Using Patterns to Divide

Transcription

1 Using Patterns to Divide 4-1 You can use division basic facts and patterns with zeros to help you divide. 560 people are coming to Sen s parents anniversary party. Each table seats 8 people. How many tables does Sen need? 4-1 You already know the basic fact Since 560 = 56 tens using zero patterns, 56 tens 8 7 tens or 70. So, Sen needs 70 tables for the guests at his parents anniversary party. In 1 through 9, find each quotient. Use mental math = = 3. 2,400 4 = 4. 1,500 5 = 5. 30, = 6. 18,000 2 = 7. 2, = , = 9. 21, = 10. Reasoning How is the number of zeros in the quotient in related to the number of zeros in the dividend? 32 Topic 4

2 Estimating Quotients 4-2 You can estimate quotients by using compatible numbers. Carly picked 738 peaches off her peach tree. She filled 9 baskets with peaches. If each basket holds the same amount, about how many peaches are in each basket? Estimate Find a compatible number for 738, and then divide So there are about 80 peaches in each basket. Another compatible number set you could use is: So there are about 70 peaches in each basket. In both cases the estimate is less than the actual answer because the compatible numbers are less than 738. You know that the actual number of peaches in each basket will be greater than 70 or 80. For questions 1 6, estimate the quotients using compatible numbers , , , Number Sense 7. If you estimate by using , is 50 greater than or less than the exact answer? How did you decide? Is 50 an overestimate or an underestimate? 8. Weston s book has 427 pages. He reads 17 pages each night. About how long will it take Weston to finish his book? 38 Topic 4

3 Connecting Models and Symbols 4-3 Divide 138 equally into 3 groups. 4-3 Step 1: You can model 138 as 13 groups of 10 plus 8 ones , so each group will get 4 groups of , so there is 1 group of 10 left. What You Think What You Write Step 2: There is 1 group of 10 plus 1 group of 8 ones left , so each group will also get 6 ones. There is nothing left. What You Think What You Write Use models to help you divide Algebra If n 3 57, what is the value of n? 44 Topic 4

4 Dividing by 1-Digit Divisors 4-4 You can use your basic division facts to divide greater numbers. Find Step 1: Estimate the quotient in order to find out how many digits the quotient will have. Step 2: Divide the tens by the divisor So, the quotient will have 2 digits. Step 3: Bring down the ones digit and continue dividing Step 4: Check your answer by multiplying subtract: 6 4 compare: 2 4 So, subtract: compare: 0 4 In 1 through 6, find the quotient. Check your answer by multiplying Jin has 774 pennies in his collection. He has his collection stored in 9 coin books. How many pennies are in each book? 50 Topic 4

5 Zeros in the Quotient 4-5 Sometimes when you divide you will need to use a zero in the quotient as a placeholder. Find 1, Step 1: Estimate your quotient to see where to place the first digit in the quotient. 1, So, the first digit will be in the hundreds place. Step 2: Divide the hundreds subtract: compare: Step 3: Bring down the tens digit and divide You cannot divide 6 into 4. To continue dividing, you need to bring down the ones digit. But you need to use a zero as the placeholder for the tens place in the quotient. Step 5: Check by multiplying ,842 So, 1, Step 4: Bring down the ones digit and divide subtract: compare: 0 6 Tip: Whenever you have a section you cannot divide because the digit is less than the divisor, use a zero as a placeholder in the quotient. Bring down the next digit and continue dividing. In 1 through 3, find each quotient , , , Estimation Valley School District received 3,240 text books. An equal number of books must go to each of the 6 high schools in the district. About how many books will each high school receive? 56 Topic 4

6 Dividing by 2-Digit Divisors 4-6 A roller coaster train holds 42 people. How many times must it run so that 354 people can ride? Find Step 1: Estimate your quotient to decide where the first digit the quotient should be placed = 7 So, the quotient will start in the ones place. Step 2: Divide the ones. Multiply and subtract Try the number from the estimate compare: 60 is NOT 42 so you need to increase the number in the quotient compare: Step 3: Since 18 42, you cannot divide anymore. This number is the remainder. 8 R In order for everyone to ride the roller coaster, the train will have to go 9 times because after 8 times, there are still 18 people left in line. In 1 through 3, find the quotient. Check by multiplying On Thursday, an apple farmer produced 515 oz of apple juice. How many 64-oz cartons were filled? How many ounces of juice were left over? 62 Topic 4

7 More Dividing by 2-Digit Quotients 4-7 You can divide larger numbers using the same steps you used to divide smaller numbers. Find Step 1: Estimate to decide where to put the first digit in the quotient = 70 So, the first digit in the quotient will be in the tens place. Step 2: Divide the tens. Multiply and subtract Remember: Sometimes you will need to adjust your estimated quotient numbers. Step 4: Check your answer by multiplying. 4-7 Step 3: Bring down the ones and continue dividing. 53 R This is your remainder In 1 through 3, copy and complete So, R R R 34 2, R 51 8, The Mystic Marble Company manufactures 743 marbles in one hour. The marble bags the company sells each hold 24 marbles. How many bags are filled in one hour? How many marbles are left over? 68 Topic 4

8 Estimating and Dividing with Greater Numbers 4-8 You can estimate the quotients of greater numbers by rounding the numbers you are dividing. Then use your estimate to check the reasonableness of the exact quotient. Estimate Then solve for the exact quotient. Check your answer by multiplying. Step 1. Round 794 up to 800. Round 46 up to 50. The quotient of Step 2. Divide the tens. 1 Divide Multiply. 46 Subtract. 33 Compare: Step 3. Divide the ones. 17 Bring down Divide. 46 Multiply. 334 Subtract. 322 Compare: Step 4. Check your answer by multiplying Then, add the remainder Find each quotient and remainder if any. Check your answer by multiplying , , , , , , Sandra has been collecting pennies to give to her grandchildren. She has 5,697 pennies. How many pennies will each of her 15 grandchildren receive if they each get the same amount? How many pennies will Sandra have left to start a new collection? 74 Topic 4

9 Problem Solving: Draw a Picture and Write an Equation 4-9 Doug needs to paint 2,472 boards for his fence building company. Using a power spray, he can paint 206 boards in a day. How many days will it take to paint all the boards? x 2, , , x 412 x 12 0 So, it will take Doug 12 days to paint all the boards. In 1 and 2, draw a picture, write an equation, and solve. 1. Using the boards he painted, Doug can install 7 fences. How many boards are in each fence? Are they any boards left over? Doug made $3,770 installing the 7 fences. He got paid a flat rate per fence plus $95 travel expenses for driving to the different locations. How much was the flat rate Doug was paid per fence? 80 Topic 4