Calculations involving decimals, fractions and negative numbers follow clear rules. Accuracy depends on handling place value, signs, and equivalent forms correctly.

 
Decimals

To add or subtract decimals, line up the decimal points, then calculate as with whole numbers.

$$
3.45 + 1.8 = 5.25
$$

$$
6.2 - 0.87 = 5.33
$$

To multiply decimals, multiply as whole numbers, then place the decimal point so the total number of decimal places matches the total in the original numbers.

$$
0.4 \times 0.6 = 0.24
$$

To divide decimals, make the divisor a whole number by multiplying both numbers by the same power of \(10\).

$$
4.5 \div 0.3 = 45 \div 3 = 15
$$

 
Fractions

To add or subtract fractions, use a common denominator, then add or subtract the numerators.

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

To multiply fractions, multiply the numerators together and the denominators together, then simplify.

$$
\frac{2}{3} \times \frac{5}{6} = \frac{10}{18} = \frac{5}{9}
$$

To divide fractions, multiply by the reciprocal of the second fraction.

$$
\frac{4}{5} \div \frac{2}{3} = \frac{4}{5} \times \frac{3}{2} = \frac{12}{10} = \frac{6}{5}
$$

 
Negative Numbers

When adding or subtracting negative numbers, think about movement on a number line.

$$
5 + (-3) = 2
$$

$$
4 - (-6) = 10
$$

For multiplication and division with negatives:

• Same signs give a positive result
• Different signs give a negative result

$$
(-4) \times (-7) = 28
$$

$$
(-18) \div 3 = -6
$$

Always slow down with signs and decimal points. Most errors come from losing track of negatives or misplacing the decimal, not from the calculation itself.