m81245 Subtract Whole Numbers By the end of this section, you will be able to: Use subtraction notation Model subtraction of whole numbers Subtract whole numbers Translate word phrases to math notation Subtract whole numbers in applications b7b437ef-73c1-446d-a42c-7a7ebe933114 Before you get started, take this readiness quiz. Model 3+4 using base-ten blocks. If you missed this problem, review . Add: 324+586. If you missed this problem, review . 910

Suppose there are seven bananas in a bowl. Elana uses three of them to make a smoothie. How many bananas are left in the bowl? To answer the question, we subtract three from seven. When we subtract, we take one number away from another to find the difference. The notation we use to subtract 3 from 7 is 7−3 We read 7−3 as seven minus three and the result is the difference of seven and three. To describe subtraction, we can use symbols and words. Operation Notation Expression Read as Result Subtraction − 7−3 seven minus three the difference of 7 and 3 Translate from math notation to words: ⓐ 8−1 ⓑ 26−14. ⓐ We read this as eight minus one. The result is the difference of eight and one. ⓑ We read this as twenty-six minus fourteen. The result is the difference of twenty-six and fourteen. Translate from math notation to words: ⓐ 12−4ⓑ 29−11 ⓐ twelve minus four; the difference of twelve and four ⓑ twenty-nine minus eleven; the difference of twenty-nine and eleven Translate from math notation to words: ⓐ 11−2ⓑ 29−12 ⓐ eleven minus two; the difference of eleven and two ⓑ twenty-nine minus twelve; the difference of twenty-nine and twelve

A model can help us visualize the process of subtraction much as it did with addition. Again, we will use base-10 blocks. Remember a block represents 1 and a rod represents 10. Let’s start by modeling the subtraction expression we just considered, 7−3. We start by modeling the first number, 7. Now take away the second number, 3. We'll circle 3 blocks to show that we are taking them away. Count the number of blocks remaining. There are 4 ones blocks left. We have shown that 7−3=4. Model the subtraction: 8−2. 8−2 means the difference of 8 and 2. Model the first, 8. Take away the second number, 2. Count the number of blocks remaining. There are 6 ones blocks left. We have shown that 8−2=6. Model: 9−6. Model: 6−1. Model the subtraction: 13−8. Model the first number, 13. We use 1 ten and 3 ones. Take away the second number, 8. However, there are not 8 ones, so we will exchange the 1 ten for 10 ones. Now we can take away 8 ones. Count the blocks remaining. There are five ones left. We have shown that 13−8=5. As we did with addition, we can describe the models as ones blocks and tens rods, or we can simply say ones and tens. Model the subtraction: 12−7. Model the subtraction: 14−8. Model the subtraction: 43−26. Because 43−26 means 43 take away 26, we begin by modeling the 43. Now, we need to take away 26, which is 2 tens and 6 ones. We cannot take away 6 ones from 3 ones. So, we exchange 1 ten for 10 ones. Now we can take away 2 tens and 6 ones. Count the number of blocks remaining. There is 1 ten and 7 ones, which is 17. 43−26=17 Model the subtraction: 42−27. Model the subtraction: 45−29.

