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State Board · Class 5 · Mathematics

Lesson 3: Addition and Subtraction

5 concepts · 40 practice questions with answers · Free to read

This lesson is also in: मराठी

Addition of six-digit and seven-digit numbers

From daily life

A temple trust collects 1,43,057 rupees in the first week and 4,21,689 rupees in the second week. To know the total, we add the two amounts column by column, exactly as we add small numbers.

Simple definition

Six-digit and seven-digit numbers are added by the same method as small numbers. Write the digits of the same place one below the other, add from the ones place, and carry over (हातचा) when a column adds up to 10 or more.

Column addition with carries: 1,43,057 + 4,21,689 = 5,64,746.117503,41,9861,24,+6474,65,carry ↑

In the figure : Column addition of 1,43,057 + 4,21,689: carry over to the next place whenever a column adds up to 10 or more.

Rule 1: Line up the places — Units under units, tens under tens, hundreds under hundreds and so on.

  • Easy : 34,567 + 21,845 = 56,412.
  • Medium : 2,45,308 + 3,17,692 = 5,63,000.
  • Exam-type : 12,34,567 + 8,76,543 = 21,11,110. Keep the commas lined up too; it helps to avoid mistakes.
Live figure

Addition of six-digit and seven-digit numbers

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Rule 2: Carry over — When a column adds to 10 or more, write the ones digit and carry the tens digit to the next column.

  • Easy : 7 + 8 = 15: write 5, carry 1.
  • Medium : 9 + 9 + 1 (carry) = 19: write 9, carry 1.
  • Exam-type : In 9,99,999 + 1, every column carries 1, so the answer is 10,00,000.
Remember

Always start from the ones place. Always add the carry before moving on.

Common mistake

Forgetting the carry, or adding the carry to the wrong column. Write a tiny 1 above the next column.

Shortcut

Memory clue: Right to left, carry the 1.

Spot the difference

StepWhat to do
1Line up the places
2Add from the ones place
3Carry 1 when the sum is 10 or more

Practice questions

Easy
  1. 1Add: 24,356 + 13,421.
  2. 2Add: 3,45,000 + 2,10,500.
  3. 3Add: 6,70,000 + 85,000.
Medium
  1. 4Add: 4,56,789 + 1,23,456.
  2. 5Add: 12,50,000 + 8,75,000.
  3. 6Add: 5,43,210 + 4,56,790.
Challenging
  1. 7Add: 25,00,000 + 18,40,000.
  2. 8A mela had 1,45,300 visitors on Saturday and 1,67,900 on Sunday. How many visitors came in all?
Show answers (try them yourself first)
  1. 137,777
  2. 25,55,500
  3. 37,55,000
  4. 45,80,245
  5. 521,25,000
  6. 610,00,000
  7. 743,40,000
  8. 81,45,300 + 1,67,900 = 3,13,200 visitors.

Adding more than two numbers and word problems

From daily life

A school's three clubs collect old books: 1,250, 3,400 and 560. The school wants the total of all three together. When there are many amounts, we keep adding in one column sum.

Simple definition

More than two numbers can be added in the same way: write them one below the other, add each column and carry over. In a word problem, find the numbers first, then choose to add.

Column addition with carries: 3,12,469 + 758 + 24,092 = 3,37,319.1219642,13,8572904,2+9137,33,carry ↑

In the figure : Three numbers added in one column sum, carrying over in the mind: 3,12,469 + 758 + 24,092 = 3,37,319.

Rule 1: Add three or more numbers — Add the whole column of digits at once and carry the tens digit.

  • Easy : 1,250 + 3,400 + 560 = 5,210.
  • Medium : 2,05,300 + 47,250 + 960 = 2,53,510.
  • Exam-type : 4,10,000 + 85,500 + 7,350 = 5,02,850.

Rule 2: Word problems — Words like "in all", "total" or "together" tell you to add.

  • Easy : A bus has 45 men and 38 women. In all 83 people.
  • Medium : A trust collected 1,24,500; 2,36,750 and 98,250 rupees in three months. Total = 4,59,500 rupees.
  • Exam-type : A library bought books for 14,250, 8,900 and 36,850 rupees and shelves for 5,000. Total = 65,000 rupees.
Remember

Line up all the numbers by place before adding. A small number such as 560 sits at the right end.

Common mistake

Starting a small number under the leftmost digit. 560 must start under the units of the others.

Shortcut

Memory clue: Look for pairs that make 10 (like 4 + 6, 7 + 3) to add a column quickly.

