PRACTICE 23 In the last practice assignment, we tried 2 numbers divided by 1 number with no leftover number. In this practice assignment we will try 2 numbers divided by 1 number with a leftover number. In long division leftover numbers are called remainders. Eample: 52 3 This question goes beyond our multiplication facts for 3 s. The highest facts we are supposed to know is 3 12 = 36. So this is clearly a long division problem. We can t solve it like this. We need to set it up using a DIVISION BOX. DIVISION BOX means sign 52 3 turns into 3 5 2 Before you begin solving the problem draw lines to separate the digits inside the division bo. This will help you see the number inside the division bo in easier to handle parts. 3 5 2
Net, write the steps on the left. 3 5 2 We begin with Ask yourself: Can the outside number (3) fit inside the first inside number (5) YES it can. So put a circle in the space on top of the division bo, above the 5. We will be putting our first answer in that circle. 3 5 2
Move on to Ask yourself: Is there a number times () 3 that equals to 5 NO there is not. Ask yourself: What number times () 3 comes closest to 5, WITHOUT GOING OVER it s 1, because 3 1 = 3. So put 1 in the circle and put the answer to 3 1 under the 5. 1 3 5 2 3 Move on to Subtract 3 from 5. Put the answer at the very bottom. 1 3 5 2 3 2
Move on to (compare) This step is used to see if your child hasn t made any mistakes before moving on. You are comparing the number outside the division bo (3) and the bottom number (2). The bottom number MUST be less than the outside number. If it is equal or greater than the outside number your child made a mistake somewhere and needs to go back and check their work. 2 IS LESS THAN 3 so I know I didn t make any mistakes, I can move on to the net step. Move on to This step can only be used if there is another number inside the division bo. If there are no more numbers inside the division bo your child does not have to do any more of the steps. For this question there IS another number inside the division bo, after the 5 it s a 2. You draw the arrow below the two and drop it down net to the bottom number. 3 1 5 2 3 2 2
Move on to Draw this step net to the 22. Have it point to the space right after the first circle on top 1 3 5 2 3 2 2 Start again with All you have to do for this step is draw a circle where the repeat arrow ends. That s it. That s all you do for the divide step! 1 3 5 2 3 2 2
Move on to Ask yourself: Is there a number times () 3 that equals to 22 NO. Ask yourself: What number times () 3 comes closest to 22, WITHOUT GOING OVER it s 7, because 3 7 = 21. So put 7 in the circle and put the answer to 3 7 under the 22. 1 7 3 5 2 3 2 2 2 1 Move on to Subtract 21 from 22 the answer is 1. 1 7 3 5 2 3 2 2 2 1 1
Move on to (compare) Remember you are comparing the outside number (3) and the bottom number (1). The bottom number MUST be less than the outside number IT IS. That means you can more on to the net step. Move on to This step can only be used if there is another number inside the division bo. If there are no more numbers inside the division bo your child does not have to do any more of the steps. THERE ARE NO MORE NUMBERS INSIDE THE DIVISION BOX AFTER THE 2. This means you are done with the steps. ONE LAST THING! Look at the bottom number. If it is a zero (0) then you have no leftovers. BUT if the bottom number is any number besides zero then you have leftovers. The number at the bottom is a 1, so you do have a leftover number for this problem. In long division leftovers are call the remainder. You write R after the answer on top of the division bo and write the bottom number net to it. 3 1 5 7 2 3 2 2 2 1 1 R 1
The Answer is 17 R1 Instructions: Answer each question to the best of your abilities. HINT: EVERY ANSWER WILL HAVE A REMAINDER (R). 1. 55 3 = 2. 76 5 = 3. 69 4 = 4. 88 7 = 5. 83 5 = 6. 95 6 = Instructions: For these division problems there will be NO REMAINDER (R). 7. 84 6 = 8. 78 3 = 9. Turn the following picture into a division problem. The Answer is
10. Create the fact families for the following numbers. 8 6 48 *Etra Work Never Hurt Anyone* 11. What is the COMBINED AREA of the two following polygons? 15 cm 6 cm 7 cm The Combined Area is 12. Arturo measured the heights of three classmates in centimeters (cm). Charlie is 146 cm tall. Gertrude is 150 cm tall. Isaac is 149 cm tall. Arturo s teacher asks him for the best estimate of the combined heights of all three classmates. What will be Arturo s answer? The Answer is 13. 4,001,832 2,654,037 =
14. Erin won 20 tickets to the circus. She keeps 2 tickets for herself. The remaining tickets she plans to give to her 3 cousins. If each cousin gets the same number of tickets how many tickets will each cousin get? Each cousin will get tickets. 15. What is the decimal, fraction, and word form? The Decimal Form is The Fraction Form is The Word Form is
