Question 1: Compare the fractions 3/4 and 2/3. Which is larger? Show your working.

Answer: 3/4 is larger

Question 2: Use cross-multiplication to compare 5/8 and 7/12. Which fraction is greater?

Answer: 5×12=60, 7×8=56, so 5/8 is larger

Question 3: Arrange the following fractions in order from smallest to largest: 2/5, 3/7, 4/9.

Answer: 4/9, 3/7, 2/5

Question 4: Calculate which of the fractions 7/10 and 11/15 is larger by cross-multiplying.

Answer: 7×15=105, 11×10=110, so 11/15 is larger

Question 5: A recipe calls for 2/3 cup of sugar, but another requires 3/4 cup. Which amount is greater? Show your working.

Answer: 3/4 is greater

Question 6: Compare 9/16 and 5/8 using cross-multiplication and determine which is larger.

Answer: 9×8=72, 5×16=80, so 9/16 is larger

Question 7: Order the fractions 7/9, 4/5, and 11/15 from smallest to largest.

Answer: 11/15, 4/5, 7/9

Question 8: Use cross-multiplication to compare 13/20 and 17/25. Which is larger?

Answer: 13×25=325, 17×20=340, so 17/25 is larger

Question 9: Identify and correct the mistake in comparing 4/7 and 2/3 by cross-multiplication.

Answer: Mistake: incorrectly comparing 4×3=12 and 2×7=14; correct comparison shows 4/7 < 2/3

Question 10: Compare 5/6 and 3/4 without cross-multiplication. Explain your reasoning.

Answer: Convert to common denominator or compare cross-multiplied values; 5/6 > 3/4 because 20/24 > 18/24

Question 11: Challenge: Which is larger, 9/13 or 11/16? Use cross-multiplication to justify.

Answer: 9×16=144, 11×13=143; so 9/13 is larger