Step-by-step Maths Level 3: Writing a number in different ways
Part of the Step-by-step Maths Level 3 hundreds, tens and ones chapter. Chapter overview · whole chapter on one page
Writing a number in different ways
To partition a number means to split it into parts that add up to the number.
352 = 300 + 50 + 2 uses hundreds, tens and ones. It can be split other ways, such as 352 = 300 + 40 + 12. Both are right.
Key ideas
- Partition means split into parts that add to the number.
- The usual way is hundreds, tens and ones.
- Another way can use different parts, if the total is the same.
Method. Split the number by its places, then write each part.
- Find the hundreds, tens and ones of 352. Read the place value table.3 hundreds, 5 tens, 2 ones
- Write each part as a number. Each part is the digit times its place value.300 + 50 + 2
- Write the answer. The parts add up to the number.300 + 50 + 2
Check. Add the parts: 300 + 50 + 2 = 352.
Watch out. Leave out a part that is zero. 204 is 200 + 4.
Method. Split the number by its places, then write each part.
- Find the hundreds, tens and ones of 208. Read the place value table.2 hundreds, 0 tens, 8 ones
- Write each part as a number. Each part is the digit times its place value.200 + 8
- Write the answer. The parts add up to the number.200 + 8
Check. Add the parts: 200 + 8 = 208.
Watch out. Leave out a part that is zero. 204 is 200 + 4.
Method. Work out the parts we know, then find what is left to make the number.
- Add the two parts we can see. These parts are already known.300 + 2 = 302
- Take this total away from the number. The missing part is what is left over.352 - 302 = 50
- Write the missing number. It makes the sum equal to the number.50
Check. Check: 300 + 50 + 2 = 352.
Watch out. The missing part is the number that makes the total exact.
Watch out
Watch out. 300 + 40 + 12 is 352, but it is not hundreds, tens and ones. Check the total before you finish.
Exam tip
Grown-up tip. Use base-ten blocks to make the number, then swap a ten for ten ones and count again.
Exercise 2E Practice: partitioning
Non-calculatorMethod. Work out the parts we know, then find what is left to make the number.
- Add the two parts we can see. These parts are already known.300 + 2 = 302
- Take this total away from the number. The missing part is what is left over.352 - 302 = 50
- Write the missing number. It makes the sum equal to the number.50
Check. Check: 300 + 50 + 2 = 352.
Watch out. The missing part is the number that makes the total exact.
Method. Work out the parts we know, then find what is left to make the number.
- Add the two parts we can see. These parts are already known.90 + 7 = 97
- Take this total away from the number. The missing part is what is left over.997 - 97 = 900
- Write the missing number. It makes the sum equal to the number.900
Check. Check: 900 + 90 + 7 = 997.
Watch out. The missing part is the number that makes the total exact.
Method. Work out the parts we know, then find what is left to make the number.
- Add the two parts we can see. These parts are already known.500 + 20 = 520
- Take this total away from the number. The missing part is what is left over.521 - 520 = 1
- Write the missing number. It makes the sum equal to the number.1
Check. Check: 500 + 20 + 1 = 521.
Watch out. The missing part is the number that makes the total exact.
Method. Work out the parts we know, then find what is left to make the number.
- Add the two parts we can see. These parts are already known.300 + 9 = 309
- Take this total away from the number. The missing part is what is left over.349 - 309 = 40
- Write the missing number. It makes the sum equal to the number.40
Check. Check: 300 + 40 + 9 = 349.
Watch out. The missing part is the number that makes the total exact.
Method. Split the number by its places, then write each part.
- Find the hundreds, tens and ones of 855. Read the place value table.8 hundreds, 5 tens, 5 ones
- Write each part as a number. Each part is the digit times its place value.800 + 50 + 5
- Write the answer. The parts add up to the number.800 + 50 + 5
Check. Add the parts: 800 + 50 + 5 = 855.
Watch out. Leave out a part that is zero. 204 is 200 + 4.
Method. Work out the parts we know, then find what is left to make the number.
- Add the two parts we can see. These parts are already known.500 + 50 = 550
- Take this total away from the number. The missing part is what is left over.558 - 550 = 8
- Write the missing number. It makes the sum equal to the number.8
Check. Check: 500 + 50 + 8 = 558.