Addition and subtraction are inverse operations. Addition undoes subtraction, and subtraction undoes addition.We know 7−3=4 because 4+3=7. Knowing all the addition number facts will help with subtraction. Then we can check subtraction by adding. In the examples above, our subtractions can be checked by addition. 7−3=4because4+3=713−8=5because5+8=1343−26=17because17+26=43 Subtract and then check by adding:ⓐ 9−7ⓑ 8−3. ⓐ 9−7 Subtract 7 from 9. 2 Check with addition.2+7=9✓ ⓑ 8−3 Subtract 3 from 8. 5 Check with addition.5+3=8✓ Subtract and then check by adding: 7−0 7 − 0 = 7; 7 + 0 = 7 Subtract and then check by adding: 6−2 6 − 2 = 4; 2 + 4 = 6 To subtract numbers with more than one digit, it is usually easier to write the numbers vertically in columns just as we did for addition. Align the digits by place value, and then subtract each column starting with the ones and then working to the left. Subtract and then check by adding: 89−61. Write the numbers so the ones and tens digits line up vertically. 89 −61____ Subtract the digits in each place value.Subtract the ones: 9-1=8Subtract the tens: 8-6=2 89 −61____ 28 Check using addition. 28 +61____ 89 Our answer is correct. Subtract and then check by adding: 86−54. 86 − 54 = 32 because 54 + 32 = 86 Subtract and then check by adding: 99−74. 99 − 74 = 25 because 74 + 25 = 99 When we modeled subtracting 26 from 43, we exchanged 1 ten for 10 ones. When we do this without the model, we say we borrow 1 from the tens place and add 10 to the ones place. Write the numbers so each place value lines up vertically. Subtract the digits in each place value. Work from right to left starting with the ones place. If the digit on top is less than the digit below, borrow as needed. Continue subtracting each place value from right to left, borrowing if needed. Check by adding. Subtract: 43−26. Write the numbers so each place value lines up vertically. Subtract the ones. We cannot subtract 6 from 3, so we borrow 1 ten. This makes 3 tens and 13 ones. We write these numbers above each place and cross out the original digits. Now we can subtract the ones. 13−6=7. We write the 7 in the ones place in the difference. Now we subtract the tens. 3−2=1. We write the 1 in the tens place in the difference. Check by adding. Our answer is correct. Subtract and then check by adding: 93−58. 93 − 58 = 35 because 58 + 35 = 93 Subtract and then check by adding: 81−39. 81 − 39 = 42 because 42 + 39 = 81 Subtract and then check by adding: 207−64. Write the numbers so each place value lines up vertically. Subtract the ones. 7−4=3. Write the 3 in the ones place in the difference. Subtract the tens. We cannot subtract 6 from 0 so we borrow 1 hundred and add 10 tens to the 0 tens we had. This makes a total of 10 tens. We write 10 above the tens place and cross out the 0. Then we cross out the 2 in the hundreds place and write 1 above it. Now we subtract the tens. 10−6=4. We write the 4 in the tens place in the difference. Finally, subtract the hundreds. There is no digit in the hundreds place in the bottom number so we can imagine a 0 in that place. Since 1−0=1, we write 1 in the hundreds place in the difference.Check by adding. Our answer is correct. Subtract and then check by adding: 439−52. 439 − 52 = 387 because 387 + 52 = 439 Subtract and then check by adding: 318−75. 318 − 75 = 243 because 243 + 75 = 318 Subtract and then check by adding: 910−586. Write the numbers so each place value lines up vertically. Subtract the ones. We cannot subtract 6 from 0, so we borrow 1 ten and add 10 ones to the 0 ones we had. This makes 10 ones. We write a 0 above the tens place and cross out the 1. We write the 10 above the ones place and cross out the 0. Now we can subtract the ones. 10−6=4. Write the 4 in the ones place of the difference. Subtract the tens. We cannot subtract 8 from 0, so we borrow 1 hundred and add 10 tens to the 0 tens we had, which gives us 10 tens. Write 8 above the hundreds place and cross out the 9. Write 10 above the tens place. Now we can subtract the tens. 10−8=2. Subtract the hundreds place. 8−5=3 Write the 3 in the hundreds place in the difference. Check by adding. Our answer is correct. Subtract and then check by adding: 832−376. 832 − 376 = 456 because 456 + 376 = 832 Subtract and then check by adding: 847−578. 847 − 578 = 269 because 269 + 578 = 847 Subtract and then check by adding: 2,162−479. Write the numbers so each place value lines up vertically. Subtract the ones. Since we cannot subtract 9 from 2, borrow 1 ten and add 10 ones to the 2 ones to make 12 ones. Write 5 above the tens place and cross out the 6. Write 12 above the ones place and cross out the 2. Now we can subtract the ones. 12−9=3 Write 3 in the ones place in the difference. Subtract the tens. Since we cannot subtract 7 from 5, borrow 1 hundred and add 10 tens to the 5 tens to make 15 tens. Write 0 above the hundreds place and cross out the 1. Write 15 above the tens place.Now we can subtract the tens.15−7=8 Write 8 in the tens place in the difference.Now we can subtract the hundreds.Write 6 in the hundreds place in the difference.Subtract the thousands. There is no digit in the thousands place of the bottom number, so we imagine a 0. 1−0=1. Write 1 in the thousands place of the difference.Check by adding.11,61813+479______2,162✓ Our answer is correct. Subtract and then check by adding: 4,585−697. 4,585 − 697 = 3,888 because 3,888 + 697 = 4,585 Subtract and then check by adding: 5,637−899. 5,637 − 899 = 4,738 because 4,738 + 899 = 5,637

