Step-by-step Maths Level 5: 10,000 more or less; comparing and ordering
Part of the Step-by-step Maths Level 5 place value to a million and decimals to tenths chapter. Chapter overview · whole chapter on one page
10,000 more or less; comparing and ordering
10,000 more than a number changes the ten thousands digit by one. 10,000 less changes it the other way.
To compare two numbers with the same number of digits, start from the left. The first column where they differ decides.
Key ideas
- Adding 10,000 changes only the ten thousands digit (carry if it is a 9).
- Compare from the left, column by column.
- Order from the smallest by comparing the digits from the left.
Method. Only the ten thousands digit changes when we add or take away 10,000.
- Look at the ten thousands digit. Adding or taking away 10,000 changes this digit by one.The ten thousands digit is 9
- Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.9 + 1 = 10, so write 0 and carry 1 into the hundred thousands
- Write the answer. All the other digits stay the same.305,000
Check. Check: 305,000 take away 10,000 gives back 295,000.
Watch out. Do not change the thousands digit. 10,000 is not 1,000.
Method. Only the ten thousands digit changes when we add or take away 10,000.
- Look at the ten thousands digit. Adding or taking away 10,000 changes this digit by one.The ten thousands digit is 4
- Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.4 - 1 = 3
- Write the answer. All the other digits stay the same.630,000
Check. Check: 630,000 add 10,000 gives back 640,000.
Watch out. Do not change the thousands digit. 10,000 is not 1,000.
Method. Compare the digits from the left. The first column where they differ decides.
- Compare the two numbers from the left. Look at the digits in the same column, starting with the largest.4 and 4 in the first column
- Find the first column where they differ. That column decides which number is greater.In the ten thousands column: 8 and 2
- Choose the greater number. The number with the greater digit in that column is greater.482,613
Check. Check: the other number is 428,613, which is smaller.
Watch out. Do not compare the last digits first. Start from the left.
Watch out
Watch out. 10,000 is not 1,000. Only the ten thousands digit changes, and it may carry into the hundred thousands.
Exam tip
Grown-up tip. Ask: “Which column changes?” before the child works out the answer.
Exercise 1B Practice: 10,000 more or less, and comparing
Non-calculatorMethod. Compare the digits from the left. The first column where they differ decides.
- Compare the two numbers from the left. Look at the digits in the same column, starting with the largest.2 and 3 in the first column
- Find the first column where they differ. That column decides which number is greater.In the hundred thousands column: 2 and 3
- Choose the greater number. The number with the greater digit in that column is greater.373,555
Check. Check: the other number is 239,181, which is smaller.
Watch out. Do not compare the last digits first. Start from the left.
Method. Compare the numbers from the left, and write them smallest first.
- Find the smallest number. Compare the digits from the left.Smallest: 155,219
- Put the rest in order. Repeat: find the next smallest number.155,219 < 429,253 < 652,205 < 770,401
- Write the list. Smallest first, as the question asks.155,219, 429,253, 652,205, 770,401
Check. Check: the first number is the smallest and the last is the largest.
Watch out. A number with more digits is greater; with the same number of digits, compare from the left.
Method. Only the ten thousands digit changes when we add or take away 10,000.
- Look at the ten thousands digit. Adding or taking away 10,000 changes this digit by one.The ten thousands digit is 7
- Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.7 - 1 = 6
- Write the answer. All the other digits stay the same.360,761
Check. Check: 360,761 add 10,000 gives back 370,761.
Watch out. Do not change the thousands digit. 10,000 is not 1,000.
Method. Compare the numbers from the left, and write them smallest first.
- Find the smallest number. Compare the digits from the left.Smallest: 231,466
- Put the rest in order. Repeat: find the next smallest number.231,466 < 737,897 < 926,988 < 976,247
- Write the list. Smallest first, as the question asks.231,466, 737,897, 926,988, 976,247
Check. Check: the first number is the smallest and the last is the largest.
Watch out. A number with more digits is greater; with the same number of digits, compare from the left.
Method. Only the ten thousands digit changes when we add or take away 10,000.
- Look at the ten thousands digit. Adding or taking away 10,000 changes this digit by one.The ten thousands digit is 7
- Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.7 + 1 = 8
- Write the answer. All the other digits stay the same.389,251
Check. Check: 389,251 take away 10,000 gives back 379,251.
Watch out. Do not change the thousands digit. 10,000 is not 1,000.
Method. Compare the numbers from the left, and write them smallest first.
- Find the smallest number. Compare the digits from the left.Smallest: 159,358
- Put the rest in order. Repeat: find the next smallest number.159,358 < 278,344 < 540,497 < 961,946
- Write the list. Smallest first, as the question asks.159,358, 278,344, 540,497, 961,946
Check. Check: the first number is the smallest and the last is the largest.
