Fraction and percentage error

Here are 10 JAMB-style multiple-choice questions on Fractions and BODMAS:

1. Evaluate:

$$\frac{3}{4} + \frac{5}{8} - \frac{1}{2}$$

A) $\frac{3}{8}$
B) $\frac{5}{8}$
C) $\frac{7}{8}$
D) $\frac{9}{8}$

2. Simplify:

$$\left( \frac{2}{3} + \frac{1}{4} \right) \div \frac{5}{6}$$

A) $\frac{5}{8}$
B) $\frac{7}{10}$
C) $\frac{9}{10}$
D) $\frac{3}{5}$

3. Solve:

$$\frac{5}{6} \times \left( \frac{3}{4} + \frac{1}{2} \right)$$

A) $\frac{5}{8}$
B) $\frac{10}{9}$
C) $\frac{25}{24}$
D) $\frac{5}{6}$

4. Simplify:

$$\frac{7}{2} - \left( \frac{3}{4} \times \frac{2}{5} \right) + \frac{1}{3}$$

A) $\frac{47}{12}$
B) $\frac{23}{6}$
C) $\frac{29}{12}$
D) $\frac{19}{6}$

5. Find the value of:

$$\frac{5}{6} \div \frac{7}{12} + \frac{2}{3}$$

A) $\frac{11}{7}$
B) $\frac{3}{2}$
C) $\frac{19}{14}$
D) $\frac{7}{6}$

6. Solve:

$$\left( \frac{2}{3} + \frac{4}{9} \right) \times \frac{3}{5}$$

A) $\frac{10}{15}$
B) $\frac{14}{15}$
C) $\frac{12}{15}$
D) $\frac{8}{15}$

7. Evaluate:

$$\frac{3}{5} \times \left( 2 - \frac{1}{2} \right)$$

A) $\frac{3}{5}$
B) $\frac{6}{5}$
C) $\frac{9}{10}$
D) $\frac{7}{10}$

8. Simplify:

$$\frac{4}{7} + \frac{2}{3} - \frac{1}{2}$$

A) $\frac{31}{42}$
B) $\frac{19}{42}$
C) $\frac{23}{42}$
D) $\frac{17}{42}$

9. Find the value of:

$$\frac{3}{8} \div \left( \frac{2}{5} + \frac{1}{10} \right)$$

A) $\frac{5}{3}$
B) $\frac{8}{5}$
C) $\frac{12}{5}$
D) $\frac{7}{3}$

10. Solve:

$$\left( \frac{5}{6} - \frac{1}{4} \right) \times \frac{3}{2}$$

A) $\frac{7}{8}$
B) $\frac{3}{5}$
C) $\frac{9}{8}$
D) $\frac{5}{12}$

11. Solve:

$$\frac{2}{5} + \frac{3}{8} - \frac{1}{4}$$

A) $\frac{23}{40}$
B) $\frac{19}{40}$
C) $\frac{21}{40}$
D) $\frac{17}{40}$

12. Simplify:

$$\frac{7}{3} \times \left( \frac{1}{2} + \frac{2}{5} \right)$$

A) $\frac{7}{5}$
B) $\frac{14}{15}$
C) $\frac{11}{5}$
D) $\frac{8}{5}$

13. Evaluate:

$$\left( \frac{3}{4} + \frac{2}{3} \right) \div \frac{5}{6}$$

A) $\frac{13}{10}$
B) $\frac{14}{9}$
C) $\frac{7}{5}$
D) $\frac{17}{12}$

14. Find the value of:

$$\frac{4}{5} \div \frac{2}{3} + \frac{1}{2}$$

A) $\frac{19}{10}$
B) $\frac{17}{10}$
C) $\frac{11}{10}$
D) $\frac{13}{10}$

15. Solve:

$$\frac{5}{8} \times \left( \frac{2}{3} - \frac{1}{6} \right)$$

A) $\frac{5}{12}$
B) $\frac{7}{16}$
C) $\frac{5}{16}$
D) $\frac{3}{10}$

16. Simplify:

$$\frac{6}{7} + \frac{5}{9} - \frac{1}{3}$$

A) $\frac{47}{63}$
B) $\frac{43}{63}$
C) $\frac{39}{63}$
D) $\frac{35}{63}$

17. Evaluate:

$$\left( \frac{1}{3} + \frac{2}{5} \right) \times \frac{4}{7}$$

A) $\frac{11}{35}$
B) $\frac{13}{35}$
C) $\frac{9}{35}$
D) $\frac{7}{35}$

18. Solve:

$$\frac{9}{10} - \frac{4}{5} + \frac{1}{2}$$

A) $\frac{11}{20}$
B) $\frac{9}{20}$
C) $\frac{7}{20}$
D) $\frac{13}{20}$

19. Find the value of:

$$\frac{5}{9} \div \left( \frac{1}{3} + \frac{2}{6} \right)$$

A) $\frac{5}{3}$
B) $\frac{5}{2}$
C) $\frac{5}{4}$
D) $\frac{5}{6}$

20. Simplify:

$$\frac{7}{12} \times \left( 2 - \frac{1}{4} \right)$$

A) $\frac{35}{48}$
B) $\frac{25}{48}$
C) $\frac{21}{48}$
D) $\frac{19}{48}$

Percentage Error in JAMB Exams

Concept of Percentage Error

Percentage error is a measure of the accuracy of a measured value compared to the actual or true value. It is used to quantify how much an estimated value deviates from the correct value.

