Add, Subtract, and Multiply Decimals

We want to add a whole number and a decimal number. c 11.22 + 12 We can do this by lining up the digits according to their place values. Since the numbers do not have the same number of decimal places, we need to insert zeros so that each place has a digit. cr & 11.22 + & 12. 00 Now we can add the numbers just like we do with whole numbers. Then we will bring down the decimal point and place it into the answer.

The sum is 23.22.

This time we will add two numbers with the same number of decimal places. c 39.59 + 41.41 Let's line up the digits according to their place values. We do not need to add any zeros this time. cr & 39. 59 + & 41.41 Now we will add the numbers as if they are whole numbers, then place the decimal point in the answer at the end of the process.

The sum of the numbers is 81.00. The zeros to the right of the decimal point do not affect the value of the number, so we can remove them. The answer is then 81.

We are given two decimal numbers that have a different number of decimal places. c 5.7 + 89.332 Like before, let's start by lining up the digits according to their place values. We need to insert zeros so that each place has a digit because these numbers do not have the same number of decimal places. cr & 5.7 00 + & 89.332 Now we add the numbers as if they are whole numbers, then place the decimal point in the answer at the end of the process.

The numbers add up to 95.032.

We want to subtract a decimal number from a whole number. c 29-9.23 The numbers do not have the same number of decimal places. Recall that placing zeros to the right of a decimal point does not affect the value of the number. This is why we can insert zeros so that each place has a digit. Let's line up the numbers. cr & 29. 00 - & 9.23 Now we can subtract the numbers just like we do with whole numbers. Then we can place the decimal point in the answer.

The difference is 19.77.

We are asked to find the following difference. c 4.567 - 2.725 Let's line up the digits according to their place values. This time we will not need to add any zeros because the numbers have the same number of decimal places. cr & 4.567 - & 2.725 Let's subtract the numbers as if they are whole numbers. We will place the decimal point in the answer at the end of the process.

The difference of the numbers is 1.842.

Let's find the given difference. c 8.83 - 2.7 We will start by lining up the digits according to their place values. We need to add a zero so that each place has a digit since the numbers do not have the same number of decimal places. cr & 8. 83 - & 2.7 0 Now that the numbers have the same number of decimal places, we can subtract them!

The difference is 6.13.

We want to evaluate the given expression. 25.92 + 17.25- 9.243 We can add the first two decimals, then subtract the third decimal from their sum. (25.92 + 17.25)- 9.243 Let's find the sum of the first two decimals. We do this by lining up the decimal points before adding the numbers as usual.

The sum of the first two numbers is 43.17. Now we will subtract 9.243 from 43.17. First we write the numbers vertically so that the place values line up. Let's also insert a zero to the right of 43.17 so that the numbers have the same number of decimal places.

As a result, we found that the given expression is 33.927.

Consider the next expression. 33.06 - 7.3 + 9.24 Let's start by subtracting 7.3 from 33.06. Then we will add the third number to the difference. (33.06 - 7.3 ) + 9.24 We will line up the decimal points. Since the number of decimal places are different for these numbers, we insert a zero to the right of 7.3. This will ensure that the digits with the same place value come under each other. Let's subtract 7.30 from 33.06!

Now we will add 25.76 to 9.24. Just like before, we will start by writing the numbers vertically so that the decimal values line up.

We found that the given expression is 35.00, or 35.

We want to estimate the given product. 12.31 * 6 We can see that the second factor is already a whole number. We will round the first factor to the greatest place value to make our estimation. This will make it easier to use mental math. The first non-zero digit on the left in 12.31 is the 1 in the tens place. This is the greatest place value of the number. 12.31 * 6 Now we look at the digit to the right of the place that is being rounded.

• If the digit is less than 5, then the number in the rounded place remains the same.
• If the digit is 5 or greater, add 1 to the number in the rounded place.

After that, we remove any decimal digits and convert the non-decimal digits to the right of the greatest place value into 0. Let's round 12.31!

We can now multiply 10 and 6. 10 * 6 = 60 Since 10* 6 is 60, we can say that the product of 12.31 and 6 is about 60.

Let's check our answer with a calculator. We will multiply 12.31 by 6 and compare the product with our estimation.

The product of 12.31 and 6 is 73.86. This is pretty close to our approximation, so we can say that our answer makes sense.

