11 plus fractions, decimals and percentages conversion questions

What a fractions, decimals and percentages conversion question looks like

FDP is the shorthand used for fractions, decimals and percentages, and in the 11 plus a conversion question takes a value written in one of those forms and asks for it in another. 1/2, 0.5 and 50% are the same amount in three different outfits, and the question is whether your child can move between them without stopping to think. That is what separates this type from the fraction and percentage questions around it: those keep a value in one form throughout, working out 3/4 of 40 or simplifying 6/8, while these change the form or line up three different forms against each other.

Every direction shows up. Fraction to decimal, decimal to fraction, fraction to percentage, percentage to fraction, decimal to percentage and percentage to decimal are all in the bank, along with three variations that make a child use the same skill in a less obvious place. One gives a child’s claim, “0.75 is the same as 75%, is she correct?”, and asks whether it holds. One gives three or four values in mixed forms and asks which is largest or for them in order. One asks which option is not equal to the others. A handful ask for a value to be read off a pie chart, a bar chart, a line graph or a Venn diagram and then converted before it can be matched. There are five options and one is right.

Example one: 35% as a fraction in its simplest form

Per cent means out of a hundred, so 35% is 35 out of 100, which is 35/100. Now simplify. Look for the biggest number that goes into both 35 and 100. That is 5. 35 divided by 5 is 7, and 100 divided by 5 is 20, so the answer is 7/20.

The tempting wrong answers are 35/10 and 35/1000. Both come from a child who knows the number sits over something but has not held on to which power of ten. Per cent gives 100 every time, whatever the number in front of it is.

Example two: 4/5 as a decimal

There are two routes and both are worth knowing. The quicker one is to make the bottom number into 10, because tenths sit in the first place after the point. 5 times 2 is 10, so multiply the top by 2 as well: 4/5 is the same as 8/10, and 8 tenths is 0.8. The other route is to divide the top by the bottom, 4 divided by 5, which also gives 0.8.

The wrong answer that catches children is 0.45. It is made by reading the digits 4 and 5 straight off the fraction and dropping a point in front of them. It never works: 4/5 is more than a half, and 0.45 is less than a half, so a moment spent asking “should this be bigger or smaller than 0.5?” catches it.

Example three: 0.45, 9/25 and 44% in order, smallest to largest

Mixed sets cannot be compared as they stand, so pick one form and put everything into it. Percentages work well here. 0.45 times 100 is 45%. For 9/25, multiply the top and bottom by 4 to get 36/100, which is 36%. The third value is already 44%. Now they line up: 36%, 44%, 45%. So the order is 9/25, then 44%, then 0.45.

The answer that tempts is 44%, 9/25, 0.45. It comes from assuming that a small-looking fraction like 9/25 must be the smallest of the three, which happens to be true here, and then putting it in the middle because it looks like a middling sort of number. Guessing at the order without converting gets the eleven plus candidate about a third of these right.

How to answer it

1. Read what form the answer has to be in, and whether the question says “in its simplest form” or “do not simplify”. Both instructions appear, and answering the wrong one loses the mark on a sum that was worked out correctly.
2. Choose one form to work in. For a single conversion, go straight to what is asked. For any question comparing several values, put everything into decimals or percentages, because those compare digit by digit and fractions do not.
3. Use the route that fits. A percentage goes over 100. A decimal is tenths, hundredths or thousandths depending on how many digits sit after the point. A fraction becomes a decimal either by making the bottom number 10 or 100, or by dividing the top by the bottom.
4. Simplify last, and only if asked. Find the biggest number that divides into both parts rather than halving repeatedly, which is where errors creep in.
5. Sense-check against something known. Is the answer above or below a half? Near a quarter? Near three quarters? Most wrong options fail this test in a second.

Common mistakes

• Moving the point the wrong number of places. 0.75 turns up as 7.5%, 0.075% and 750% among the wrong options. Decimal to percentage always means times 100, and percentage to decimal always means divide by 100.
• Reading the digits instead of converting. 4/5 becomes 0.45, 3/10 becomes 0.03, 1.7 becomes 1/7. The digits in a fraction are not the digits in its decimal.
• Counting decimal places wrong. 0.09 is 9 hundredths, so 9/100. Two digits after the point means hundredths, three means thousandths.
• Comparing forms without converting. 3/5 looks bigger than 0.62 and it is not, because 3/5 is 0.60. 7/12 looks nothing like 58% and is very close to it, at 0.583.
• Expecting every fraction to give a tidy percentage. 5/6 is 83.3%, not 83%. When a conversion does not come out exactly, the answer that says “approximately” is usually the right one.

How to practise 11 plus fractions, decimals and percentages conversion questions

The single most useful thing is a small set of conversions known by heart: a half, a quarter, three quarters, a fifth, a tenth and an eighth, each in all three forms. Everything else in this topic is built on top of them, and a child who has to work out 1/4 from scratch every time runs out of clock. After that it is repetition in short bursts rather than long sessions, which is the pattern we set out in how much 11 plus practice a child needs each day. When one comes back wrong, ask your child to say the value in all three forms out loud before moving on, because the error is nearly always in one specific direction rather than across the topic. 11+ Daily has an FDP Conversions project alongside the other maths topics, on laptop, tablet or phone, and the full list sits on our 11 plus maths practice page. Every question is original to 11+ Daily, nothing is a past paper and nothing is licensed from another publisher, and the bank is re-checked in rounds.

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