KS2 Mathematics: Fractions, Decimals and Percentages

Fractions, decimals and percentages are three ways of writing the same thing, and Year 6 is where a pupil is expected to move between them without stopping to think. These ten questions do exactly that. They begin inside fractions — adding two with different denominators, multiplying one by a whole number, finding three fifths of an amount, and reducing a fraction until nothing is left to divide by, a question whose difficulty is that two of the wrong options are equal to the starting fraction and simply have not been finished. Then they cross between the forms: a fraction written as a decimal, a decimal written as a percentage, fifteen per cent of a number found by taking ten per cent and adding half of it again, and four values in three different notations put side by side to see which is biggest. The last two are the everyday versions: a coat reduced in a sale, where the trap is answering with the size of the discount instead of the price, and water poured from a jug, where the trap is forgetting to write the whole number as two decimal places before subtracting. Every explanation shows the steps and names the slip behind each wrong answer. Zestly is an independent study tool. It is not affiliated with any exam board and it is not an exam centre.

• Add fractions by finding a common denominator, and see why adding tops and bottoms separately is wrong
• Multiply a fraction by a whole number and simplify the result
• Find a fraction and a percentage of an amount, including 15 per cent by splitting it into 10 and 5
• Reduce a fraction to its simplest form and recognise an equivalent fraction that is not yet simplified
• Convert between a fraction, a decimal and a percentage in both directions
• Compare values written in all three forms by putting them into one form first
• Work out a sale price after a percentage reduction, and subtract a decimal from a whole number

Which of these is 18/24 written in its simplest form? — 3/4. The tricky part is that 9/12 and 6/8 are both exactly equal to 18/24, but neither is finished: 9 and 12 still share a factor of 3, and 6 and 8 still share a factor of 2.