Number Column Addition and Subtraction for Decimals

Learning Objective Success Criteria To use column addition and subtraction for decimals. Success Criteria To use column addition for decimals. To use column subtraction for decimals. To solve problems using column addition and subtraction.

Starter: Converting Decimals to Fractions Change each of the following decimals into a fraction. Give your answers in fully simplified form. Thinking about the place value of each digit may help you with this: 7 10 0.7 2 5 0.4 1 2 0.5 0.03 3 100 0.05 1 20 2 25 0.08 57 100 0.57 0.68 17 25 0.25 1 4 0.048 6 125

Using Column Addition for Decimals You should remember, from adding whole numbers: all digits of the same place value are lined up vertically; we start working from right to left; when the result of adding 2 digits is 10 or more, we carry the first digit into the sum for the next column. The same applies to adding decimals, but you will need to consider the decimal point when lining up the numbers according to their place value. When we add 4.9 to 16.405, we must use the decimal points to line up the digits. As long as the decimal points are lined up, everything else will follow – the tenths are always immediately to the right of the decimal point, the units to the left: 1 6 . 4 0 5 4 . 9 +

Using Column Addition for Decimals You may wish to fill in any gaps with zeroes, so that there are 2 digits in every column, although this is less important with addition than with subtraction. 1 6 . 4 0 5 0 4 . 9 0 0 + 2 1 . 3 5 1 1 We add the digits in each column, from right to left. Place a decimal point in the answer, in line with the decimal points in the numbers we’re adding. 16.405 + 4.9 = 21.305

Using Column Addition for Decimals You may be asked to add a whole number to a decimal, e.g. 94 + 45.983 We need to follow the same method of lining up the decimal point, so we need to find where the decimal point in 94 would go. As 94 is a whole number, the 9 must be in the tens column and the 4 in the units column. That means that the decimal point is immediately to the right of the 4. This gives: 94 + 45.983 = 139.983 9 4 . 0 0 0 4 5 . 9 8 3 + 1 3 9 . 9 8 3 1

Using Column Subtraction for Decimals When we use column subtraction with decimals, we use the same principles: locate the position of the decimal points in any whole numbers; line up the decimal points in the numbers and put a decimal point in line with these in the answer space; work from right to left. We must also remember to borrow when the top number in a column is smaller than the bottom number.

Using Column Subtraction for Decimals Let’s have a go with: 9 – 7.49 The decimal point in 9 goes to the right of the 9, since 9 is a unit: We need to fill the gaps with zeroes when we’re subtracting. Starting from the right, we subtract. We won’t take 9 from 0 as 9 is larger than 0, instead, we must borrow. Initially, the 0 in the hundredths column cannot borrow from the 0 in the tenths column. The 0 in the tenths column has to borrow from the 9, first. When this happens, the 9 becomes an 8, and the 0 in the tenths column a 10. That means that the 0 in the hundredths column is now able to borrow from its left-hand neighbour. The 10 becomes a 9 and the 0 a 10. Now we subtract to give 1.51 8 9 9 . 0 0 7 . 4 9 - 1 1 1 . 5 1

Activity Sheet Now complete the activity sheet independently.

Plenary Evaluate the following then place the results in order of size, from smallest to largest. In order: 41.08, 41.587, 41.6 14.68 + 26.4 90 – 48.4 20.257 + 21.33 41.08 41.6 41.587