ANSWERs for figure it out Class 8 Mathematics – NCERT (Ganita Prakash) Part 2 Chapter 1: FRACTIONS IN DISGUISE

ANSWERs for figure it out Class 8 Mathematics – NCERT (Ganita Prakash) Part 2  Chapter 1: FRACTIONS IN DISGUISE

1.1 Fractions as Percentages

what the symbol ʻ%ʼ means? This symbol is read as per cent.

The word ‘per cent’ is derived from the Latin phrase ‘per centum’, meaning ‘by the hundred’ or ‘out of hundred’.

Thus, percentages are simply fractions where the denominator is 100.

Expressing Fractions as Percentages

Example 1: Surya wants to use a deep orange colour to capture the sunset. He mixes some red paint and yellow paint to make this colour. The red paint makes up 3 4 of this mixture. What percentage of the colour is made with red?

 3/4 is 3 out of every 4. 

That is, 6 out of every 8 (equivalent fraction). 

That is, 30 out of every 40. 

That is, 75 out of every 100. This means 75%

Example 2: Surya won some prize money in a contest. He wants to save 2 5 of the money to purchase a new canvas. Express this quantity as a percentage.

A fraction is of a unit, while a percentage is per 100. Therefore, to express a fraction as a percentage, we can just multiply the fraction by 100

Example 3: Given a percentage, can you express it as a fraction? For example, express 24% as a fraction.

A percentage is a fraction, 24% is the same as \( \frac{24}{100} \) . 

other equivalent forms of \( \frac{24}{100} \)  = \( \frac{12}{50} \)  =  \( \frac{6}{25} \)  = \( \frac{48}{200} \) .

A percentage, z%, can be expressed by any of the fractions that are equivalent to \( \frac{z}{100} \).

Figure it Out Page 3 PART 2

1. Express the following fractions as percentages. 

(i) \( \frac{3}{5} \)

(ii) \( \frac{7}{14} \)

(iii) \( \frac{9}{20} \)

(iv) \( \frac{72}{150} \)

(v) \( \frac{1}{3} \)

(vi) \( \frac{5}{11} \)
Solution:

$$\text{Percentage}=\text{Fraction}\times 100$$

(i) $\frac{5}{8}$

$$\frac{5}{8}\times 100=62.5\mathrm{\%}$$

(ii) $\frac{7}{14}$

$$\frac{7}{14}=\frac{1}{2}\Rightarrow \frac{1}{2}\times 100=50\mathrm{\%}$$

(iii) $\frac{9}{20}$

$$\frac{9}{20} \times 100 = 45\%$$

(iv) $\frac{72}{150}$

$$\frac{72}{150} = \frac{24}{50} = \frac{12}{25}$$
$$\frac{12}{25} \times 100 = 48\%$$

(v) $\dfrac{1}{3}$

$$\dfrac{1}{3} \times 100 = 33.33\% \ (\text{approximately})$$

(vi) $\dfrac{5}{11}$

$$\dfrac{5}{11} \times 100 = 45.45\% \ (\text{approximately})$$
2. Nandini has 25 marbles, of which 15 are white. What percentage of her marbles are white? 

(i) 10% (ii) 15% (iv) 60% (v) 40% (iii) 25% (vi) None of these

​ $$\frac{3}{5} \times 100 = 60\%$$

Correct answer: 60% (Option iv)

3. In a school, 15 of the 80 students come to school by walking. What percentage of the students come by walking?

$$\frac{15}{80} = \frac{3}{16}$$ $$\frac{3}{16} \times 100 = 18.75\%$$

Answer: 18.75%

4. A group of friends is participating in a long-distance run. The positions of each of them after 15 minutes are shown in the following picture. Match (among the given options) what percentage of the race each of them has approximately completed. 

Position A

• A is just a little ahead of the start.

• Clearly less than 25% of the total distance.

 Best match: 20%

Position B

• B is around the middle, but still before halfway.

• Slightly less than 50%.