We want to estimate the given product. 36.47 * 22.98 To make our estimation, we will round each factor to the greatest place value. The digit with the greatest place value in 36.47 is 3, and it is 2 in the second factor. 36.47 * 22.98 The greatest place value of each number is the tens place, so we need to look at the digits in the ones places.

• If the digit is less than 5, then the underlined number remains the same.
• If the digit is 5 or greater, add 1 to the underlined number.

After that, we remove any decimal digits and convert the non-decimal digits to the right of the greatest place value into 0.

We can now multiply 40 and 20. Notice that both of these numbers are multiples of 10. We can use the Commutative and Associative Properties of Multiplication to mentally find this product.

We found that the product of 36.47 and 22.98 is about 800.

We can check our answer with a calculator. We will multiply 13.92 by 2.7 and compare the product with our estimation.

The product of the numbers is 837.8508. We can say that our answer is correct because our estimation is close to the actual product.

We want to multiply a decimal number by a whole number. 0.017 * 8 Let's recall the steps we follow when multiplying decimals.

1. Multiply the numbers as if the decimal factors were whole numbers.
2. Count the number of decimal places in each factor.
3. The number of decimal places in the product is the sum of the number of decimal places in the factors.

We can start by multiplying 17 and 8. cr & 1 7 * & 8 & 1 3 6 The product of the numbers is 136. Now let's count the number of decimal places in each factor. cr & 0. 017 * & 8 & 136 l→ → r 3 decimal places + 0 decimal places 3 decimal places The sum is equal to 3. This means that the product must have three decimal places. cr & 0. 017 * & 8 & 0. 136 l→ → ← r 3 decimal places + 0 decimal places 3 decimal places The product of the given numbers is 0.136.

Let's find the given product. 0.65 * 2.22 We first ignore the decimal points and multiply, just like we do with two whole numbers.

Then we place the decimal point in the product by counting the number of decimal places in each factor.

The product of 0.65 and 2.22 is 1.4430. Since the zeros to the right of a decimal point do not affect the value of the number, we can ignore the zero at the end of the number. This means that 1.443 is also an answer.

We want to calculate the product of 17.1 and 3.012. 17.1 * 3.012 The first thing we will do is to ignore the decimal points for now to multiply the numbers just as we do with two whole numbers.

Now we place the decimal point in the product by counting the number of decimal places in each factor.

The product of 3.012 and 17.1 is 51.5052.

Our expression includes multiple operations, so let's start by recalling the order of operations. Note that expressions inside parentheses are evaluated first, followed by exponents, then multiplication and division, and then finally, addition and subtraction. Let's consider our expression again. 20.23(8.55-3.25) For the given expression, we will evaluate the expression inside the parentheses completely before multiplying. Let's first subtract 3.25 from 8.55. We can do this by lining up the decimal points so that place-value positions correspond to each other. cr & 8 . 5 5 -& 3 . 2 5 & 5 . 3 0 The difference in the parentheses is equal to 5.30, or simply 5.3. We will now multiply this number by 20.23. Let's ignore the decimal points and multiply the numbers. cr & 2 0 2 3 * & 5 3 & 6 0 6 9 + & 1 0 1 1 5 0 & 1 0 7 2 1 9 Next we will place the decimal point in the product by counting the number of decimal places in each factor. cr & 20. 23 * & 5. 3 & 6069 + & 101150 & 107. 219 l ⟶ ⟶ ⟵ cl & 2 decimal places + & 1 decimal place & 3 decimal places The expression is equal to 107.219.

Once again, let's examine the given expression to decide which operation will be done first. 0.25 + 2.5* 5.2 For this expression, we will first perform the multiplication, then the addition. Let's multiply 2.5 by 5.2. Recall that we ignore the decimal points and multiply the numbers as usual. cr & 2 5 * & 5 2 & 5 0 + & 1 2 5 0 & 1 3 0 0 Next we place the decimal point in the product by counting the number of decimal places in each factor. cr & 2. 5 * & 5. 2 & 50 + & 1250 & 13. 00 l ⟶ ⟶ ⟵ cl & 1 decimal place + & 1 decimal place & 2 decimal places The product of the numbers is 13.00. We will now add 0.25 to this number. We line up the decimal points so that place-value positions line up as well. cr & 1 3 . 0 0 +& 0 . 2 5 & 1 3 . 2 5 The expression is equal to 13.25.