Practice with the help of **Spectrum Math Grade 5 Answer Key Chapter 3 Lesson 3.5 Inserting Zeros to Add and Subtract** regularly and improve your accuracy in solving questions.

## Spectrum Math Grade 5 Chapter 3 Lesson 3.5 Inserting Zeros to Add and Subtract Answers Key

You may insert zero to help you add.

You may insert zeros to help you subtract.

Question 1.

a.

Answer:

For adding or subtracting a decimal and a whole number, the whole number is changed into a decimal number. This is done by placing a decimal after the whole number and then writing the required number of zeros after the decimal point.

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 2.35

b.

Answer:

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 1.58

c.

Answer:

For adding or subtracting a decimal and a whole number, the whole number is changed into a decimal number. This is done by placing a decimal after the whole number and then writing the required number of zeros after the decimal point.

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

Therefore, the sum is 15.96

d.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

Therefore, the sum is 52.86

e.

Answer:

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 9.24

Question 2.

a.

Answer:

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values.

Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.

Step 2: Now subtract the decimal numbers starting from the tenth column, moving on to the one’s column, and then the tens column. Copy the decimal as it comes.

Therefore, the difference is 0.47

b.

Answer:

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values.

Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.

Step 2: Now subtract the decimal numbers starting from the tenth column, moving on to the one’s column, and then the tens column. Copy the decimal as it comes.

Therefore, the difference is 1.26

c.

Answer:

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values.

Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.

Step 2: Now subtract the decimal numbers starting from the tenth column, moving on to the one’s column, and then the tens column. Copy the decimal as it comes.

Therefore, the difference is 2.36

d.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 3.21

e.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 10.15

Question 3.

a.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 17.37

b.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 31.55

c.

Answer:

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 8.94

d.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum

Therefore, the sum is 7.73

e.

Answer:

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 12.11

Question 4.

a.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values.

Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.

Step 2: Now subtract the decimal numbers starting from the tenth column, moving on to the one’s column, and then the tens column. Copy the decimal as it comes.

Therefore, the difference is 6.09

b.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values.

Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.

Step 2: Now subtract the decimal numbers starting from the tenth column, moving on to the one’s column, and then the tens column. Copy the decimal as it comes.

Therefore, the difference is 8.84

c.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values.

Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.

Step 2: Now subtract the decimal numbers starting from the tenth column, moving on to the one’s column, and then the tens column. Copy the decimal as it comes.

Therefore, the difference is 11.04

d.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 12.06

e.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 29.61

Question 5.

a.

Answer:

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 13.22

b.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 1.02

c.

Answer:

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 5.00

d.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 8.91

e.

Answer:

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 11.37

Question 6.

a.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values.

Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.

Step 2: Now subtract the decimal numbers starting from the tenth column, moving on to the one’s column, and then the tens column. Copy the decimal as it comes.

Therefore, the difference is 57.96

b.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values.

Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.

Step 2: Now subtract the decimal numbers starting from the tenth column, moving on to the one’s column, and then the tens column. Copy the decimal as it comes.

Therefore, the difference is 0.64

c.

Answer:

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values.

Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.

Step 2: Now subtract the decimal numbers starting from the tenth column, moving on to the one’s column, and then the tens column. Copy the decimal as it comes.

Therefore, the difference is 94.86

d.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values.

Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.

Step 2: Now subtract the decimal numbers starting from the tenth column, moving on to the one’s column, and then the tens column. Copy the decimal as it comes.

Therefore, the difference is 2.79

e.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values.

Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.

Step 2: Now subtract the decimal numbers starting from the tenth column, moving on to the one’s column, and then the tens column. Copy the decimal as it comes.

Therefore, the difference is 7.03

Question 7.

a.

Answer:

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 12.37

b.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The addition of decimals is done by starting from the right-hand side and then we move on to the left adding each column.

step 1: Write the numbers one below the other such that they are aligned as per their place values and the decimal point is placed one below the other.

step 2: Now add the decimal numbers to get the sum.

Therefore, the sum is 15.27

c.

Answer:

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values.

Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.

Step 2: Now subtract the decimal numbers starting from the tenth column, moving on to the one’s column, and then the tens column. Copy the decimal as it comes.

d.

Answer:

‘Unlike decimals’ are those decimal numbers that do not have the same number of digits after the decimal point. In other words, unlike decimals are said to be of different lengths. The operation of addition and subtraction can be conveniently performed even with these, unlike decimals. We just need to convert the ‘unlike decimals’ to ‘like decimals’ by writing zeros in the places wherever the length of decimal numbers is not the same. In this way, the decimal digits in each of the numbers become equal and it is easier to add or subtract the numbers.

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values.

Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.

Step 2: Now subtract the decimal numbers starting from the tenth column, moving on to the one’s column, and then the tens column. Copy the decimal as it comes.

Therefore, the difference is 6.01

e.

Answer:

The subtraction of decimals is done in the same way as the subtraction of whole numbers. We just need to write the numbers correctly according to their place values.

Step 1: Write the numbers one below the other such that the larger number is on top and the smaller number is written below it.

Step 2: Now subtract the decimal numbers starting from the tenth column, moving on to the one’s column, and then the tens column. Copy the decimal as it comes.

Therefore, the difference is 0.07