Spot the difference

WordMeaning
totaladd
altogetheradd
how many in alladd

Practice questions

Easy
  1. 1Add: 2,000 + 3,500 + 1,500.
  2. 2Add: 12,000 + 25,000 + 8,000.
  3. 3Add: 1,50,000 + 25,000 + 4,000.
Medium
  1. 4Add: 3,12,000 + 45,500 + 800.
  2. 5Add: 2,05,000 + 1,10,000 + 90,000.
  3. 6Add: 5,00,000 + 75,250 + 9,750.
Challenging
  1. 7A trust collected 1,24,500; 2,36,750 and 98,250 rupees in three months. Find the total.
  2. 8A library bought books for 14,250, 8,900 and 36,850 rupees and shelves for 5,000. What was the total spent?
Show answers (try them yourself first)
  1. 17,000
  2. 245,000
  3. 31,79,000
  4. 43,58,300
  5. 54,05,000
  6. 65,85,000
  7. 74,59,500 rupees.
  8. 865,000 rupees.

Subtraction of six-digit and seven-digit numbers

From daily life

A town had 15,40,000 people in 2001 and 18,25,000 in 2011. To find how many more people live there now, we subtract.

Simple definition

Subtraction of six-digit and seven-digit numbers uses the same method as small numbers. When a digit cannot be subtracted, borrow from the next higher place. Check by adding the answer to the smaller number.

Column subtraction with borrowing: 65,07,843 − 9,25,586 = 55,82,257.13137101453487,05,66855,29,−7522,85,5↑ borrowed (changed) digit

In the figure : Column subtraction of 65,07,843 − 9,25,586: when a digit cannot be subtracted, borrow from the next higher place (the changed digits are shown in orange).

Rule 1: Borrow — Take 1 from the next left place; it becomes 10 in the place you are working in.

  • Easy : 56,000 − 19,500 = 36,500.
  • Medium : 7,45,000 − 2,38,764 = 5,06,236.
  • Exam-type : 40,00,000 − 12,34,567 = 27,65,433. Check: 27,65,433 + 12,34,567 = 40,00,000.

Rule 2: Check by adding — Answer + smaller number should give the bigger number.

  • Easy : 9 − 4 = 5, check 5 + 4 = 9.
  • Medium : 18,25,000 − 15,40,000 = 2,85,000, check 2,85,000 + 15,40,000 = 18,25,000.
  • Exam-type : If the check does not match, subtract again from the units place.
Remember

The bigger number goes on top. Borrowing makes the borrowed place smaller by 1.

Common mistake

Subtracting the smaller digit from the bigger digit in every column. In 52 − 38, subtract 8 from 12, not 2 from 8.

Shortcut

Memory clue: Cannot take? Borrow 1 ten from the left neighbour.

Spot the difference

StepWhat to do
1Bigger number on top
2Subtract from the ones place
3Borrow from the left if needed

Practice questions

Easy
  1. 1Subtract: 9,000 − 4,500.
  2. 2Subtract: 75,000 − 28,000.
  3. 3Subtract: 3,00,000 − 1,25,000.
Medium
  1. 4Subtract: 8,40,000 − 3,56,000.
  2. 5Subtract: 10,00,000 − 4,35,000.
  3. 6Subtract: 52,40,000 − 18,75,000.
Challenging
  1. 7Subtract 4,67,850 from 9,05,400 and check by adding.
  2. 8A town had 15,40,000 people in 2001 and 18,25,000 in 2011. How many more people were there in 2011?
Show answers (try them yourself first)
  1. 14,500
  2. 247,000
  3. 31,75,000
  4. 44,84,000
  5. 55,65,000
  6. 633,65,000
  7. 74,37,550. Check: 4,37,550 + 4,67,850 = 9,05,400.
  8. 818,25,000 − 15,40,000 = 2,85,000.

Subtraction by another method and word problems

From daily life

Ravi wants a bike that costs 85,000 rupees and has saved 62,500. The difference is what he still needs: this is a subtraction word problem.

Simple definition

If we add 10 or 100 to both numbers, the difference stays the same. This helps when a digit cannot be subtracted. Words like "how many more", "left" and "difference" tell us to subtract.

Rule 1: Add the same to both — Add ten to the top ones digit and 1 ten to the bottom tens digit, then subtract.

  • Easy : 83 − 47: 3 − 7 is not possible. Add 10 to 83's ones: 13 − 7 = 6; tens: 8 − (4 + 1) = 3. Answer 36.
  • Medium : 826 − 458: 16 − 8 = 8; 2 tens + 10 = 12 tens, 12 − 6 = 6; 8 − (4 + 1) = 3 hundreds. Answer 368.
  • Exam-type : 5,000 − 2,347 = 2,653. Check by adding: 2,653 + 2,347 = 5,000.

Rule 2: Word problems — Find the numbers first, then decide whether to add or subtract.

  • Easy : Bike 85,000, saved 62,500: needed 85,000 − 62,500 = 22,500 rupees.
  • Medium : A farmer wants 1,00,000 rupees and has 37,500: he needs 1,00,000 − 37,500 = 62,500 more.
  • Exam-type : A shop sold 12,50,000 rupees of goods in a year. The target was 8,75,000. It sold 3,75,000 rupees above the target.
Remember

Adding the same number to both numbers keeps the difference the same.

