DOUBLING AND HALVING

Doubling and halving are fundamental arithmetic operations that can be applied to various types of numbers, whether integers or fractions. Here’s how each operation works:

Doubling:

Doubling a number means multiplying it by 2. This operation can be useful in various contexts, from simple arithmetic to financial calculations.

How to Double a Number:

1. For Whole Numbers: Multiply the number by 2.

   • Example: Doubling 15 gives $15 \times 2 = 30$
     

2. For Decimals: Multiply the decimal by 2.

   • Example: Doubling 4.5 gives $4.5 \times 2 = 9.0$
     

3. For Fractions: Multiply the numerator by 2.

   • Example: Doubling $\frac{3}{4}$ gives $\frac{3 \times 2}{4} = \frac{6}{4} = 1.5$
     

Halving:

Halving a number means dividing it by 2. This operation is often used to find half of a quantity or to simplify problems involving division.

How to Halve a Number:

1. For Whole Numbers: Divide the number by 2.

   • Example: Halving 20 gives $20 \div 2 = 10$.

2. For Decimals: Divide the decimal by 2.

   • Example: Halving 7.8 gives $7.8 \div 2 = 3.9$.

3. For Fractions: Divide the numerator by 2 or multiply the fraction by $\frac{1}{2}$.

   • Example: Halving $\frac{5}{6}$ gives $\frac{5}{6} \times \frac{1}{2} = \frac{5}{12}$.

Practical Examples:

1. Doubling:

   • Double 25: $25\times 2=50$
   • Double 0.75: $0.75 \times 2 = 1.5$
     
   • Double $\frac{2}{5}$: $\frac{2}{5} \times 2 = \frac{4}{5}$

2. Halving:

   • Half of 50: $50 \div 2 = 25$
     
   • Half of 1.2: $1.2 \div 2 = 0.6$
     
   • Half of $\frac{3}{4}$: $\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$

Useful Tips:

• For Multiples of 10: Doubling or halving is straightforward because you only need to move the decimal point. For example, doubling 70 is 140, and halving 60 is 30.

• For Larger Numbers: Doubling or halving large numbers might be simplified using multiplication or division by smaller factors first. For example, halving 400 is the same as halving 200 twice.

These operations are fundamental and can be applied in various scenarios, from everyday calculations to more complex mathematical problems.