Basic Decimals: Lessons and Problems

How Can My Child Learn Decimal Concepts?

Place Values and How to Read Decimals

Start by reviewing the place values of whole numbers. Beginning at the right and moving to the left, they are ones, tens, hundreds, thousands, ten thousands, hundred thousands and millions. Decimal place values begin at the decimal point and move to the right. Most fourth graders learn tenths and hundredths.

When learning to read decimals, start by reviewing whole numbers. Your child should read 762 as 'seven hundred sixty-two,' not 'seven hundred and sixty-two.' The decimal point is read as 'and.' So 6.3 is read as 'six and three tenths.' A larger decimal, such as 8.43, is read as 'eight and forty-three hundredths.'

Changing Decimals to Fractions

Show your child that if the decimal is .1, it is read as 'one tenth' and written as 1/10. If you have .43, you would write the fraction 43/100, because it's read as 'forty-three hundredths.'

Adding and Subtracting Decimals

Adding decimals is like doing regular addition; just be careful to line up the decimal points. The place values, both before and after the decimal point, also line up. The decimal point is also placed in its column in the answer.

Subtracting decimals follows the same process as adding them. Line up the decimal points and subtract like you would any other numbers. Just remember to bring down the decimal in the answer.

Multiplying Decimals

For multiplication, decimal points are not lined up as in addition and subtraction. The numbers are lined up so that those at the right end are in the same column. However, the decimals are written in the numbers. Multiply as for whole numbers.

So the work for 15.3 x 3.21 will look just the same as for 153 x 321. Once you have the answer (49,113), look at the decimal numbers and count how many numbers in all follow decimal points. There is one in 15.3 and two in 3.21. The total of numbers that follow decimal points is 1 + 2, or 3. Put the decimal point in front of the third number from the right so that the answer is 49.113.

Dividing Decimals

When you divide a decimal by a whole number, there is one difference from standard division. In the answer position, you put the decimal point exactly above the decimal point in the dividend (the number being divided). Ignore that decimal point until you finish working the problem; it is then part of the answer.

When you divide a decimal number by another decimal number, the first thing you need to do is turn the divisor (the number that divides into the dividend) into a whole number. You do this by moving the decimal point to the right side of the number. So in the problem 6.54 ÷ .2, you change .2 to 2.

Just like working with fractions, what you do to one number is done to all the numbers. Since you moved the decimal point one number to the right in the divisor, you have to do that in the dividend also. Therefore 6.54 become 65.4. You show these movements by using a ^ symbol where the new decimals will be. Then you can divide the new decimal by the new whole number.

For the problem 6.75 ÷ .25, you would change the .25 to 25. Since you moved the decimal point two numbers to the right, you would do the same for 6.75 to make it 675. The problem is now 675 ÷ 25.

Practice Decimal Problems

1. How would you read 9.56? Write it out.

2. Convert these decimals into fractions:

• .4
• .72
• .9
• .98

3. Solve the following problems (round to the nearest hundredth if necessary):

• 3.6 + 5.4
• 8.34 + 7.22
• 5.8 - 2.6
• 6.93 - .51
• 2.7 x 9.1
• 4.5 x 6.7
• 3.4 x 8.7
• 6.2 ÷ 4
• 7.75 ÷ 2.25
• 4.4 ÷ 2.2

Answer Key

1. Nine and fifty-six hundredths

2. Convert these decimals into fractions:

• 4/10
• 72/100
• 9/10
• 98/100

3. Solve the following problems (round to the nearest hundredth if necessary):

• 9
• 15.56
• 3.2
• 6.42
• 24.57
• 30.15
• 29.58
• 1.55
• 3.44
• 2