As with addition, word phrases can tell us to operate on two numbers using subtraction. To translate from a word phrase to math notation, we look for key words that indicate subtraction. Some of the words that indicate subtraction are listed in . Operation Word Phrase Example Expression Subtraction minus 5 minus 1 5−1 difference the difference of 9 and 4 9−4 decreased by 7 decreased by 3 7−3 less than 5 less than 8 8−5 subtracted from 1 subtracted from 6 6−1 Translate and then simplify: ⓐ the difference of 13 and 8 ⓑ subtract 24 from 43 ⓐ The word difference tells us to subtract the two numbers. The numbers stay in the same order as in the phrase. the difference of 13 and 8 Translate. 13−8 Simplify. 5 ⓑ The words subtract from tells us to take the first number away from the second. We must be careful to get the order correct. subtract 24 from 43 Translate. 43−24 Simplify. 19 Translate and simplify: ⓐ the difference of 14 and 9 ⓑ subtract 21 from 37 ⓐ 14 − 9 = 5 ⓑ 37 − 21 = 16 Translate and simplify: ⓐ 11 decreased by 6ⓑ 18 less than 67 ⓐ 11 − 6 = 5 ⓑ 67 − 18 = 49

To solve applications with subtraction, we will use the same plan that we used with addition. First, we need to determine what we are asked to find. Then we write a phrase that gives the information to find it. We translate the phrase into math notation and then simplify to get the answer. Finally, we write a sentence to answer the question, using the appropriate units. The temperature in Chicago one morning was 73 degrees Fahrenheit. A cold front arrived and by noon the temperature was 27 degrees Fahrenheit. What was the difference between the temperature in the morning and the temperature at noon? We are asked to find the difference between the morning temperature and the noon temperature. Write a phrase. the difference of 73 and 27 Translate to math notation. Difference tells us to subtract. 73−27 Then we do the subtraction. Write a sentence to answer the question. The difference in temperatures was 46 degrees Fahrenheit. The high temperature on June1st in Boston was 77 degrees Fahrenheit, and the low temperature was 58 degrees Fahrenheit. What was the difference between the high and low temperatures? The difference is 19 degrees Fahrenheit. The weather forecast for June 2 in St Louis predicts a high temperature of 90 degrees Fahrenheit and a low of 73 degrees Fahrenheit. What is the difference between the predicted high and low temperatures? The difference is 17 degrees Fahrenheit. A washing machine is on sale for $399. Its regular price is $588. What is the difference between the regular price and the sale price? We are asked to find the difference between the regular price and the sale price. Write a phrase. the difference between 588 and 399 Translate to math notation. 588−399 Subtract. Write a sentence to answer the question. The difference between the regular price and the sale price is $189. A television set is on sale for $499. Its regular price is $648. What is the difference between the regular price and the sale price? The difference is $149. A patio set is on sale for $149. Its regular price is $285. What is the difference between the regular price and the sale price? The difference is $136. Model subtraction of two-digit whole numbers Model subtraction of three-digit whole numbers Subtract Whole Numbers

Operation Notation Expression Read as Result Subtraction − 7−3 seven minus three the difference of 7 and 3 Subtract whole numbers. Write the numbers so each place value lines up vertically. Subtract the digits in each place value. Work from right to left starting with the ones place. If the digit on top is less than the digit below, borrow as needed. Continue subtracting each place value from right to left, borrowing if needed. Check by adding.