The formula for percentage error is:

$$\text{Percentage Error} = \left( \frac{|\text{Measured Value} - \text{True Value}|}{\text{True Value}} \right) \times 100\%$$

Where:

• Measured Value is the value obtained from an experiment or estimation.
• True Value is the correct or actual value.
• |Measured Value - True Value| is the absolute difference between the measured and true values (ignoring negative signs).

Application in JAMB Exams

JAMB questions on percentage error typically involve:

1. Finding the percentage error when given a measured and true value.
2. Determining the measured or true value given the percentage error.
3. Applying percentage error in real-life situations, such as approximations in physics or engineering calculations.

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Worked Examples

Example 1

A student measures the length of a rod as 48 cm, but the actual length is 50 cm. Find the percentage error.

Solution:
Using the formula:

$$\text{Percentage Error} = \left( \frac{|\text{Measured Value} - \text{True Value}|}{\text{True Value}} \right) \times 100$$ $$= \left( \frac{|48 - 50|}{50} \right) \times 100$$ $$= \left( \frac{2}{50} \right) \times 100$$ $$= 4\%$$

Answer: 4%

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Example 2

A digital thermometer records a temperature of 36.8°C, but the actual temperature is 37.0°C. What is the percentage error?

Solution:

$$\text{Percentage Error} = \left( \frac{|36.8 - 37.0|}{37.0} \right) \times 100$$ $$= \left( \frac{0.2}{37.0} \right) \times 100$$ $$= 0.54\%$$

Answer: 0.54%

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Example 3

A student estimates the mass of a book as 2.5 kg, but its actual mass is 2.8 kg. Find the percentage error.

Solution:

$$\text{Percentage Error} = \left( \frac{|2.5 - 2.8|}{2.8} \right) \times 100$$ $$= \left( \frac{0.3}{2.8} \right) \times 100$$ $$= 10.71\%$$

Answer: 10.71%

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Example 4

A car's speedometer shows a speed of 90 km/h, while the actual speed is 95 km/h. What is the percentage error?

Solution:

$$\text{Percentage Error} = \left( \frac{|90 - 95|}{95} \right) \times 100$$ $$= \left( \frac{5}{95} \right) \times 100$$ $$= 5.26\%$$

Answer: 5.26%

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Example 5

A factory machine fills a bottle with 990 mL of liquid instead of the intended 1000 mL. Find the percentage error.

Solution:

$$\text{Percentage Error} = \left( \frac{|990 - 1000|}{1000} \right) \times 100$$ $$= \left( \frac{10}{1000} \right) \times 100$$ $$= 1\%$$

Answer: 1%

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Key Points to Remember

• The percentage error is always positive (absolute value is taken).
• Smaller errors mean higher accuracy.
• In JAMB exams, questions may require conversions of units before applying the formula.
• Round off answers to two decimal places if necessary.

Would you like more examples or explanations?

Here are 10 additional JAMB-style questions on Percentage Error for practice:

1. A student measures the weight of an object as 5.4 kg, but the actual weight is 5.5 kg. Find the percentage error.

A) 0.18%
B) 1.82%
C) 0.5%
D) 2.5%

2. A laboratory balance measures the mass of a sample as 2.2 g, but the true mass is 2.4 g. What is the percentage error?

A) 8.33%
B) 10%
C) 5%
D) 4.5%

3. A car's fuel gauge shows 30 liters in the tank, but the actual amount is 32 liters. Calculate the percentage error.

A) 6.25%
B) 8.33%
C) 7.14%
D) 5.5%

4. A thermometer measures the temperature of water as 98.6°C, but the true temperature is 100°C. Find the percentage error.

A) 1.4%
B) 1%
C) 2.4%
D) 0.6%

5. A student measures the length of a rod to be 120 cm, but the true length is 122 cm. What is the percentage error?

A) 2.5%
B) 1.64%
C) 0.8%
D) 1.5%

6. A thermometer shows a temperature of 73°C, while the true temperature is 75°C. Calculate the percentage error.

A) 2.67%
B) 3.33%
C) 4%
D) 2.5%

7. A barometer reads 760 mm Hg, but the actual atmospheric pressure is 765 mm Hg. What is the percentage error?

A) 0.65%
B) 1.32%
C) 0.5%
D) 1.75%

8. A student estimates the speed of a vehicle as 80 km/h, but the actual speed is 85 km/h. What is the percentage error?

A) 4.5%
B) 6.25%
C) 7.5%
D) 5%

9. A digital scale records the weight of an object as 50.2 kg, while the true weight is 51 kg. Find the percentage error.

A) 1.57%
B) 1.25%
C) 1.75%
D) 2%

10. A student measures the volume of a liquid as 150 mL, but the true volume is 160 mL. Find the percentage error.

A) 6.25%
B) 5%
C) 7%
D) 6.67%

These questions offer a wide range of scenarios where percentage error is calculated, helping students prepare for the JAMB exam. Let me know if you'd like the solutions for these questions!