4.	Work out
(i)  7/210 – 2/5 =      	 				(ii)  5½  - 1¾ =

(iii)  4/5  x  2/3  = 					(iv)  ¼ of 64/7 =

Let's solve these one by one:

### (i) \(\frac{7}{210} - \frac{2}{5}\)

To subtract these fractions, we need to have the same denominator. 

1. The LCM (least common multiple) of 210 and 5 is 210.
2. Convert \(\frac{2}{5}\) to a fraction with denominator 210:
   \[
   \frac{2}{5} = \frac{2 \times 42}{5 \times 42} = \frac{84}{210}
   \]
3. Now, subtract the fractions:
   \[
   \frac{7}{210} - \frac{84}{210} = \frac{7 - 84}{210} = \frac{-77}{210}
   \]
4. Simplify the fraction by dividing both the numerator and denominator by 7:
   \[
   \frac{-77}{210} = \frac{-11}{30}
   \]
Thus, \(\frac{7}{210} - \frac{2}{5} = \frac{-11}{30}\).

---

### (ii) \(5\frac{1}{2} - 1\frac{3}{4}\)

1. Convert the mixed numbers to improper fractions:
   \[
   5\frac{1}{2} = \frac{11}{2}, \quad 1\frac{3}{4} = \frac{7}{4}
   \]
2. To subtract, we need the same denominator. The LCM of 2 and 4 is 4.
3. Convert \(\frac{11}{2}\) to a fraction with denominator 4:
   \[
   \frac{11}{2} = \frac{11 \times 2}{2 \times 2} = \frac{22}{4}
   \]
4. Now subtract the fractions:
   \[
   \frac{22}{4} - \frac{7}{4} = \frac{22 - 7}{4} = \frac{15}{4}
   \]
5. Convert \(\frac{15}{4}\) back to a mixed number:
   \[
   \frac{15}{4} = 3\frac{3}{4}
   \]
Thus, \(5\frac{1}{2} - 1\frac{3}{4} = 3\frac{3}{4}\).

---

### (iii) \(\frac{4}{5} \times \frac{2}{3}\)

To multiply fractions, multiply the numerators and denominators:

\[
\frac{4}{5} \times \frac{2}{3} = \frac{4 \times 2}{5 \times 3} = \frac{8}{15}
\]

Thus, \(\frac{4}{5} \times \frac{2}{3} = \frac{8}{15}\).

---

### (iv) \(\frac{1}{4} \text{ of } \frac{64}{7}\)

"Of" in mathematics usually means multiplication. So, we multiply the two fractions:

\[
\frac{1}{4} \times \frac{64}{7} = \frac{1 \times 64}{4 \times 7} = \frac{64}{28}
\]

Now, simplify \(\frac{64}{28}\) by dividing both numerator and denominator by 4:

\[
\frac{64}{28} = \frac{16}{7}
\]

Thus, \(\frac{1}{4} \text{ of } \frac{64}{7} = \frac{16}{7}\).

---

### Summary of Results:
1. (i) \(\frac{7}{210} - \frac{2}{5} = \frac{-11}{30}\)
2. (ii) \(5\frac{1}{2} - 1\frac{3}{4} = 3\frac{3}{4}\)
3. (iii) \(\frac{4}{5} \times \frac{2}{3} = \frac{8}{15}\)
4. (iv) \(\frac{1}{4} \text{ of } \frac{64}{7} = \frac{16}{7}\)

Would you like more details on any part of the solutions? Here are some related questions:

1. How do you find the least common multiple of two numbers?
2. How can you simplify improper fractions?
3. What are the steps to convert a mixed number into an improper fraction?
4. Why is multiplying fractions easier than adding or subtracting them?
5. How do you check your work when simplifying fractions?

**Tip**: Always simplify your fractions to their lowest terms to ensure the answer is in its simplest form.

4. Work out (i) 7/210 – 2/5 = (ii) 5½ - 1¾ = (iii) 4/5 x 2/3 = (iv) ¼ of 64/7 =

Learn how to subtract and multiply fractions, solve mixed numbers, and simplify the results. This step-by-step guide covers subtraction of fractions with different denominators, multiplication of fractions, and working with mixed numbers. Suitable for students in Grades 5-7.

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