Lesson Guide
Explanation
Cut the whole into enough parts that both fractions are whole numbers of parts — here ten. Two fifths is four parts eaten, leaving six. Then half of what is left is half of six, three more, leaving three parts: three tenths of the original. The trap is taking half of the original instead, which would be five parts and a completely different answer. Read whether the second fraction is of the whole or of the remainder.
Your Turn
A third is used, then half of what is left. What fraction remains? Check: 2/3 left, half of that is 1/3, so 1/3 remains.
Watch Out
"Half of what is left" is half of the remainder, not half of the whole.
Explanation
To compare or subtract fractions, rewrite both with the same bottom number and then just compare the tops. Thirds and fifths both go into fifteenths, so a third is five fifteenths and two fifths is six fifteenths — two fifths is bigger, by one fifteenth. Comparing each with a half is a quick filter but does not always separate them, as here where both are under a half.
Your Turn
Which is bigger, 1/3 or 2/5? Check: 5/15 against 6/15, so 2/5.
Watch Out
A bigger bottom number means smaller parts. 1/5 is less than 1/3, even though 5 is more than 3.
Explanation
Mixed numbers get much easier if everything goes into the smallest part. With quarters, one and a quarter is five quarters, three quarters is three, and a half is two — ten quarters used out of the sixteen in four pizzas, so six quarters are left, one and a half pizzas. Converting once at the start means no mixed-number arithmetic at all, and it also makes the comparison easy: six quarters beats Ana's five.
Your Turn
How many quarters are there in 4 whole pizzas? Check: 16.
Watch Out
Convert the whole amount too. Four pizzas is 16 quarters, not 4.
Explanation
When a question lists the chances of every outcome, they must add to exactly one — and that is the equation you need. If red and blue take four tenths between them, green and yellow share the other six tenths. If green is twice yellow, that six tenths splits into three parts of two tenths — yellow takes one and green takes two, so green is zero point four. Always finish by checking that all four add back to one.
Your Turn
Green and yellow share 0.6, and green is twice yellow. Find both. Check: yellow 0.2, green 0.4.
Watch Out
"Twice as likely" means the pair splits into THREE parts, not two.
Explanation
Claim questions on fractions work the same way as everywhere else: turn every statement into the same parts before judging it. Red is two of ten, which is one fifth; blue is four of ten, two fifths; together they are six of ten, three fifths. Is that more than three quarters? Three quarters would be seven and a half of ten, so no. Two ticks and a cross. Quiz and exercises now.
Your Turn
Is 6 out of 10 more than three quarters? Check: no — three quarters is 7.5 out of 10.
Watch Out
Convert the claim to the same parts as the picture. Comparing 3/5 with 3/4 by their tops alone is meaningless.
📌 Key Points — this lesson in a nutshell
- A fraction of what is left is not a fraction of the original. Work out what is left first.
- Turn the fractions into the same number of parts and the whole question becomes counting.
- Probabilities of all the outcomes always add to 1. That is usually the equation you need.
- Compare fractions by making the bottoms the same, or by comparing each with a half.
Step 1: Introduction
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