Fractions, Decimals, Approximations & Percentages

Question 1

How do you perform basic operations (multiplication, addition, subtraction, division) on fractions?

Answer 1

1. Addition/Subtraction: Convert fractions to a common denominator, then add or subtract the numerators.
2. Multiplication: Multiply the numerators together and the denominators together.
3. Division: Flip the second fraction (take its reciprocal) and multiply.

Question 2

How do you perform basic operations (multiplication, addition, subtraction, division) on decimals?

Answer 2

1. Addition/Subtraction: Align the decimal points and perform the operation as you would with whole numbers.
2. Multiplication: Multiply as whole numbers, then place the decimal point in the product based on the sum of decimal places in the factors.
3. Division: Move the decimal point in the divisor to make it a whole number, then do the same for the dividend, and divide as usual.

Question 3

How do you express a number to a specified number of significant figures?

Answer 3

1. Identify the first non-zero digit (this is the first significant figure).
2. Count the desired number of significant figures.
3. Round the number accordingly.

Question 3

How do you express a number to a specified number of decimal places?

Answer 3

1. Locate the decimal point.
2. Count the number of digits to the right of the decimal point.
3. Round to the specified number of decimal places.

Question 4

How do you calculate percentage error?

Answer 4

1. Find the difference between the measured value and the true value.
2. Divide the difference by the true value.
3. Multiply by 100 to get the percentage error.

Question 5

How do you calculate simple interest?

Answer 5

Use the formula: Simple Interest (SI) = Principal (P) × Rate (R) × Time (T).
Ensure that the rate is in decimal form (e.g., 5% = 0.05).

Question 6

How do you calculate profit and loss percentage?

Answer 6

1. Profit % = (Profit/Cost Price) × 100.
2. Loss % = (Loss/Cost Price) × 100.
3. Profit is the difference between selling price and cost price if selling price > cost price.
4. Loss is the difference between cost price and selling price if cost price > selling price.

Question 7

How do you solve problems involving shares and VAT?

Answer 7

Shares: Divide the total value according to the given ratio.

VAT: Multiply the original price by the VAT rate to find the amount of VAT, then add it to the original price.

Question 7

How do you solve problems involving ratio, proportion, and rate?

Answer 7

Ratio: Compare two quantities by division.

Proportion: Set up an equation where two ratios are equal and solve for the unknown.

Rate: Divide the quantity by time or another related quantity.