# ## Lesson: Operations With Decimals Developing the Concept

Many problem-solving situations involve operations with decimals. Now that your students have reviewed operations with decimals, it's time for them to practice their skills.

• Say: Understanding addition and subtraction of decimals helps us solve many problems we encounter in our daily activities. Here is a problem that requires these skills.

Present this problem to the class.
Eric started the day with two \$20 bills in his pocket. He paid \$16.98 for a soccer jersey, \$12.99 for a music CD, and \$1.50 for a slice of pizza. How much money does he have left?

• Ask: Who can show the class the first step in solving this problem?
Students should add the costs of the items to determine what Eric spent. They should have the decimal points lined up.
\$16.98
12.99
+ 1.50
\$31.47
• Ask: Now that we know the total amount spent by Eric, how do we compute how much he has left?
Students should respond with this subtraction problem.
\$40.00
−31.47
\$8.53

Eric's change is \$8.53

For independent practice, write the following problems on the board. Have students find the sum or difference, making sure they correctly line up the decimal points. The solutions are provided.

• 2.473 + 1.505 = (3.978)
• 15.27 − 9.58 = (5.69)
• 0.07 + 2.76 + 15.293 = (18.123)
• 63.09 − 4.683 = (58.407)
• 2.76 + 8 + 0.073 = (10.833)

Now, write these multiplication problems on the board and ask students to find the products.  • Ask: Who can explain the placement of the decimal points in these products?
Students should be able to explain that the sum of the number of decimal places in the factors equals the number of decimal places in the product.
• Say: Find the product of these factors. Students should remember to add a zero placeholder to the left of the 5 and then place the decimal point. If students need a review, remind them that the product must have five decimal places to match the five total decimal places in the factors. Zeros can be placed on the left to make the correct number of decimal places.

Provide the following practice division problems to check students' mastery. (Answers are provided.)

• 2.541 ÷ 3= (0.847)
• 23.76 ÷ 15 = (1.584)
• 105.75 ÷ 2.5= (42.3)
• 0.24675 ÷ 4.7 = (0.0525)

Wrap-Up and Assessment Hints
Mental math exercises are helpful in strengthening students' skills with decimals. Ask students to tell how many decimal places are the product of pairs of decimals, for example, 0.6 x 0.75 (3 places), 0.05 x 0.09 (4 places).

You can also give students a decimal and ask by what power of ten they should multiply to make it a whole number, for example, decimal: 1.7 (multiply by 10), decimal: 0.08 (multiply by 100), decimal: 0.043 (multiply by 1,000).

Students who have difficulty writing multiplication and division problems neatly and aligned will benefit from writing their solutions on graph paper. You can easily see any problems they are having by checking the alignment of their numbers on the graph paper.