Category: Add and Subtract Whole Numbers

Definition

Consider a table of values; represented by an independent variable (x) and a dependent variable (y). We often use atable of valuesto display the values we record. Using the table, we can find the relationship between the two variables and write it as a rule. There may be an increasing or decreasing pattern in the relationship between the two variables.

Example

Consider that the total cost (y) of x items is two times the no of items, i.e., y =2 x. The total cost (y) increases as the number of items (x) increase. So it is clear that there is an increasing pattern here in the values of the variables.

Problem 1

Consider the values of the variables in the table given below.

Solution

Step 1:

Consider pairs of consecutive x values and find the difference.

4 2 = 6 4 = 8 6 = 10 8 = 2

Step 2:

Similarly consider pairs of consecutive y values and see the difference.

9 7 = 11 9 = 13 11 = 15 13 = 2

Step 3:

We find that for 2-unit increase in x, there is a 2-unit increase in the y value. So we see an increasing pattern in this table of values.

Problem 2

Consider the values of the variables in the table given below.

Solution

Step 1:

Consider pairs of consecutive x values and find the difference.

5 2 = 8 5 = 11 8 = 14 11= 3

Step 2:

Similarly consider pairs of consecutive y values and see the difference.

4 6 = 2 4 = 0 2 = -2 0 = – 2

Step 3:

We find that for 3-unit increase in x, there is a 2-unit decrease in the y value. So we see a decreasing pattern in this table of values.

Word problem 1 (on addition)

Yesterday, John had 237 baseball cards. Today he got 105 more. How many cards does John have now?

Solution

Step 1:

Number of baseball cards John had = 237

Number of cards John got more = 105

Step 2:

Number of cards John has now = 237 + 105 = 342

Word problem 2 (on subtraction)

Yesterday, Boris had 345 game cards. Today he gave 132 away. How many cards does Boris have left?

Solution

Step 1:

Number of game cards Boris had = 345

Number of cards Boris gave away = 132

Step 2:

Number of cards remaining with Boris = 345 132 = 213

Definition

A fact family is a group of math facts using the same numbers. In the case of addition and subtraction, you use three numbers and get four facts.

For example, you can form a fact family using the three numbers 3, 10, and 13: 10 + 3 = 13, 3 + 10 = 13, 13 10 = 3, and 13 3 = 10.

Addition facts − Here the sum of two of the three given numbers is the remaining third number. This sum is expressed in two possible orders. Thus, there are two addition facts for any three given numbers

For 3, 10 and 13, the two addition facts are:

3 + 10 = 13;

10 + 3 = 13

Subtraction facts − Here the difference of two of the three given numbers is the remaining third number. There are two such differences. Thus, there are two subtraction facts for any three given numbers.

For 3, 10 and 13, the two subtraction facts are:

13 10 = 3;

13 3 = 10

We use fact families to reinforce the connection between addition and subtraction, and to help students learn and memorize the basic addition & subtraction facts.

Problem 1

Make four related number sentences using each set of 3 numbers.

10, 7, 3:

There should be two additions and two subtractions.

Solution

10, 7, 3:

Step 1:

The addition facts using above three numbers are:

7 + 3 = 10;

3 + 7 = 10;

Step 2:

The subtraction facts using above three numbers are:

10 7 = 3;

10 3 = 7

Problem 2

Make four related number sentences using each set of 3 numbers.

13, 8, 5

There should be two additions and two subtractions.

Solution

13, 8, 5

Step 1:

The addition facts using above three numbers are:

5 + 8 = 13;

8 + 5 = 13;

Step 2:

The subtraction facts using above three numbers are:

13 5 = 8;

13 8 = 5

Problem 1

Subtract 6804 2547

Solution

Step 1:

Align the numbers vertically.

Step 2:

Since 4 is less than 7, we need to regroup in the ones place. We cannot borrow from zero, so we need to regroup in tens place as well. We regroup 8 to get 7 in hundreds place and ten in tens place.

Step 3:

We regroup again to get 9 in tens place and fourteen in ones place. We then subtract 7 from 14, 4 from 9, 5 from 7 and 2 from 6 to complete the subtraction.

Problem 2

Subtract 7059 886

Solution

Step 1:

Align the numbers vertically

Step 2:

In ones column subtract 6 from 9 to get 3.

Step 3:

In the tens column 8 is bigger than 5, so we need to regroup and borrow.

We cannot borrow from zero in hundreds place. So we borrow from 7 in thousands place. We cross out 7 and write 6 and put 1 beside 0 to make it ten.

Step 4:

To subtract 8 from 5 in tens column, we borrow from left. Cross out 10 and write 9 and put 1 beside 5 to make it 15. Then subtract 15 8 = 7.

Step 5:

Now subtract 8 from 9 in hundreds column and bring down 6 in thousands column to get final answer as 6173.

Problem 1

Subtract 836 647

Solution

Step 1:

Line up the numbers vertically.

Step 2:

In ones column, 7 is bigger than 6. So we borrow from 3 in tens column. We cross out 3 and write a 2. We put borrowed 1 beside 6 to make it 16. Then we subtract 7 from 16 to get 9.

Step 3:

In tens column, 4 is bigger than 2. So we borrow from left. We cross out 8 and write a 7. We put borrowed 1 beside 2 to make it 12. Then we subtract 12 4 = 8.