Watch out. A number with more digits is greater; with the same number of digits, compare from the left.
Method. Compare the digits from the left. The first column where they differ decides.
- Compare the two numbers from the left. Look at the digits in the same column, starting with the largest.1 and 7 in the first column
- Find the first column where they differ. That column decides which number is greater.In the hundred thousands column: 1 and 7
- Choose the greater number. The number with the greater digit in that column is greater.726,162
Check. Check: the other number is 183,696, which is smaller.
Watch out. Do not compare the last digits first. Start from the left.
Method. Only the ten thousands digit changes when we add or take away 10,000.
- Look at the ten thousands digit. Adding or taking away 10,000 changes this digit by one.The ten thousands digit is 3
- Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.3 + 1 = 4
- Write the answer. All the other digits stay the same.345,794
Check. Check: 345,794 take away 10,000 gives back 335,794.
Watch out. Do not change the thousands digit. 10,000 is not 1,000.
Method. Compare the numbers from the left, and write them smallest first.
- Find the smallest number. Compare the digits from the left.Smallest: 147,407
- Put the rest in order. Repeat: find the next smallest number.147,407 < 161,173 < 714,563 < 993,272
- Write the list. Smallest first, as the question asks.147,407, 161,173, 714,563, 993,272
Check. Check: the first number is the smallest and the last is the largest.
Watch out. A number with more digits is greater; with the same number of digits, compare from the left.
Method. Only the ten thousands digit changes when we add or take away 10,000.
- Look at the ten thousands digit. Adding or taking away 10,000 changes this digit by one.The ten thousands digit is 6
- Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.6 - 1 = 5
- Write the answer. All the other digits stay the same.155,825
Check. Check: 155,825 add 10,000 gives back 165,825.
Watch out. Do not change the thousands digit. 10,000 is not 1,000.
Method. Compare the numbers from the left, and write them smallest first.
- Find the smallest number. Compare the digits from the left.Smallest: 275,739
- Put the rest in order. Repeat: find the next smallest number.275,739 < 289,999 < 341,550 < 731,589
- Write the list. Smallest first, as the question asks.275,739, 289,999, 341,550, 731,589
Check. Check: the first number is the smallest and the last is the largest.
Watch out. A number with more digits is greater; with the same number of digits, compare from the left.
Method. Only the ten thousands digit changes when we add or take away 10,000.
- Look at the ten thousands digit. Adding or taking away 10,000 changes this digit by one.The ten thousands digit is 4
- Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.4 - 1 = 3
- Write the answer. All the other digits stay the same.138,018
Check. Check: 138,018 add 10,000 gives back 148,018.
Watch out. Do not change the thousands digit. 10,000 is not 1,000.
Method. Only the ten thousands digit changes when we add or take away 10,000.
- Look at the ten thousands digit. Adding or taking away 10,000 changes this digit by one.The ten thousands digit is 8
- Change that digit by one. Carry or borrow if the digit goes past 9 or below 0.8 - 1 = 7
- Write the answer. All the other digits stay the same.373,161
Check. Check: 373,161 add 10,000 gives back 383,161.
Watch out. Do not change the thousands digit. 10,000 is not 1,000.
Method. Compare the numbers from the left, and write them smallest first.
- Find the smallest number. Compare the digits from the left.Smallest: 196,313
- Put the rest in order. Repeat: find the next smallest number.196,313 < 298,764 < 654,369 < 876,216
- Write the list. Smallest first, as the question asks.196,313, 298,764, 654,369, 876,216
Check. Check: the first number is the smallest and the last is the largest.
Watch out. A number with more digits is greater; with the same number of digits, compare from the left.
Method. Compare the numbers from the left, and write them smallest first.
- Find the smallest number. Compare the digits from the left.Smallest: 616,936
- Put the rest in order. Repeat: find the next smallest number.616,936 < 694,987 < 842,660 < 971,828
- Write the list. Smallest first, as the question asks.616,936, 694,987, 842,660, 971,828
Check. Check: the first number is the smallest and the last is the largest.
Watch out. A number with more digits is greater; with the same number of digits, compare from the left.
Method. Compare the numbers from the left, and write them smallest first.
- Find the smallest number. Compare the digits from the left.Smallest: 208,820
- Put the rest in order. Repeat: find the next smallest number.208,820 < 657,061 < 721,924 < 765,484
- Write the list. Smallest first, as the question asks.208,820, 657,061, 721,924, 765,484
Check. Check: the first number is the smallest and the last is the largest.
Watch out. A number with more digits is greater; with the same number of digits, compare from the left.