In Grade 5 you added, subtracted, multiplied and divided by decimals. Here are the four rules side by side, with the reason each one works.
Idea clave
Add or subtract: line up the decimal points. Multiply: multiply as whole numbers, then give the product as many decimal places as the factors have together. Divide: move the decimal point in both numbers until the divisor is a whole number.
Por qué funciona
Each rule keeps place value honest. Lining up the points adds tenths to tenths and hundredths to hundredths. In $2.4 \times 1.5$, you are multiplying 24 tenths by 15 tenths, and tenths times tenths are hundredths: 360 hundredths, or 3.60. In a division, multiplying both numbers by 10 does not change the quotient, just as $6 \div 3 = 60 \div 30$.
Ejemplo resuelto: Add with different places
Find $12.5 + 3.875$.
- Line up the points and write $12.5$ as $12.500$.
- $12.500 + 3.875 = 16.375$.
- Estimate: $12.5 + 4 \approx 16.5$. Close.
Respuesta: $16.375$
Ejemplo resuelto: Multiply
Find $2.4 \times 1.5$.
- Ignore the points: $24 \times 15 = 360$.
- The factors have $1 + 1 = 2$ decimal places, so the product has 2: $3.60$.
Respuesta: $3.6$
Ejemplo resuelto: Divide by a decimal
Find $7.56 \div 0.4$.
- Multiply both by 10 so the divisor is whole: $75.6 \div 4$.
- $75.6 \div 4 = 18.9$.
- Check: $18.9 \times 0.4 = 7.56$.
Respuesta: $18.9$
Ejemplo resuelto: Subtract from a whole number
Find $40 - 7.35$.
- Write 40 as $40.00$.
- $40.00 - 7.35 = 32.65$.
- Check: $32.65 + 7.35 = 40$.
Respuesta: $32.65$
Error común
Lining up the last digits instead of the decimal points. Written that way, $12.5 + 3.875$ adds 5 tenths to 5 thousandths. Quick check: round first. $12.5 + 3.875$ is about $13 + 4 = 17$, so an answer like 4.0 or 160 cannot be right.