•  Best match: 38%

Position C

• C is past the halfway point, but not close to the finish.

• Roughly around 70–75%.

Best match: 72%

 Position D

• D is very close to the finish line, but not exactly at the end.

• So it must be more than 90%, but not 100%.

 Best match: 93%

Final Matching Answer

Position	Percentage
A	20%
B	38%
C	72%
D	93%

 5. Pairs of quantities are shown below. Identify and write appropriate symbols ‘>’, ‘<‘=‘in the blanks. Try to do it without calculations.

 (i) 50% ____ 5%(ii) 5 /10 ____ 50%(iii) 3/ 11 _____ 61% (iv) 30% ____ 1/3

(i) 50% ___5%

$$50\mathrm{\%}=0.5$$

5% = 0.05

50% > 5%

(ii) $\frac{5}{10}$ ___ 50%

$\frac{5}{10} =$  50% 

Answer $\frac{5}{10}$= 50% 

(iii) $\frac{1}{3}$ ___ 61%

$$\frac{1}{3} \approx 33.3\%$$
$$\frac{3}{11}<61\mathrm{\%}$$

(iv) 30% ___ $\frac{1}{3}$

$$30\% < 33.3\%$$
$$30\% < \frac{1}{3}$$

Try to calculate (without using pen and paper) the indicated percentages of the values shown in the table below. Write your answers in the table.

The FDP Trio — Fractions, Decimals, and Percentages

Example 2: We can find 50% of a value by multiplying 1 2 with the value. Will multiplying the value by 0.5 also give the answer for 50% of the value?

Yes, since 1/2 = 0.5

50% = 50 /100 = 1/2 = 0.5

50% of 24 = 12

0.5 x 24 = 12

Complete the following table

Example 3: The maximum marks in a test are 75. If students score 80% 

or above in the test, they get an A grade. How much should Zubin score 

at least to get an A grade?

Example 4: To prepare a particular millet kanji (porridge), suppose the ratio of millet to water to be mixed for boiling is 2:7. What percentage does the millet constitute in this mixture? If 500 ml of the mixture is to be made, how much millet should be used?

The ratio of millet to the volume of the mixture is 2:9. 

In other words, in one unit of the mixture, millet occupies 2 /9 units and water occupies 7/ 9 units.

The percentage (i.e., in 100 such units) of millet in the mixture is 2/9 x 100 = 22.22%.

 The percentage of water in the mixture will be 100 – 22.22 = 77.78%. 

A mixture with 22.22% millet means 100 ml mixture will have 22.22 ml millet. 

 Therefore, 500 ml with 22.22% millet will have 5 × 22.22 = 111.1 ml of millet.

Example 5: A cyclist cycles from Delhi to Agra and completes 40% of the journey. If he has covered 92 km, how many more kilometres does he have to travel to reach Agra?

Example 6: Kishanlal recently opened a garment shop. He aims to achieve a daily sales of at least ₹5000. The sales on the first 2 days were ₹2000 and ₹3500. What percentage of his target did he achieve? 

It is 40% on Day 1 and 70% on Day 2. Another way of saying it is — he was 60% short of his target on Day 1 and 30% short of his target on Day 2.

His target is ₹5000, and he made ₹5000 on Day 3 — this is 100%. On Day 4, he made ₹6000, which is 1000 more than his target.

1000 is 20% of 5000. Therefore, 6000, (5000 + 1000) is 100% + 20% = 120% of 5000. It can also be computed as 6000 5000 × 100 = 6 5 × 100 = 120%. This means he achieved 120% of his target, i.e., 20% more than his target.

On Day 7, he achieved 150% of his target. On Day 8, he achieved 210% of his target.

Suppose on some day, he made ₹2500. This can be expressed as “He achieved 1 2 of his target” or “He achieved 50% of his target” or “He achieved 0.5 of his target”. On some other day, he made ₹10,000. We can say “He achieved twice/double/2 times his target” or “He achieved 200% of his target”

Complete the table below. Mark the approximate locations in the following diagram.