Use Subtraction Notation In the following exercises, translate from math notation to words. 15−9 fifteen minus nine; the difference of fifteen and nine 18−16 42−35 forty-two minus thirty-five; the difference of forty-two and thirty-five 83−64 675−350 six hundred seventy-five minus three hundred fifty; the difference of six hundred seventy-five and three hundred fifty 790−525 Model Subtraction of Whole Numbers In the following exercises, model the subtraction. 5−2 8−4 6−3 7−5 18−5 19−8 17−8 17−9 35−13 32−11 61−47 55−36 Subtract Whole Numbers In the following exercises, subtract and then check by adding. 9−4 5 9−3 8−0 8 2−0 38−16 22 45−21 85−52 33 99−47 493−370 123 268−106 5,946−4,625 1,321 7,775−3,251 75−47 28 63−59 461−239 222 486−257 525−179 346 542−288 6,318−2,799 3,519 8,153−3,978 2,150−964 1,186 4,245−899 43,650−8,982 34,668 35,162−7,885 Translate Word Phrases to Algebraic Expressions In the following exercises, translate and simplify. The difference of 10 and 3 10 − 3; 7 The difference of 12 and 8 The difference of 15 and 4 15 − 4; 11 The difference of 18 and 7 Subtract 6 from 9 9 − 6; 3 Subtract 8 from 9 Subtract 28 from 75 75 − 28; 47 Subtract 59 from 81 45 decreased by 20 45 − 20; 25 37 decreased by 24 92 decreased by 67 92 − 67; 25 75 decreased by 49 12 less than 16 16 − 12; 4 15 less than 19 38 less than 61 61 − 38; 23 47 less than 62 Mixed Practice In the following exercises, simplify. 76−47 29 91−53 256−184 72 305−262 719+341 1,060 647+528 2,015−1,993 22 2,020−1,984 In the following exercises, translate and simplify. Seventy-five more than thirty-five 75 + 35; 110 Sixty more than ninety-three 13 less than 41 41 − 13; 28 28 less than 36 The difference of 100 and 76 100 − 76; 24 The difference of 1,000 and 945 Subtract Whole Numbers in Applications In the following exercises, solve. Temperature The high temperature on June 2 in Las Vegas was 80 degrees and the low temperature was 63 degrees. What was the difference between the high and low temperatures? The difference between the high and low temperature was 17 degrees Temperature The high temperature on June 1 in Phoenix was 97 degrees and the low was 73 degrees. What was the difference between the high and low temperatures? Class size Olivia’s third grade class has 35 children. Last year, her second grade class had 22 children. What is the difference between the number of children in Olivia’s third grade class and her second grade class? The difference between the third grade and second grade was 13 children. Class size There are 82 students in the school band and 46 in the school orchestra. What is the difference between the number of students in the band and the orchestra? Shopping A mountain bike is on sale for $399. Its regular price is $650. What is the difference between the regular price and the sale price? The difference between the regular price and sale price is $251. Shopping A mattress set is on sale for $755. Its regular price is $1,600. What is the difference between the regular price and the sale price? Savings John wants to buy a laptop that costs $840. He has $685 in his savings account. How much more does he need to save in order to buy the laptop? John needs to save $155 more. Banking Mason had $1,125 in his checking account. He spent $892. How much money does he have left?

Road trip Noah was driving from Philadelphia to Cincinnati, a distance of 502 miles. He drove 115 miles, stopped for gas, and then drove another 230 miles before lunch. How many more miles did he have to travel? 157 miles Test Scores Sara needs 350 points to pass her course. She scored 75,50,70,and80 on her first four tests. How many more points does Sara need to pass the course?

Explain how subtraction and addition are related. Answers may vary. How does knowing addition facts help you to subtract numbers?

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?

difference The difference is the result of subtracting two or more numbers.