Watch out. The missing part is the number that makes the total exact.
Method. Split the number by its places, then write each part.
- Find the hundreds, tens and ones of 848. Read the place value table.8 hundreds, 4 tens, 8 ones
- Write each part as a number. Each part is the digit times its place value.800 + 40 + 8
- Write the answer. The parts add up to the number.800 + 40 + 8
Check. Add the parts: 800 + 40 + 8 = 848.
Watch out. Leave out a part that is zero. 204 is 200 + 4.
Method. Split the number by its places, then write each part.
- Find the hundreds, tens and ones of 396. Read the place value table.3 hundreds, 9 tens, 6 ones
- Write each part as a number. Each part is the digit times its place value.300 + 90 + 6
- Write the answer. The parts add up to the number.300 + 90 + 6
Check. Add the parts: 300 + 90 + 6 = 396.
Watch out. Leave out a part that is zero. 204 is 200 + 4.
Method. Split the number by its places, then write each part.
- Find the hundreds, tens and ones of 978. Read the place value table.9 hundreds, 7 tens, 8 ones
- Write each part as a number. Each part is the digit times its place value.900 + 70 + 8
- Write the answer. The parts add up to the number.900 + 70 + 8
Check. Add the parts: 900 + 70 + 8 = 978.
Watch out. Leave out a part that is zero. 204 is 200 + 4.
Method. Split the number by its places, then write each part.
- Find the hundreds, tens and ones of 770. Read the place value table.7 hundreds, 7 tens, 0 ones
- Write each part as a number. Each part is the digit times its place value.700 + 70
- Write the answer. The parts add up to the number.700 + 70
Check. Add the parts: 700 + 70 = 770.
Watch out. Leave out a part that is zero. 204 is 200 + 4.
Method. Work out the parts we know, then find what is left to make the number.
- Add the two parts we can see. These parts are already known.100 + 50 = 150
- Take this total away from the number. The missing part is what is left over.153 - 150 = 3
- Write the missing number. It makes the sum equal to the number.3
Check. Check: 100 + 50 + 3 = 153.
Watch out. The missing part is the number that makes the total exact.
Method. Work out the parts we know, then find what is left to make the number.
- Add the two parts we can see. These parts are already known.500 + 8 = 508
- Take this total away from the number. The missing part is what is left over.598 - 508 = 90
- Write the missing number. It makes the sum equal to the number.90
Check. Check: 500 + 90 + 8 = 598.
Watch out. The missing part is the number that makes the total exact.
Method. Split the number by its places, then write each part.
- Find the hundreds, tens and ones of 420. Read the place value table.4 hundreds, 2 tens, 0 ones
- Write each part as a number. Each part is the digit times its place value.400 + 20
- Write the answer. The parts add up to the number.400 + 20
Check. Add the parts: 400 + 20 = 420.
Watch out. Leave out a part that is zero. 204 is 200 + 4.
Method. Split the number by its places, then write each part.
- Find the hundreds, tens and ones of 734. Read the place value table.7 hundreds, 3 tens, 4 ones
- Write each part as a number. Each part is the digit times its place value.700 + 30 + 4
- Write the answer. The parts add up to the number.700 + 30 + 4
Check. Add the parts: 700 + 30 + 4 = 734.
Watch out. Leave out a part that is zero. 204 is 200 + 4.
Method. Work out the parts we know, then find what is left to make the number.
- Add the two parts we can see. These parts are already known.90 + 8 = 98
- Take this total away from the number. The missing part is what is left over.998 - 98 = 900
- Write the missing number. It makes the sum equal to the number.900
Check. Check: 900 + 90 + 8 = 998.
Watch out. The missing part is the number that makes the total exact.
Method. Split the number by its places, then write each part.
- Find the hundreds, tens and ones of 480. Read the place value table.4 hundreds, 8 tens, 0 ones
- Write each part as a number. Each part is the digit times its place value.400 + 80
- Write the answer. The parts add up to the number.400 + 80
Check. Add the parts: 400 + 80 = 480.
Watch out. Leave out a part that is zero. 204 is 200 + 4.