Reasoning · Grade 3-2 Applying Fractions

Problem

Find fractions meeting conditions

Six fractions - 8/12, 2 4/7, 12/5, 23/9, 19/4 and 3 1/6 - go into a three-circle Venn diagram. A is improper fractions, B is denominators divisible by 3, C is greater than 5/2. Each fraction sits in every region it satisfies. Place all six.
Your answer
How to solve
Strategy Draw a Venn Diagram — The task is literally a Venn-diagram sort by which of three conditions each fraction meets. I make a systematic A/B/C checklist for every fraction, then drop each into the region for its set of true conditions.
1STEP 1

Check condition A (improper fraction) for each

Only 12/5, 23/9, 19/4 are improper; the mixed numbers drop out.

A: 12/5, 23/9, 19/4
2STEP 2

Check condition B (denominator divisible by 3)

Denominators divisible by 3: 8/12, 23/9, 3 1/6.

12 = 3×4, 9 = 3×3, 6 = 3×2 → B: 8/12, 23/9, 3 1/6
3STEP 3

Check condition C (greater than 5/2)

Past 5/2 = 2.5: 2 4/7, 23/9, 19/4, 3 1/6.

5/2=2.5; 2 4/7,23/9,19/4,3 1/6 ＞ 2.5, but 12/5=2.4 ＜ 2.5
4STEP 4

Place each fraction in its region

Meeting all three, 23/9 takes the centre.

8/12 → B, 2 4/7 → C, 12/5 → A, 19/4 → A∩ C, 3 1/6 → B∩ C, 23/9 → A∩ B∩ C
Answer
A only 12/5, B only 8/12, C only 2 4/7, A and C 19/4, B and C 3 1/6, centre 23/9
All six fractions are placed, each in a different region, and the only fraction meeting every condition (23/9: improper, denominator 9 divisible by 3, and ≈2.56 ＞ 2.5) correctly lands in the center. Re-reading each check confirms no fraction was double-counted or missed.
Takeaway

Make a quick yes/no checklist for each fraction against the three rules, and the Venn diagram practically fills itself in!

  • Check condition A (improper fraction) for each
  • Check condition B (denominator divisible by 3)
  • Check condition C (greater than 5/2)
  • Place each fraction in its region