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Combining fractions

This task is about adding fractions.

a)	Chen, Malachi, and Rory ordered a giant pizza. Chenate $1 \over 3$ , Malachi ate $1 \over 4$ , and Rory ate $1 \over 5$ of the pizza. Altogether, what fraction of the pizza did they eat? __________

In a relay, Toby ran 2

\frac{1}{2}

$1 \over 2$ laps, Celia ran 3

\frac{1}{3}

$1 \over 3$ laps, and Danica ran 4

\frac{1}{4}

$1 \over 4$ laps.

Altogether, how many laps, including part laps, did they run? __________

pets

c)	A pet shop has puppies with different-coloured coats. $1 \over 4$ are pure white, $1 \over 5$ are pure black, and $2 \over 5$ are both black and white. The remaining puppies have no black or white colouring. What fraction of the puppies ...

ii)

iii)

are pure black or pure white in colouring? __________

have at least some white colouring? __________

have no black or white colouring? __________

			Y10 (10/1998)
a)		[Accept 0.783]	moderate
b)		10 [Accept 10.08 or ]	moderate
c)	i) ii) iii)	[Accept 0.45] [Accept 0.65] [Accept 0.15]	moderate difficult difficult

	Student response	Likely reason
a)		Calculates
c)	9, 13, 3 respectively	Gives numerator of answers rather than whole fractions.
c) ii)	²/₅	Sees "at least some white" to exclude "pure white"

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