5.2 Adding and Subtracting Decimals Adding/Subtracting Decimals. Stack the numbers (one digit on top of another digit). Make sure the decimal points align. 2. Add/Subtract the numbers as if they were whole numbers. 3. Drop the decimal point straight down into your answer. It should line up with the previous decimal points. Note: Remember you can always add zeros, after the decimal point, to the back of a number, if needed. Example : Add 3.25 and 4.84. Solution: 3.25 4.84 3.25 4.84 7.939 7.939 You Try It : Add. 2.864 3.029 Example 2: Desiree has $4.35 in her purse. Matt has $5.68 in his wallet. If they combine their money, how much money do they have in total? Solution: 4.35 5.68 $4.35 $5.68 $0.03 0.03 You Try It 2: Elliot has $8.92 in his wallet and Ruben has $0.73. If they combine their money, how much money do they have in total? 205 Worrel
Example 3: Add. 7.8 2.9 Solution: Remember you can add zeros to the back without changing the value of the number. This is helpful so that we can have the same number of digits and can line them up appropriately. 7.8 2.9 7.80 5.9 7.8 2.9 23.7 23.7 You Try It 3: Add. 9.7 5.86 Example 4: Find the sum. 2.9 8.672 22.84 Solution: 2.9 8.672 22.84 2 2.900 8.672 22.840 2.9 8.672 22.84 44.42 44.42 You Try It 4: Add. 2.2 4.286 33.97 Example 5: Subtract 2.73 from 33.57. Solution: Remember subtract from is a backwards statement, hence the back number goes first. 2 33.57 2.73 20.84 33.57 2.73 20.84 You Try It 5: Subtract. 58.76 38.95 205 Worrel 2
Example 6: Find the difference. 3.3 8.572 Solution: Remember you can add zeros to the back without changing the value of the number. We definitely need to add zeros to the back of the top number so that we can subtract correctly. 3.3 8.572 2 2 9 3. 3 0 0 8. 5 7 2 3.3 8.572 4.728 4. 7 2 8 You Try It 6: Add. 5.2 8.756 Adding Two Decimals with Like Signs. Add the magnitudes of the decimal numbers. (ie. ignore the signs and add the numbers as usual.) 2. Carry the like sign into your answer. Example 7: Simplify. 3.2 8.95 Solution: Since both numbers have like signs (both are negative) ignore the signs and add the numbers. Remember to carry the like sign into your answer (ie. your answer should be negative). 3.2 8.95 3.20 8.95 3.2 8.95 22.5 22.5 Don t forget to put back the sign! You Try It 7: Simplify. 5.7 83.85 205 Worrel 3
Adding Two Decimals with Unlike Signs. Subtract the smaller magnitude from the larger magnitude of the decimal numbers. [ie. ignore the signs and subtract (larger magnitude smaller magnitude)] 2. Carry the sign of number with the larger magnitude. Example 8: Simplify. 3 2.24 Solution: If we ignore the signs, we have 3 and 2.24. 3 has a larger magnitude so we will subtract, 3 2.24. Make note that 3, which has a larger magnitude, is negative. Therefore we know our answer should be negative (since we carry the sign of the number with the larger magnitude). 3 2.24 You Try It 8: Simplify. 8 5.74 2 9 3. 0 0 2. 2 4 3 2.24 0.76 0. 7 6 Example 9: Simplify. 8.567 2.3 Solution: First we take care of the double negative by turning it into a positive. 8.567 2.3 8.567 2.3 Now, we have numbers with different signs. We ignore the signs for now and we have 8.567 and 2.3. 2.3 has a larger magnitude so we will subtract, 2.3 8.567. Make note that 2.3, which has the larger magnitude, is positive. Therefore we know our answer should be positive (since we carry the sign of the number with the larger magnitude). 2.3 8.567 2 9 2. 3 0 0 8. 5 6 7 8.567 2.3 3.733 3. 7 3 3 You Try It 9: Simplify. 2.384 5.2 Remember your answer is positive because the number with the larger magnitude was positive! 205 Worrel 4
Example 0: Simplify..2 8.45 2.7 Solution: You need to use order of operations to simplify. Although it s tempting to turn the double negative into a positive we cannot do that yet since that is a multiplication, and we have the inside grouping symbol to do first. So let s start with simplifying inside the parentheses..2 8.45 2.7 FIRST Inside the grouping symbol we have, 8.45 2.7. We have numbers with different signs. We ignore the signs for now and we have 8.45 and 2.7. 8.45 has a larger magnitude so we will subtract 8.45 2.7. Make note that 8.45, which has the larger magnitude, is negative. Therefore we know our answer should be negative (since we carry the sign of the number with the larger magnitude). 8.45 2.7 7 8. 4 5 2. 7 0 So, 8.45 2.7 5.75 5. 7 5 5.75.2 5.75.2 5.75 So now we have,.2 8.45 2.7.2 5.75 into a positive. 0. Now we can change the double negative We are left with numbers with different signs. We ignore the signs for now and we have.2 and 5.75..2 has a larger magnitude so we will subtract,.2 5.75. Make note that.2, which has the larger magnitude, is negative. Therefore we know our answer should be negative (since we carry the sign of the number with the larger magnitude)..2 5.75. 2 0 5. 7 5 So,.2 5.75 5.45 5. 4 5 You Try It 0: Simplify. 2.8 7.44 3.7 205 Worrel 5
Example : Simplify. 2.3 4.6 2.84 Solution: You need to use order of operations to simplify. We need to simplify inside grouping symbol first. So let s start with simplifying inside the absolute value. 2.3 4.6 2.84 FIRST Inside the grouping symbol we have, 4.6 2.84. We get rid of the double negative and change it into a positive. 4.6 2.84 4.6 2.84 We now have numbers with different signs. We ignore the signs for now and we have 4.6 and 2.84. 4.6 has a larger magnitude so we will subtract, 4.6 2.84. Make note that 4.6, which has the larger magnitude, is negative. Therefore we know our answer should be negative (since we carry the sign of the number with the larger magnitude). 4.6 2.84 3 5 4. 6 0 2. 8 4 So, 4.6 2.84.76. 7 6 So now we have, 2.3 4.6 2.84 2.3 4.6 2.84 2.3.76..76 Now finish the grouping symbol by taking the absolute value,.76. So, we have, 2.3 4.6 2.84 2.3.76 2.3.76. Since both numbers have like signs (both are negative) ignore the signs and add the numbers. Remember to carry the like sign into your answer (ie. your answer should be negative). 2.3.76 2. 3 0.76. 7 6 So, 2.3.76 4.06 4. 0 6 Don t forget to put the sign back! You Try It : Simplify. 8.6 5.5 8.32 205 Worrel 6