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Fractions and Factor Trees
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Fractions and Factor Trees
🌳 Part 1: Factor Trees and Simplifying Fractions
1. Complete the factor tree for 24 and use it to simplify the fraction 24/36:
2. Which of these fractions is equivalent to 3/4?
6/8
9/15
15/20
12/18
3. Find the HCF of 18 and 30 using factor trees. Show your working:
4. Simplify these fractions using the HCF method:
a) 12/18 = _______
b) 20/25 = _______
c) 15/45 = _______
🔄 Part 2: Converting Between Improper Fractions and Mixed Numbers
5. Convert these improper fractions to mixed numbers:
a) 13/4 = _______
b) 22/7 = _______
c) 17/5 = _______
6. Convert these mixed numbers to improper fractions:
a) 3 2/5 = _______
b) 2 3/8 = _______
c) 4 1/3 = _______
7. Explain why improper fractions are called "top-heavy" fractions and give one reason why they are useful in mathematics:
🧮 Part 3: Problem Solving
8. A whānau is sharing kai. They have 19/4 cups of kumara soup to share equally among 3 people. How much soup does each person get? Express your answer as a mixed number.
9. Find the LCM of 12 and 18 using factor trees. Show all your working:
10. Challenge Question (Extension): If 5/8 of a pizza equals 2 1/2 pieces, how many pieces make up the whole pizza? Show your reasoning:
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