Step 4:

In hundreds column, we subtract 7 6 = 1. So final answer is 189

Problem 2

Subtract 658 379

Solution

Step 1:

Line up the numbers vertically.

Step 2:

In ones column, 9 is bigger than 8. So we borrow from 5 in tens column. We cross out 5 and write a 4. We put borrowed 1 beside 8 to make it 18. We then subtract 18 9 = 9.

Step 3:

In tens column, 7 is bigger than 4. So we borrow from left. We cross out 6 and write a 5. We put borrowed 1 beside 4 to make it 14. We then subtract 14 7 = 7.

Step 4:

In hundreds column, we subtract 5 3 = 2. So final answer is 279

Problem 1

Subtract the numbers 74 57

Solution

Step 1:

We line up the numbers vertically.

Step 2:

In the ones column, we cannot subtract 7 from 4 as 7 is greater than 4. So we borrow a ten from tens column. We strike off 7 and write a 6 and put a 1 beside 4 to make it 14. Now we subtract 14 7 = 7. 7 is written down below ones column.

Step 3:

Next in the tens column, we subtract 6 5 = 1. 1 is written down below tens column. So the answer is 17.

Problem 2

Subtract 53 39

Solution

Step 1:

Align the numbers vertically.

Step 2:

In the ones column, we cannot subtract 9 from 3 as 9 is greater than 3. So we borrow a ten from 5 in the tens column. We strike off 5 and write a 4 to its left. We put a 1 to left of 3 to make it 13. (1 ten = 10 ones). Now we 13 9 = 4. 4 is written below ones column.

Step 3:

Next in the tens column, 4 3 = 1. 1 is then written below tens column and the final answer is 14.

Problem 1

Subtract the numbers 76 42

Solution

Step 1:

We line up the numbers vertically.

Step 2:

Here, subtract the numbers in the ones column first. 6 2 = 4. Write 4 below ones column.

Step 3:

Next subtract the numbers in the tens column. 7 4 = 3. Write down 3 below tens column. So the final answer is 34.

Problem 2

Subtract 25 from 98

Solution

Step 1:

Align the numbers vertically.

Step 2:

Here, subtract the numbers in the ones column first. 8 5 = 3. Write down 3 below ones column.

Step 3:

Next the numbers in the tens column are subtracted. 9 2 = 7. Write 7 below tens column. So the final answer is 73.

Problem 1

Subtract the numbers 17 8

Solution

Method 1

We subtract the numbers using a number line here. On the number line, start from the larger number 17 and then make 8 jumps to the left to land on 9. This is the difference between 17 and 8.

Method 2

Counting backwards

We represent number 17 with 17 little diamonds. Since 8 is to be subtracted from 17, we strike off 8 diamonds while counting backward. The 9 diamonds that are left, are the result of the subtraction.

17 8 = 9

Problem 2

Subtract the numbers 15 6

Solution

Method 1

We subtract the numbers using a number line here. On the number line, start from the larger number 15 and then make 6 jumps to the left to land on 9. This is the difference between 15 and 6.

Method 2

Counting backwards

We represent number 15 with 15 little stars. Since 6 is to be subtracted from 15, we strike off 6 stars while counting backward. The 9 stars that are left, are the result of the subtraction.

15 6 = 9

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Problem 1

Find the sum 3473 + 53 + 682

Solution

Step 1:

We line up the numbers vertically.

Step 2:

The digits in ones column are added. 3 + 3 + 2 = 8. So 8 is written below ones column.

Step 3:

Then the digits in tens column are added. 7 + 5 + 8 = 20. 0 is written below tens column and 2 is carried over to hundreds column.

Step 4:

In hundreds column, 4 + 6 + 2 = 12. 2 is written below hundreds column and 1 is carried over to thousands column.

Step 5:

In thousands column, 3 + 1 = 4. 4 is written below thousands column. So the final sum is 4208.

Problem 2

Find the sum 7465 + 72 + 651

Solution

Step 1:

We line up the numbers vertically.

Step 2:

The digits in ones column are added. 5 + 2 + 1 = 8. So 8 is written below ones column.

Step 3:

Then the digits in tens column are added. 6 + 7 + 5 = 18. 8 is written below tens column and 1 is carried over to hundreds column.

Step 4:

In hundreds column, 4 + 6 + 1 = 11. 1 is written below hundreds column and 1 is carried over to thousands column.

Step 5:

In thousands column, 7 + 1 = 8. 8 is written below thousands column. So the final sum is 8188.

Problem 1

Find the sum 562 + 76

Solution

Step 1:

We line up the numbers vertically.

Step 2:

We add the digits in ones column. 2 + 6 = 8. 8 is written below ones column.

Step 3:

Then we add the digits in tens column. 6 + 7 = 13. 3 is written below tens column. 1 is carried over to hundreds column.

Step 4:

We add 5 and 1 in hundreds column. 5 + 1 = 6. 6 is written below hundreds column to give the final sum as 638.

Problem 2

Find the sum 754 + 65

Solution

Step 1:

We line up the numbers vertically.

Step 2:

We add the digits in ones column. 4 + 5 = 9. 9 is written below ones column.

Step 3:

Then we add the digits in tens column. 5 + 6 = 11. 1 is written below tens column. 1 is carried over to hundreds column.

Step 4:

We add 7 and 1 in hundreds column. 7 + 1 = 8. 8 is written below hundreds column to give the final sum as 819.