The worksheet on proportion and continued proportion help students to practice and acquire more knowledge on the concept of proportion where it also assists them in real-life incidents too. The proportion is a mathematical comparison of two numbers, and also we can compare the four quantities. Proportions are represented by the symbol “::” or “=”. If three quantities are in continued proportion then the ratio between the first and second quantity of ratio is equal to the second and the third quantity of the ratio.

For example, if the three quantities a, b, and c are continued proportion, then a: b = b: c i.e., \(\frac{a}{b}\) = \(\frac{b}{c}\). This free printable proportion and continued proportion worksheet pdf with answers is fun to practice and express the following ratios whether they are proportion and continued proportion or not.

Do Refer:

- Worksheet on Proportions
- Practice Test on Ratio and Proportion
- Worked out Problems on Ratio and Proportion

## Worksheet on Proportion and Continued Proportion PDF with Answers

1. Check the following numbers are in proportion or not.

(i) 1.5, 5.5, 2.7, 9.9

(ii) 2.5, 4.5, 1\(\frac{1}{4}\), 2\(\frac{1}{4}\)

**Solution: **

(i) Given numbers are 1.5, 5.5, 2.7, 9.9.

For example, to say the numbers are in proportion or not. We have to prove a: b = c: d.

Now, we find 1.5: 5.5 = 2.7: 9.9.

1.5: 5.5 = \(\frac{1.5}{5.5}\) = \(\frac{1.5×10}{5.5×10}\) = \(\frac{15}{55}\) = \(\frac{3}{11}\)

2.7: 9.9 = \(\frac{2.7}{9.9}\) = \(\frac{2.7×10}{9.9×10}\) = \(\frac{27}{99}\) = \(\frac{3}{11}\)

Thus, \(\frac{1.5}{5.5}\) = \(\frac{2.7}{9.9}\).

Therefore, the numbers 1.5, 5.5, 2.7, 9.9 are in **proportion.**

(ii) Given numbers are 2.5, 4.5, 1\(\frac{1}{4}\), 2\(\frac{1}{4}\).

As you know earlier, the numbers to be in proportion when a: b = c: d.

Now, 2.5: 4.5 = \(\frac{2.5}{4.5}\) = \(\frac{2.5×10}{4.5×10}\) = \(\frac{25}{45}\)= \(\frac{5}{9}\).

1\(\frac{1}{4}\): 2\(\frac{1}{4}\) = \(\frac{5}{4}\): \(\frac{9}{4}\) = \(\frac{5}{4}\)× 4: \(\frac{9}{4}\)× 4 = 5: 9 = \(\frac{5}{9}\).

Hence, \(\frac{5}{9}\) = \(\frac{5}{9}\).

Therefore, the numbers 2.5, 4.5, 1\(\frac{1}{4}\), 2\(\frac{1}{4}\) are in **proportion**.

2. Find x in the following proportions.

(i) 4: 3 = 8: x

(ii) 2.5: x = 8.1: 1.4

(iii) 1.0 : 2 = x: 4

**Solution: **

(i) Given 4: 3 = 8: x

⇒ \(\frac{4}{3}\) = \(\frac{6}{x}\)

⇒ 4x = 8×3

⇒ 4x = 24

⇒ x = \(\frac{24}{4}\)

⇒ x = 6.

Thus, the value of x is **6**.

(ii) Given 2.5: x = 8.1: 1.4

⇒ \(\frac{2.5}{x}\) = \(\frac{8.1}{1.4}\)

⇒ \(\frac{25}{10x}\) = \(\frac{81}{14}\)

⇒ 25 × 14 = 81 × 10x

⇒ 350 = 810x

⇒ x = \(\frac{810}{350}\)

⇒ x = 2.3

Hence, the x value is **2.3**.

(iii) Given 1.0 : 2 = x: 4

⇒ \(\frac{1.0}{2}\) = \(\frac{x}{4}\)

⇒ \(\frac{10}{20}\) = \(\frac{x}{4}\)

⇒ 10 × 4 = 20x

⇒ 20x = 40

⇒ x = \(\frac{40}{20}\)

⇒ x = 2.

The value of x is **2**.

3. Find the following are in continued proportion or not?

(i) 0.2, 2.4, 4.0

(ii) 4, 6, 9

**Solution: **

(i) Given numbers are 0.2, 2.4, 4.0.

If we have three numbers to find whether they are continued proportion or not, thus a:b = b:a.