Common mistake

Adding 10 to only one number. Add to both: 10 to the top ones and 1 ten to the bottom tens.

Shortcut

Memory clue: Add ten up there, add one ten down here.

Spot the difference

WordMeaning
how many moresubtract
leftsubtract
differencesubtract

Practice questions

Easy
  1. 1Subtract by adding the same to both: 83 − 47.
  2. 2Subtract: 726 − 458.
  3. 3Subtract: 5,000 − 2,347.
Medium
  1. 4Subtract: 1,000 − 678.
  2. 5Subtract: 7,00,000 − 3,45,800.
  3. 6A bike costs 85,000 rupees. Ravi has 62,500. How much more does he need?
Challenging
  1. 7A shop sold goods worth 12,50,000 rupees. The target was 8,75,000. By how much did it cross the target?
  2. 8A farmer needs 1,00,000 rupees for a well and has saved 37,500. Find the amount still needed and check by adding.
Show answers (try them yourself first)
  1. 136
  2. 2268
  3. 32,653
  4. 4322
  5. 53,54,200
  6. 622,500 rupees.
  7. 73,75,000 rupees.
  8. 81,00,000 − 37,500 = 62,500. Check: 62,500 + 37,500 = 1,00,000.

Mixed addition and subtraction

From daily life

A family's trip costs 7,45,000 rupees: the hall is 2,50,000, food is 1,75,000, and the rest is decoration. Here, adding and subtracting are mixed.

Simple definition

When both signs are given, do the operations in the order in which they are given, from left to right. In a word problem, if a total is known, subtract the known parts from it to get the missing part.

A bar for the house cost 87,14,530 split into plot 24,72,615, material 50,43,720 and labour 11,98,195.House cost: 87,14,530plotmaterialplot 24,72,615material 50,43,720labour 11,98,195

In the figure : The house cost is the total of the plot, the material and the labour. Subtract the known parts from the total to get the labour.

Rule 1: Left to right — Do the signs in the given order.

  • Easy : 500 + 300 − 200 = 600.
  • Medium : 7,50,000 + 2,35,000 − 4,10,000 = 5,75,000.
  • Exam-type : 9,00,000 − 3,25,000 + 1,50,000 = 7,25,000.

Rule 2: Find the missing part — Missing part = total − all known parts.

  • Easy : A bill is 100. Food is 60. The rest is 100 − 60 = 40.
  • Medium : Total 12,00,000; plot 4,50,000; material 3,25,000: labour = 12,00,000 − 4,50,000 − 3,25,000 = 4,25,000.
  • Exam-type : Second method: add the known parts, 4,50,000 + 3,25,000 = 7,75,000, then subtract from 12,00,000: 4,25,000. Both ways agree.
Remember

Check the answer by adding all the parts: they must give the total.

Common mistake

Doing + first and − next regardless of order. Follow the order given: 9 − 4 + 3 is (9 − 4) + 3 = 8, not 9 − 7.

Shortcut

Memory clue: Total − parts = missing part; parts + missing = total.

Spot the difference

SituationDo
all parts knownadd
total and some parts knownsubtract the known parts
a check is neededadd all parts

Practice questions

Easy
  1. 1Find: 500 + 300 − 200.
  2. 2Find: 12,000 + 5,000 − 7,000.
  3. 3Find: 90,000 − 25,000 + 10,000.
Medium
  1. 4Find: 7,50,000 + 2,35,000 − 4,10,000.
  2. 5Find: 9,00,000 − 3,25,000 + 1,50,000.
  3. 6A shop earned 4,50,000 rupees in one month and 3,25,000 in the next. It spent 2,00,000. How much is left?
Challenging
  1. 7A house costs 12,00,000 rupees: plot 4,50,000, material 3,25,000. Find the labour cost in two ways.
  2. 8The total bill of a function is 7,45,000 rupees. Hall costs 2,50,000 and food 1,75,000. Find the decoration cost and check by adding.
Show answers (try them yourself first)
  1. 1600
  2. 210,000
  3. 375,000
  4. 45,75,000
  5. 57,25,000
  6. 64,50,000 + 3,25,000 − 2,00,000 = 5,75,000 rupees.
  7. 7Way 1: 12,00,000 − 4,50,000 − 3,25,000 = 4,25,000. Way 2: 4,50,000 + 3,25,000 = 7,75,000; 12,00,000 − 7,75,000 = 4,25,000.
  8. 87,45,000 − 2,50,000 − 1,75,000 = 3,20,000. Check: 2,50,000 + 1,75,000 + 3,20,000 = 7,45,000.

Quick revision

  • Add and subtract from the units place; carry over in addition, borrow in subtraction.
  • Adding 10 or 100 to both numbers does not change the difference.
  • Verify a subtraction answer by adding.