This worksheet provides practice problems for calculating fractions of whole numbers and finding the whole number when given a fraction.

Here's the complete solution to all 20 problems on the worksheet, with explanations for each type of problem.

---

## Type 1: Find a Fraction of a Number
*(e.g., “Find 2/8 of 80”)*
👉 Multiply the fraction by the number:
Formula: `(fraction) × (number)`

---

Solutions:

1) Find 2/8 of 80
= (2/8) × 80 = (1/4) × 80 = 20
*(Simplify 2/8 to 1/4 first for easier calculation)*

6) Find 3/5 of 165
= (3/5) × 165 = (3 × 165) ÷ 5 = 495 ÷ 5 = 99

8) Find 1/3 of 6
= (1/3) × 6 = 2

9) Find 5/8 of 440
= (5/8) × 440 = (5 × 440) ÷ 8 = 2200 ÷ 8 = 275

10) Find 2/5 of 20
= (2/5) × 20 = (2 × 20) ÷ 5 = 40 ÷ 5 = 8

11) Find 7/8 of 336
= (7/8) × 336 = (7 × 336) ÷ 8 = 2352 ÷ 8 = 294

12) Find 1/4 of 48
= (1/4) × 48 = 12

14) Find 2/3 of 72
= (2/3) × 72 = (2 × 72) ÷ 3 = 144 ÷ 3 = 48

15) Find 3/4 of 60
= (3/4) × 60 = (3 × 60) ÷ 4 = 180 ÷ 4 = 45

18) Find 7/10 of 280
= (7/10) × 280 = (7 × 280) ÷ 10 = 1960 ÷ 10 = 196

---

## Type 2: Find the Whole Number When Given a Fraction of It
*(e.g., “294 is 7/10 of what number?”)*
👉 Divide the given number by the fraction:
Formula: `given number ÷ (fraction)` → same as `given number × (reciprocal of fraction)`

---

Solutions:

2) 294 is 7/10 of what number?
= 294 ÷ (7/10) = 294 × (10/7) = (294 × 10) ÷ 7 = 2940 ÷ 7 = 420

3) 512 is 8/10 of what number?
= 512 ÷ (8/10) = 512 × (10/8) = (512 × 10) ÷ 8 = 5120 ÷ 8 = 640
*(Note: 8/10 simplifies to 4/5, but we used 10/8 directly)*

4) 7 is 1/8 of what number?
= 7 ÷ (1/8) = 7 × 8 = 56

5) 40 is 2/3 of what number?
= 40 ÷ (2/3) = 40 × (3/2) = (40 × 3) ÷ 2 = 120 ÷ 2 = 60

7) 8 is 1/4 of what number?
= 8 ÷ (1/4) = 8 × 4 = 32

13) 144 is 4/5 of what number?
= 144 ÷ (4/5) = 144 × (5/4) = (144 × 5) ÷ 4 = 720 ÷ 4 = 180

16) 90 is 3/4 of what number?
= 90 ÷ (3/4) = 90 × (4/3) = (90 × 4) ÷ 3 = 360 ÷ 3 = 120

17) 144 is 6/10 of what number?
= 144 ÷ (6/10) = 144 × (10/6) = (144 × 10) ÷ 6 = 1440 ÷ 6 = 240
*(Simplify 6/10 to 3/5: 144 ÷ 3/5 = 144 × 5/3 = 240 — same answer)*

19) 28 is 2/5 of what number?
= 28 ÷ (2/5) = 28 × (5/2) = (28 × 5) ÷ 2 = 140 ÷ 2 = 70

20) 3 is 1/3 of what number?
= 3 ÷ (1/3) = 3 × 3 = 9

---

## ✔ Final Answer Key:

1) 20
2) 420
3) 640
4) 56
5) 60
6) 99
7) 32
8) 2
9) 275
10) 8
11) 294
12) 12
13) 180
14) 48
15) 45
16) 120
17) 240
18) 196
19) 70
20) 9

---

## 📝 Summary of Methods:

- “Find X/Y of N” → Multiply: `(X/Y) × N`
- “N is X/Y of what number?” → Divide: `N ÷ (X/Y) = N × (Y/X)`

These are foundational fraction operations. Practice helps build fluency in converting between fractions and whole numbers!

Let me know if you’d like step-by-step work shown for any specific problem!