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Fractions and Factor Trees
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Fractions and Factor Trees
Show your working where asked. Give fraction answers in simplest form.
Factor Trees and Simplifying Fractions
1.Use a factor tree to write 30 as a product of prime factors. Then use the HCF of 30 and 42 to simplify 30/42.
2.Which fraction is equivalent to 5/6?
- 10/12
- 15/24
- 20/30
- 25/36
3.Find the HCF of 24 and 40 by writing each number as a product of prime factors. Show how you chose the common factors.
4.Reduce 28/44 to its simplest form.
5.Reduce 21/35 to its simplest form.
6.Reduce 32/48 to its simplest form.
Improper Fractions and Mixed Numbers
7.Write 19/6 as a mixed number.
8.Write 31/8 as a mixed number.
9.Write 26/5 as a mixed number.
10.Convert 2 4/7 to an improper fraction.
11.Convert 5 2/9 to an improper fraction.
12.Convert 3 5/8 to an improper fraction.
13.In your own words, explain why a fraction such as 11/4 is called an improper fraction. Give one situation in which an improper fraction can be useful.
Using Fractions in Problems
14.A jug contains 17/3 litres of juice. It is poured equally into 4 bottles. How many litres go into each bottle? Give your answer as a mixed number.
15.Use prime factorisation to find the LCM of 15 and 24. Show the prime factors you use.
16.A baker finds that 3/5 of a tray holds 1 1/2 dozen muffins. How many dozen muffins would fill the whole tray? Show your calculation.
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