➗ Divide Decimals (Grade 5)

Complete Notes & Formulae — Stepwise, Models, Word Problems

Estimate decimal quotients by rounding decimals and using friendly values.
Decimals can be divided using place value, area, block models, and traditional algorithms.
Always keep track of where the decimal goes (in both division and quotient).

1️⃣ Estimate Decimal Quotients

Round the decimal to the nearest whole/tenth for easy estimates.
Divide rounded numbers to get a quick approximate answer.
Example: $3.69 \div 1.8 \approx 4 \div 2 = 2$
Word Problem: Lisa runs 7.8 km in 2.1 hours. Estimate km/h: $8 \div 2 = 4$ km/h.

Use base-10 blocks to visualize dividing small groups out of 1 whole.
Area models: break the divisor into place values, match with the dividend, and find the part.
Example (using blocks): Divide $0.8$ into 4 equal parts (blocks). Each part: $0.2$.

Divide the grid so each group represents $0.12$
How many groups in $0.36$? 3 groups ($0.12 \times 3 = 0.36$) so $0.36 \div 0.12 = 3$.

Example: $4.92 \div 4$
Place decimal above:
$4.92$ ÷ 4 = $1.23$

If dividing by a decimal divisor (e.g., $3.15 \div 0.5$), multiply both numbers by 10, 100, etc., to make the divisor a whole number.
Then, divide as usual and place the decimal.
Example: $2.43 \div 0.3$ → $24.3 \div 3 = 8.1$

Example: $0.75 \div 0.25$
Make divisor whole: $0.75 \div 0.25$ = $75 \div 25 = 3$

After dividing, round the quotient to the required place (tenths, hundredths, ...).
Example: $7.89 \div 4 = 1.9725$, round to hundredths: 1.97

Rounding rule: If digit to the right is 5 or greater, round up.

Problem: Garcia has \$16.8 and divides it equally among 8 friends. How much for each?
Solution: $16.8 \div 8 = 2.1$ dollars

To divide by decimals, "move the decimal" in both numbers to the right the same number of times to make the divisor (after) a whole number.
Then divide as usual.
Example: $1.2 \div 0.3$ → $12 \div 3 = 4$

Answers:
1) 0.07 2) 1.43 3) 3.2 4) 972 5) $5 \div 2 \approx 2.5$