HCF, LCM, and Fractions

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Date:

$Mathematical fractions and numbers illustration$

📚 Part 1: HCF and Simplifying Fractions

1. Find the HCF of 18 and 24, then use it to simplify the fraction 18/24.

HCF(18, 24) = _______ Simplified fraction: _______

2. Which fraction is 20/30 simplified to its lowest terms?

4/6

2/3

10/15

5/8

3. Sarah has 15 red marbles and 25 blue marbles. She wants to put them into groups with the same number of red and blue marbles in each group. What is the largest number of groups she can make?

Answer: _______ groups

4. Simplify these fractions using HCF:

a) 12/16 = _______

b) 21/28 = _______

c) 30/45 = _______

✏️ Part 2: LCM and Renaming Fractions

5. Find the LCM of 4 and 6, then rename 3/4 and 5/6 using this common denominator.

LCM(4, 6) = _______ 3/4 = _______/_______ 5/6 = _______/_______

6. A recipe calls for 2/3 cup of flour and 3/8 cup of sugar. To add these amounts, what common denominator should you use?

7. Rename these pairs of fractions with a common denominator using LCM:

a) 1/3 and 1/4 → _______/_______ and _______/_______

b) 2/5 and 3/10 → _______/_______ and _______/_______

8. Tom completed 3/8 of his homework on Monday and 1/6 on Tuesday. To find the total fraction completed, what should the common denominator be?

🎯 Part 3: Connecting HCF and LCM with Fractions

9. Explain in your own words: How does finding the HCF help you simplify fractions?

10. A chocolate bar is divided into 36 pieces. If you eat 24 pieces, what fraction of the chocolate bar did you eat? Write your answer in simplest form.

Fraction eaten: _______ (in simplest form)

11. Check all the statements that are TRUE:

HCF is used to simplify fractions

LCM is used to find common denominators

6/8 simplified is 3/4

The LCM of 3 and 4 is 7

12. Challenge: If 18/24 = 3/4, explain how this shows the connection between HCF and fraction simplification.