Study guide: Use Large Whole Numbers and Explain Algorithms
Read larger place values, round them, multiply, and divide with interpreted remainders.
Ideas to explain in your own words
- Each place to the left is ten times the place next to it.
- Rounding a large number still compares neighboring multiples of the requested place.
- A multi-digit factor can be decomposed into its place-value parts.
- Whole-number division finds how many complete groups fit and what remains.
Useful vocabulary
- partial product
- The product of one part of a split factor.
- remainder
- What is left after the maximum number of complete equal groups.
Watch your reasoning
- A zero placeholder is necessary even though it contributes no groups.
- Repeated rounding can differ from rounding the original number directly.
- Every part of the split factor must be multiplied.
- Round up only when the question requires capacity for every item.
A worked review example
In 43,208, the four represents 40,000 and the three represents 3,000. Expanded form is 40,000+3,000+200+8. Multiplying 4,320 by ten gives 43,200 because every digit’s represented value becomes ten times as large. Read a digit together with its place name. A zero placeholder is necessary even though it contributes no groups. Use a place chart through hundred-thousands and write expanded values beneath the digits.
Make a practice plan
- Read Large Place Values and Tenfold Changes: Write 507,060 in expanded form. Expected: 500,000+7,000+60.
- Round to a Requested Large Place: Round 73,550 to the nearest ten-thousand. Expected: 70,000.
- Explain Multi-Digit Multiplication with Partial Products: Find 47×18. Expected: 470+376=846.
- Divide and Interpret the Remainder: Pack 125 cards in groups of eight. Expected: fifteen full groups and five leftover; sixteen containers for all cards.