Study guide: Explain Whole-Number and Decimal Algorithms
Multiply larger whole numbers, divide by two digits, and calculate decimal sums and products.
Ideas to explain in your own words
- A standard multiplication algorithm records partial products by the multiplier’s places.
- Two-digit division finds equal groups just as one-digit division does.
- Decimal sums and differences combine equal units, so align decimal points and place values.
- Decimal multiplication combines fractional place values: a tenth times a tenth is a hundredth.
Useful vocabulary
- algorithm
- An ordered procedure that reliably carries out a calculation.
- quotient check
- Divisor times quotient reconstructs the dividend, including any stated remainder.
Watch your reasoning
- A misplaced tens row can make a plausible-looking product ten times too small.
- Check divisor times quotient rather than assuming a remainder-free layout is correct.
- Aligning rightmost digits alone can mix unequal place units.
- Scaling only one input of a division changes the quotient.
A worked review example
For 236×42, the ones-row product is 472 and the tens-row product is 9440. Add them to get 9912. An estimate 240×40=9600 has the right scale. The tens digit four means forty, so its row is not merely 944. Write the multiplier’s full tens value before generating its row. A misplaced tens row can make a plausible-looking product ten times too small. Label each partial-product row by the actual multiplier place value.
Make a practice plan
- Connect Standard Multiplication to Place Values: Find 408×37. Expected: 12,240+2,856=15,096.
- Divide by Two-Digit Divisors and Check: Calculate 936÷26. Expected: 36; 26×36=936.
- Add and Subtract Decimals with Aligned Places: Find 4.7+3.86 and 8.25−2.9. Expected: 8.56 and 5.35.
- Explain Decimal Products and Quotients: Calculate 2.4×0.25 and 6.3÷0.9. Expected: 0.6 and 7.