Whole Numbers. Solve.

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Whole Numbers

Thinking Skills

PROBLEM SOLVING CHAPTER

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Solve.

1. A bag contains a yellow ball and a red ball.

a. Daisy picked the yellow ball with a 4-digit number written on it. When she rounded the number to the nearest thousand, she got 7,000. Write the least and greatest possible number that could be on the

yellow ball.

Least possible number: Greatest possible number:

b. Erik picked the red ball with a 5-digit number written on it. When he rounded the number to the nearest thousand, he got 38,000.

Write the least and greatest possible number that could be on the red ball.

Least possible number: Greatest possible number:

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Chapter 1 Whole Numbers

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2. A thief left a secret code at the crime scene for the police to break. These were the clues that the police found:

There is a 4 in the thousands place.

The digit in the tens place is 2 times the digit in the thousands place. The digit in the ten thousands place is 7 less than the digit in the ones place.

The digit in the ones place is 3 more than 6.

Multiply the digit in the ten thousands place by 3 to ﬁ nd the digit in the millions place.

The digit in the hundreds place is 5 less than the digit in the tens place. The difference between the digit in the thousands place and the digit in the tens place is the digit in the hundred thousands place.

Help the police to ﬁ nd the code.

Millions Hundred Thousands

Ten

Thousands Thousands Hundreds Tens Ones

3. Find the actual sum. Then ﬁ nd the estimated sum using front-end estimation. Which sum is greater?

111 ⫹ 1,111 ⫹ 11,111 ⫹ 111,111 ⫹ 1,111,111

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Solve. Show your work.

4. Estimate the sum of these numbers using front-end estimation with adjustment. Find the difference between the actual sum and the estimated sum.

2,354 4,563 4,343

5. Look at the number line.

120,000 130,000 B

A

Round the numbers represented by A and B to the nearest thousand. Then estimate the difference between the numbers.

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PROBLEM SOLVING

Strategies

6. Complete the number pattern.

454,546 479,546 504,546

7. How many subtraction signs should be placed between these digits to get a value of 23? Show where the subtraction signs should be placed.

9 8 2 3 5 4 7

All the numbers are less than 100.

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8. How many addition and subtraction signs should be placed between these digits to get a value of 34? Show where the addition and subtraction signs should be placed.

1 3 4 6 2 9 4

All the numbers are less than 100.

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PROBLEM SOLVING

Exploration

9. a. Write ten 6-digit numbers formed by the given digits.

8 3 0 5

9 1

b. Write the greatest 6-digit number using the given digits.

c. Write the least 6-digit number using the given digits.

d. Find the difference between your answers in Exercises b and c. Is this the greatest difference between two 6-digit numbers formed by the digits 8, 3, 0, 5, 9 and 1?

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10. These numbers are arranged in a pattern.

739,406 742,416 745,426 748,436 751,446

Change any two digits in each number and keep the numbers in the same pattern.

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Journal Writing

Explain.

11. Sean and Kit rounded 256,537 to the nearest thousand. Sean’s answer: 256,500

Kit’s answer: 256,000

Explain the mistakes made by Sean and Kit.