Now, 0.2: 2.4 = 2.4: 4.0

⇒ \(\frac{0.2}{2.4}\) = \(\frac{2.4}{4.0}\)

⇒ \(\frac{2}{24}\) = \(\frac{24}{40}\)

⇒ \(\frac{1}{12}\) ≠ \(\frac{3}{5}\)

Hence, the given numbers are not in continued proportion because **0.2: 2.4 ≠ 2.4: 4.0**.

(ii) Given numbers are 4, 6, 9.

As we know, a:b = b:a

Now, 4: 6 = 6:9

⇒ \(\frac{4}{6}\) = \(\frac{6}{9}\)

⇒ \(\frac{2}{3}\) = \(\frac{2}{3}\)

Thus, the given numbers 4, 6, and 9 are in continued proportion because **4: 6 = 6: 9**.

4. Find m, if the numbers 8, 4, and m are in continued proportion.

**Solution: **

Given the numbers 8, 4, and m are in continued proportion.

8: 4 = 4: m

⇒ \(\frac{8}{4}\) = \(\frac{4}{m}\)

⇒ 8m = 16

⇒ m = \(\frac{16}{8}\)

⇒ m = 2.

Hence, the value of m is **2**.

Check out all other similar concepts that give you a grip on the topic proportion and continued proportion by referring to the 10th Grade Math page and understand the topics well.

5. Find the fourth proportion of 6, 2, and 9.

**Solution: **

Given proportion numbers are 6, 2, and 9.

Let the fourth proportional be p.

Now, according to given problem 6, 2, 9, and p are proportionality.

Thus,

\(\frac{6}{2}\) = \(\frac{9}{p}\)

⇒ 6p = 9 × 2

⇒ 6p = 18

⇒ p = \(\frac{18}{6}\)

⇒ p = 3.

Therefore, the fourth proportional number is **3**.

6. Find the third proportion to the following numbers.

(i) 4, 6

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

(iii) 3.4, 7.2

**Solution: **

(i) Given proportion numbers 4, 6.

Now, find the third proportion.

Let the third proportion be k.

Thus,

\(\frac{4}{6}\) = \(\frac{6}{k}\)

⇒ 4k = 6 × 6

⇒ 4k = 36

⇒ k = \(\frac{36}{4}\)

⇒ k = 9.

Therefore, the third proportion number is **9**.

(ii) Given proportion numbers are 1\(\frac{2}{3}\), \(\frac{4}{5}\)

Let the third proportion be k.

Thus,

\(\frac{5}{3}\) × \(\frac{5}{4}\) = \(\frac{4}{5}\) × \(\frac{1}{k}\)

⇒ \(\frac{25}{12}\) = \(\frac{4}{5k}\)

⇒ 25 × 5k = 4 × 12

⇒ 125k = 48

⇒ k = \(\frac{48}{125}\)

Hence, the third proportion number is \(\frac{48}{125}\).

(iii) Given proportion numbers are 3.4, 7.2.

Let the third proportion be k.

Now,

\(\frac{3.4}{7.2}\) = \(\frac{7.2}{k}\)

⇒ \(\frac{34}{72}\) = \(\frac{72}{10k}\)

⇒ 34 × 10k = 72 × 72

⇒ 340k = 5184

⇒ k = \(\frac{5184}{340}\)

⇒ k = 15.2

Thus, the third proportion value is **15.2.**

7. Find q in the following numbers so that the numbers are proportional.

(i) 10, q, 20, 15

(ii) 8, 16, 24, q

(iii) q, 35, 15, 40

**Solution: **

(i) Given numbers are 10, q, 20, 15

To find the proportion numbers, we use a:b = c:d i.e., \(\frac{a}{b}\) = \(\frac{c}{d}\).

Now,

\(\frac{10}{q}\) = \(\frac{20}{15}\)

⇒ 10 × 15= 20q

⇒ 20q = 150

⇒ q = \(\frac{150}{20}\)

⇒ q = 7.5

Thus, the value of q is **7.5**.

(ii) Given numbers are 8, 16, 24, q.

Now,

\(\frac{8}{16}\) = \(\frac{24}{q}\)

⇒ \(\frac{1}{2}\) = \(\frac{24}{q}\)

⇒ q = 24 × 2

⇒ q = 48

Hence, the value of q is **48**.

(iii) Given numbers are q, 35, 15, 40.

We use the proportion formula, a:b = c:d i.e., \(\frac{a}{b}\) = \(\frac{c}{d}\).

Now,

\(\frac{q}{35}\) = \(\frac{15}{40}\)

⇒ 40q = 15 × 35

⇒ 40q = 525

⇒ q = \(\frac{525}{40}\)

⇒ q = 13.12

Therefore, the value of q for given proportional numbers is **13.12**.