notes posted around the room or other active learning techniques. Extend the use of decimals and fractions to include numbers greater than one and negative numbers.
Compound interest has many interesting real-life situations which could be explored, students could investigate different savings options currently available, population growth or half-lives.
Suitable for teaching maths at GCSE in England, Wales and Northern Ireland and National 4/5 or Higher in Scotland.
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