Comparing Fractions — Solutions

1. Compare each pair using <, > or =

   1. 12 vs 34: < ▶ View Solution
   2. 23 vs 46: = ▶ View Solution
   3. 35 vs 58: < ▶ View Solution
   4. 56 vs 79: > ▶ View Solution
   5. 47 vs 35: < ▶ View Solution
   6. 710 vs 34: < ▶ View Solution
   7. 29 vs 14: < ▶ View Solution
   8. 512 vs 38: > ▶ View Solution

2. Order each set from smallest to largest

   1. 14, 13, 12: 14 < 13 < 12 ▶ View Solution
   2. 23, 34, 56: 23 < 34 < 56 ▶ View Solution
   3. 14, 38, 25: 14 < 38 < 25 ▶ View Solution
   4. 23, 710, 34, 56: 23 < 710 < 34 < 56 ▶ View Solution
   5. 16, 29, 14, 310: 16 < 29 < 14 < 310 ▶ View Solution
   6. 1120, 712, 58: 1120 < 712 < 58 ▶ View Solution
   7. 512, 37, 49: 512 < 37 < 49 ▶ View Solution
   8. 78, 89, 910, 1112: 78 < 89 < 910 < 1112 ▶ View Solution

3. Describe the position and explain your reasoning

   1. Position of 35 on number line: Just past halfway — 0.6 is closer to 1 than 0 ▶ View Solution
   2. 78 vs 56, which is closer to 1?: 78 — only 18 from 1 vs 16 ▶ View Solution
   3. Two fractions between 14 and 12: e.g. 13 and 25 ▶ View Solution
   4. Is 45 closer to 1 than 34?: True — 45 > 34 ▶ View Solution

4. Benchmark estimation — is each fraction closer to 0, ½ or 1?

   1. 19: closer to 0 ▶ View Solution
   2. 511: closer to ½ ▶ View Solution
   3. 78: closer to 1 ▶ View Solution
   4. 37: closer to ½ ▶ View Solution
   5. 910: closer to 1 ▶ View Solution
   6. 213: closer to 0 ▶ View Solution
   7. 49: closer to ½ ▶ View Solution
   8. 1112: closer to 1 ▶ View Solution

5. Real-world comparisons

   1. Sugar in banana bread (34) vs carrot cake (58): Banana bread uses more sugar ▶ View Solution
   2. Sam ran 710 km vs Alex 23 km: Sam ran further by 130 km ▶ View Solution
   3. Maya (56) vs Leo (79) homework done: Maya completed more ▶ View Solution
   4. Cam (512), Ava (25), Ben (38) — most to least: Cam, Ava, Ben ▶ View Solution

6. Compare mixed numbers

   1. Fractional parts 23 vs 34: < ▶ View Solution
   2. Fractional parts 12 vs 38: > ▶ View Solution
   3. Fractional parts 56 vs 79: > ▶ View Solution
   4. Fractional parts 25 vs 37: < ▶ View Solution
   5. Fractional parts 14 vs 29: > ▶ View Solution
   6. Fractional parts 1112 vs 56: > ▶ View Solution

7. Convert mixed numbers and order

   1. 113, 54, 116: 116 < 54 < 113 ▶ View Solution
   2. 214, 94, 238: 214 = 94 < 238 ▶ View Solution
   3. 116, 158, 179: 158 < 179 < 116 ▶ View Solution
   4. 227, 325, 312: 227 < 325 < 312 ▶ View Solution

8. Fractions on a number line

   1. Plot 14, 34, 112, 74 on [0, 2]: 14, 34, 112, 74 in increasing order ▶ View Solution
   2. Position of 58: Between 12 and 34, closer to 34 ▶ View Solution
   3. Midpoint of 14 and 34: 12 ▶ View Solution
   4. Midpoint of 25 and 45: 35 ▶ View Solution

9. Fraction puzzle and reasoning

   1. Fractions with denominator 12 between 12 and 34: 712 and 812 (= 23) ▶ View Solution
   2. Is 37 > 49?: No — 37 < 49 ▶ View Solution
   3. Pizza problem (Ali 38, Bo 512, Cal 13): Bo ate most; total 118 pizzas ▶ View Solution
   4. Order 57, 710, 1115, 34: 710 < 57 < 1115 < 34 ▶ View Solution

10. Fractions in context

    1. Votes: Option A (512) vs Option B (38): Option A got more votes; neither = 524 ▶ View Solution
    2. Finn swam 79 km vs 34 km target: Finn rested later — swam further ▶ View Solution
    3. Container A (23 of 1.5 L) vs Container B (34 of 2 L): Container B holds more ▶ View Solution
    4. Create a real-world fraction comparison: Accept any valid scenario with correct comparison ▶ View Solution