Expressing as Fractions — Solutions

1. Express as a fraction in simplest form (same units)

   1. 39: 13 ▶ View Solution
   2. 420: ¼ ▶ View Solution
   3. 615: 25 ▶ View Solution
   4. 824: 13 ▶ View Solution
   5. 1216: 34 ▶ View Solution
   6. 1525: 35 ▶ View Solution
   7. 1830: 35 ▶ View Solution
   8. 721: 13 ▶ View Solution

2. Express each as a percentage

   1. 14: 25% ▶ View Solution
   2. 35: 60% ▶ View Solution
   3. 28: 25% ▶ View Solution
   4. 320: 15% ▶ View Solution
   5. 710: 70% ▶ View Solution
   6. 425: 16% ▶ View Solution
   7. 930: 30% ▶ View Solution
   8. 1150: 22% ▶ View Solution

3. Unit conversions required — express as a fraction in simplest form

   1. 30 cm out of 1 m: 310 ▶ View Solution
   2. 20 min out of 1 hr: 13 ▶ View Solution
   3. 400 mL out of 1 L: 25 ▶ View Solution
   4. 250 g out of 1 kg: ¼ ▶ View Solution
   5. 45 min out of 1 hr: 34 ▶ View Solution
   6. 600 m out of 1 km: 35 ▶ View Solution
   7. 75 cm out of 1 m: 34 ▶ View Solution
   8. 500 mL out of 2 L: ¼ ▶ View Solution

4. Identify the “whole” and check same-unit rule

   1. 5 min out of 2 hr: 124 ▶ View Solution
   2. 750 mL out of 1.5 L: ½ ▶ View Solution
   3. 3648 as a fraction and percentage: 34 = 75% ▶ View Solution
   4. Is 400 m out of 2 km equal to 15?: True ▶ View Solution

5. Word problems

   1. 18 correct out of 24: 75% ▶ View Solution
   2. 9 wins out of 15 games: 60% ▶ View Solution
   3. $35 saved out of $140: 25% ▶ View Solution
   4. 20 green marbles out of 40: ½ green; ½ not green ▶ View Solution
   5. 15 passed month 1, 20 passed month 2 (out of 25): 60%; 80%; 20 percentage point improvement ▶ View Solution

6. Express as a fraction and percentage — mixed units

   1. 4 out of 16: ¼ = 25% ▶ View Solution
   2. 35 min out of 2 hr: 724 ≈ 29.2% ▶ View Solution
   3. 80 cm out of 2 m: 25 = 40% ▶ View Solution
   4. 200 g out of 1.5 kg: 215 ≈ 13.3% ▶ View Solution
   5. 450 mL out of 3 L: 320 = 15% ▶ View Solution
   6. 15 min out of 2 hr: 18 = 12.5% ▶ View Solution
   7. 120c out of $4.80: ¼ = 25% ▶ View Solution
   8. 50 sec out of 5 min: 16 ≈ 16.7% ▶ View Solution

7. Identify what the “whole” is

   1. 18 correct, 6 wrong: 34 correct ▶ View Solution
   2. 5 boys, 15 girls out of 20: Boys: ¼; Girls: 34 ▶ View Solution
   3. 8 not red out of 12: 23 ▶ View Solution
   4. 42 goals scored out of 60 total: 710 = 70% ▶ View Solution
   5. 8 SUVs out of 24: 13 ≈ 33.3% ▶ View Solution

8. Percentage change and comparison

   1. 75 sales this month vs 60 last month: 125% of last month’s sales ▶ View Solution
   2. 12 more sales out of 40: 30% growth ▶ View Solution
   3. Before: 56 out of 80; after: 69 out of 80: Before 70%; after 86.25%; 16.25 pp improvement ▶ View Solution
   4. 45 affected out of 120; 30 of those fixed: 37.5% affected; 66.7% of roadworks complete ▶ View Solution

9. Fraction as rate and density

   1. 150 out of 200 prefer tea: 34 = 0.75 = 75% ▶ View Solution
   2. 120 Year 7 out of 480 students: ¼ = 25% ▶ View Solution
   3. 2 328 pass out of 2 400 items: Pass: 97%; Rejected: 3% ▶ View Solution
   4. 12 on field, 6 scored out of 18: On field: 23; scored: 13 ▶ View Solution

10. Multi-step problems connecting fractions, decimals and percentages

    1. 135 sold out of 180 original, discount given: 34 = 75% of original; 25% discount ▶ View Solution
    2. 35 of 30 passed Test 1; 70% of 30 passed Test 2: 18 passed Test 1; 21 passed Test 2; 3 more passed Test 2 ▶ View Solution
    3. 38 of 840 kg kept: 315 kg = 37.5% ▶ View Solution
    4. Roommates split $240: 13, 35%, remainder: 2nd roommate pays most ($84) ▶ View Solution