Practice the questions given in the worksheet on proportion and continued proportion.

**1. Check whether the following numbers are in proportion or
not:**

(i) 3, 5, 6, 10

(ii) 0.25, 0.5, 50, 100

(iii) 3, 4\(\frac{1}{2}\), 6, 9\(\frac{2}{3}\)

(iv) 4\(\frac{1}{2}\), 1\(\frac{1}{3}\), 2\(\frac{1}{4}\), \(\frac{2}{3}\)

**2. Verify whether the following numbers are proportional.**

(i) 5, 13, 15, 39

(ii) 7, 14, 56, 28

(iii) 0.3, 1.5, 0.06, 0.21

(iv) a, b, a\(^{2}\)b, ab\(^{2}\)

(v) a\(^{2}\) + ab, b\(^{2}\) + ab, ac\(^{2}\) + a\(^{2}\)c, b\(^{2}\)c + bc\(^{2}\)

**3. Find x in the following proportions:**

(i) 3.5 : 7.0 = x : 20

(ii) 6 : x = 4 : 25

(iii) \(\frac{2}{5}\) : \(\frac{1}{4}\) = x : \(\frac{5}{3}\)

(iv) x : 1\(\frac{1}{2}\) = 2\(\frac{1}{3}\) : 3\(\frac{2}{3}\)

**4. Find k in each case so that the numbers are proportional.**

(i) k, 25, 80, 16

(ii) 16, k, 38, 57

(iii) 7, 49, k, 112

(iv) 20, 80, 21, x

(v) (a\(^{2}\)b -ab\(^{2}\)), k, (am\(^{2}\) -ap\(^{2}\)), (cm\(^{2}\) - cp\(^{2}\))

**5. Find the fourth proportional to:**

(i) 25, 125, 3.5

(ii) \(\frac{1}{3}\), \(\frac{3}{7}\), 2\(\frac{3}{4}\)

(iii) 9, 48, 36

(iv) 85, 170, 34

**6. Find the fourth proportional of the following sets numbers.**

(i) a\(^{2}\)b, b\(^{2}\)c, c\(^{2}\)a

(ii) m - n, m\(^{2}\) - n\(^{2}\), m\(^{2}\) - mn + n\(^{2}\)

(iii) 36, 48, 75

(iv) 0.15, 0.225, 0.64

(v) 2ab, a\(^{2}\), b\(^{2}\)

(vi) a + b, a\(^{2}\) - b\(^{2}\), a\(^{2}\) + ab + b\(^{2}\)

**7. Check the following are in continued proportion or not:**

(i) 0.4, 3.6, 3.24

(ii) 2.4, 9.6, 38.4

**8. Find p in each case so that the numbers are in continued
proportion.**

(i) p, \(\frac{1}{2}\), 2

(ii) 16, p, 9

(iii) a - b, a(a - b), p

**9. Find the third proportional of the following set of
numbers:**

(i) 7, 14

(ii) 2.5, 3.5

(iii) 1\(\frac{2}{5}\), 5\(\frac{3}{5}\)

(iv) 0.5, 4.5

(v) p\(^{3}\)q\(^{2}\), q\(^{2}\)r

(vi) (x - y)\(^{2}\), (x\(^{2}\) - y\(^{2}\))\(^{2}\)

**10.** (i) If m, 10, n, 40 are in continued proportion hen find the positive values of m and n.

(ii) If 4, 16, m, n are in continued proportion then find m and n.

Answers for the worksheet on proportion and continued proportion are given below.

**Answers**

**1.** (i) Numbers are in proportion

(ii) Numbers are in proportion

(iii) Numbers are not in proportion

(iv) Numbers are in proportion

**2.** (i) Yes

(ii) No

(iii) No

(iv) Yes

(v) No

**3.** (i) 10

(ii) 37\(\frac{1}{2}\)

(iii) 2\(\frac{2}{3}\)

(iv) \(\frac{21}{22}\)

**4.** (i) 125

(ii) 24

(iii) 16

(iv) 84

(v) bc(a - b)

**5.** (i) 17.5

(ii) 3\(\frac{15}{28}\)

(iii) 192

(iv) 68

**6.** (i) \(\frac{bc^{3}}{a}\)

(ii) m\(^{3}\) + n\(^{3}\)

(iii) 100

(iv) 0.96

(v) \(\frac{1}{2}\)ab

(vi) a\(^{3}\) - b\(^{3}\)

**7.** (i) Numbers are not in continued proportion

(ii) Numbers are in continued proportion

**8.** (i) \(\frac{1}{8}\)

(ii) 12

(iii) a\(^{2}\)(a - b)

**9.** (i) 28

(ii) 4.9

(iii) 22\(\frac{2}{5}\)

(iv) 40.5

(v) \(\frac{q^{2}r^{2}}{pq}\)

(vi) (x + y)\(^{4}\)(x - y)\(^{2}\) or, (x + y)\(^{2}\)(x\(^{2}\) - y\(^{2}\))\(^{2}\)

**10.** (i) m = 5, n = 20

(ii) 64, 256

● **Ratio and proportion**

**Basic Concept of Ratios****Important Properties of Ratios****Ratio in Lowest Term****Types of Ratios****Comparing Ratios****Arranging Ratios****Dividing into a Given Ratio****Divide a Number into Three Parts in a Given Ratio****Dividing a Quantity into Three Parts in a Given Ratio****Problems on Ratio****Worksheet on Ratio in Lowest Term****Worksheet on Types of Ratios****Worksheet on Comparison on Ratios****Worksheet on Ratio of Two or More Quantities****Worksheet on Dividing a Quantity in a Given Ratio****Word Problems on Ratio****Proportion****Definition of Continued Proportion****Mean and Third Proportional****Word Problems on Proportion****Worksheet on Proportion and Continued Proportion****Worksheet on Mean Proportional****Properties of Ratio and Proportion**

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