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2. 2 Adding and Subtracting Decimals Activity You can use base-ten pieces to model decimal addition and subtraction. 0.76 1 Model the sum of 0.76 and 0.58 using base-ten pieces. 2 Combine and group the pieces. 3 Trade 10 tenths for 1 one and 10 hundredths for 1 tenth. 0.58 = 1.34 Adding and Subtracting Decimals 2. 2 Use a vertical format to add or subtract decimals. Begin by lining up the decimal points. Then add or subtract as you would with whole numbers. Be sure to write the decimal point in the answer. EXAMPLE 1 Adding and Subtracting Decimals 6.047 + 13.46 SOLUTION 6.047 + 13.460 ––––––– 19.507 Write zero as a placeholder. Adding and Subtracting Decimals 2. 2 Use a vertical format to add or subtract decimals. Begin by lining up the decimal points. Then add or subtract as you would with whole numbers. Be sure to write the decimal point in the answer. EXAMPLE 1 Adding and Subtracting Decimals 9 – 5.28 6.047 + 13.46 SOLUTION 6.047 + 13.460 ––––––– 19.507 SOLUTION Write zero as a placeholder. 9 .00 – 5.28 –––––– 3.72 Write zeros as placeholders. Adding and Subtracting Decimals 2. 2 EXAMPLE 2 Evaluating a Variable Expression Evaluate 6.7 + r – t when r = 2.14 and t = 5.2. SOLUTION 6.7 + r – t = 6.7 + 2.14 r – 5.2 t Substitute 2.14 for r and 5.2 for t. = 6.78.84 + 2.14 – 5.2 Add. = 3.64 Subtract. 2. 2 Adding and Subtracting Decimals Estimation When you do not need to find an exact sum, you can estimate. One type of estimation is front-end estimation. To use front-end estimation to estimate a sum, add the front-end digits, estimate the sum of the remaining digits, and then add the results. Adding and Subtracting Decimals 2. 2 EXAMPLE 3 Estimating a Sum Video Games For your birthday you receive a $25 gift certificate. You want to buy 3 used video games whose prices are shown. Can you buy all 3 games using the gift certificate? SOLUTION 1 Add the front-end digits: the dollars. $8.79 $7.29 + $7.89 ––––––– $22 ANSWER 2 Estimate the sum of the remaining digits: the cents. $8.79 $7.29 + $7.89 ––––––– $1 $1 __ $2 3 Add the results. $22 + $2 –––– $24 The estimated sum is less than $25, so you can buy all three games using the gift certificate.