Core Focus on Decimals & Fractions Lesson 2.4

Warm-Up ÷ 6 = ÷ 4 = 3. Karina made 293 cookies for a sale. She put 8 cookies on each plate. How many plates did she use? How many cookies were left over? 4. Gordon worked 621 hours in the last six months. He worked the same number of hours each month. How many hours did he work each month? R1 36 plates, 5 cookies left over

Dividing by 2-digit Numbers Find quotients of expressions where whole numbers are divided by multi- digit whole numbers, including remainders. Lesson 2.4

For her club fundraiser, Stacy has to sell magazines. Each magazine subscription costs a different amount. Stacy has a goal of selling at least 80 subscriptions for her club. Famous - $13 per year subscriptionWorking with Wood - $11 per year subscription Sports For All - $20 per year subscription Scrapbooking Ideas - $15 per year subscription Stacy made $273 by selling subscriptions to Famous. How many subscriptions did she sell of this magazine? Sean, Mia, Jabar and Angelina chose four different ways to solve this problem. The next slides show tables that give the four solution strategies. Use these tables to complete the steps: Step 1Which method do you like best? Why? Step 2Here are the total amounts Stacy made for each magazine title. Choose a method shown on the next slides. Use the method to figure out how many of each subscription Stacy sold. a.Sports for All: $520 b.Working with Wood: $154 c.Scrapbooking Ideas: $285 Step 3Did Stacy sell enough subscriptions to meet her goal? Support your answer with words and/or symbols.

Estimate & GuessSubtraction Sean chose a number to multiply by  5 = 65 He could subtract that from – 65 = 208 He was still left with a large number so he tried a larger estimate, 13  10 = 130, and subtracted this from 208: 208 – 130 = 78. He saw that 78 is not much more than 65 so he tried 13  6 = 78 and subtracted this: 78 – 78 = 0 He added all the factors he had multiplied by 13: = 21 Mia chose to subtract 13 until she got to 0. She counted how many 13s she subtracted. Stacy sold 21 subscriptions to Famous. 273 – – – – – – – – – – – – – – – – – – – – – 13 0

AdditionStandard Algorithm Angelina chose to use the standard algorithm: Stacy sold 21 subscriptions to Famous.

Example 1 What is the quotient of 168 ÷ 12 ? Divide: There are no full groups of 12 in the number 1. Put a 0 over the 1 in the quotient. There is a full group of 12 in the number 16. Multiply: 12 × 1 = 12 (closest number to 16). Write the factor (1) in the quotient above the 6 (tens place). Write the product (12) below the 16. Subtract: 16 – 12 = 4. Write this difference under the 12. DIVIDE – MULTIPLY – SUBTRACT – DROP DOWN – REPEAT –

Example 1 Continued… What is the quotient of 168 ÷ 12 ? Drop Down: Bring the next number (8) in the dividend down to the right of the partial difference in the ones column. Repeat: 1.Divide 48 by Multiply 4 × 12 = 48. The factor (4) goes in the quotient above the 8 (ones column). 3.Subtract the product from 48. (48 − 48 = 0) 4.Drop Down: Nothing to drop down from dividend. Answer: 168 ÷ 12 = 14 DIVIDE – MULTIPLY – SUBTRACT – DROP DOWN – REPEAT – – Always check your answer by using multiplication. If 168  12 = 14, then 14  12 = 168.

Example 2 A bolt of fabric measured 1,380 inches in length. The seamstress wants to cut it into 16 equal pieces for her students. How long will each piece be? – Divide: There are no full groups of 16 in the number 1. Put a 0 over the 1 in the quotient. There are no full groups of 16 in the number 13. Put a 0 over the 3 in the quotient. There are full groups of 16 in the number 138. Multiply: 16 × 8 = 128 (closest number to 138). Write the factor (8) in the quotient above the 8 (tens place). Write the product (128) below the 138. Subtract: 138 – 128 = 10. Write this difference under the 138. Drop Down: Bring the next number (0) in the dividend down to the right of the partial difference

Repeat: 1.Divide 100 by Multiply 16 × 6 = 96. The factor (6) goes in the quotient above the 0 (ones column). 3.Subtract the answer from 100. (100 − 96 = 4) 4. Drop Down: Nothing to drop down from dividend. Write the remainder as a fraction after the whole number part of the quotient. The seamstress cut each piece 86 inches long. Example 2 Continued… A bolt of fabric measured 1,380 inches in length. The seamstress wants to cut it into 16 equal pieces for her students. How long will each piece be? – – Always check your answer by using multiplication. If 1380  16 = 86, then 86  = 1380.

Communication Prompt What do you find most challenging about dividing numbers by 2-digit divisors?

Exit Problems 1.What is 897 ÷ 39? 2.A DVD company has 987 DVDs to box and ship. Each box holds 22 DVDs. a.How many boxes do they need? b.How many DVDs were left over? boxes 19 DVDs