A N S W E R S Instructions: Answer each question to the best of your abilities. HINT: EVERY ANSWER WILL HAVE A REMAINDER (R). 1. 55 3 = 18 R1 1 8 3 5 5 3 2 5 2 4 1 R 1 2. 76 5 = 15 R 1 1 5 5 7 6 5 2 6 2 5 1 R 1
3. 69 4 = 17 R 1 1 7 4 6 9 4 2 9 2 8 1 R 1 4. 88 7 = 12 R 4 1 2 7 8 8 7 1 8 1 4 4 R 4
5. 83 5 = 16 R 3 1 6 5 8 3 5 3 3 3 0 3 R 3 6. 95 6 = 15 R 5 1 5 6 9 5 6 3 5 3 0 5 R 5
Instructions: For these division problems there will be NO REMAINDER (R). 7. 84 6 = 14 1 4 6 8 4 6 2 4 2 4 0 8. 78 3 = 26 2 6 3 7 8 6 1 8 1 8 0
9. Turn the following picture into a division problem. How many total stars do you have? 6 How many groups do you have? 3 How many stars are in each group? 2 The Answer is 6 3 = 2
10. Create the fact families for the following numbers. 8 6 48 You will use the numbers given to create 2 multiplication and 2 division problems (UNLESS you have the same number twice then it will only be 1 multiplication and 1 division problem). The largest number goes on the answer side for multiplication. For division the largest number is the first number you write down on the problem. 8 6 = 48 6 8 = 48 48 8 = 6 48 8 = 6
*Etra Work Never Hurt Anyone* 11. What is the COMBINED AREA of the two following polygons? 15 cm 6 cm 7 cm Area takes two sides and multiplies them together. The formula for area is LENGTH WIDTH. The rectangle has given you one long side (15 cm) and one short side (6). All you need to do is multiply these numbers together. tens +3 1 5 ones 6 9 0 Move on the square. It is only showing you the length of one side. But you need two sides, what do you do?? We know that all sides on a square are the SAME LENGTH. So every side is 7
cm. We only need two of those 7 s to multiply together to find the AREA. 7 7 = 49 One last step. The word COMBINED means take the two answers and add them together. That will be your final answer. 90 + 17 = 107 The Combined Area is 107
12. Arturo measured the heights of three classmates in centimeters (cm). Charlie is 146 cm tall. Gertrude is 150 cm tall. Isaac is 149 cm tall. Arturo s teacher asks him for the best estimate of the combined heights of all three classmates. What will be Arturo s answer? Best estimate means ROUND. We will be using all three numbers. We need to round them first. The question does not tell you what to round to (tens place, hundreds place, or one thousands place) so what do you do?? Round ALL the numbers to the highest place value they have in common. hundreds tens ones 1 4 6 1 5 0 1 4 9 The HUNDREDS PLACE is the highest place value all the numbers have in common. So, round each number to the hundreds place. If your child does not have a method for rounding they can use my ROUNDING RAP found on my web page.
1 4 6 1 0 0 1 5 0 2 0 0 1 4 9 1 0 0 The question asked for the COMBINED heights. Combined is usually a clue for addition. So, add all the rounded numbers to get your final answer. 1 0 0 2 0 0 + 1 0 0 4 0 0 The Answer is 4 0 0 13. 4,001,832 2,654,037 = 1, 3 4 7, 7 9 5 9 9 12 3 10 10 11 7 2 12 4, 0 0 1, 8 3 2 2, 6 5 4, 0 3 7 1, 3 4 7, 7 9 5
14. Erin won 20 tickets to the circus. She keeps 2 tickets for herself. The remaining tickets she plans to give to her 3 cousins. If each cousin gets the same number of tickets how many tickets will each cousin get? This is a multiple step question (a perfect eample of what to epect on the STAAR Test). First, subtract 20 and 2 to find out how many tickets Erin is giving her cousins. 20 2 = 18 Second, the phrase same number is used. That usually is a hint for division. Take 18 and divide it by 3 (number of cousins). 18 3 = 6 Each cousin will get 6 tickets. 15. What is the decimal, fraction, and word form? This is a TENTHS MODEL. How do I know? Because it has ten pieces. Let s start with the decimal. The entire model is not colored in so start with a 0. Tenths models only have one number after the decimal. That number is the colored pieces in the picture 2.
The Decimal Form is 0.2 Moving on to the fraction. There are no entire rectangles all colored in so there will not be a BIG whole number net to the fraction. The numerator (top number) is the number of colored pieces 2, and the denominator (bottom number) is the total number of pieces for the entire rectangle (both colored and white) 10. The Fraction Form is 2/10 Finally the word form. Look at the decimal answer 0.2 You do not say Zero and two tenths. A zero (0) on the left of the decimal is not written as words. You also don t say and because of that zero. You say the number on the right of the decimal two The model once again has ten pieces so that makes it a TENTHS MODEL so you wrap it up by saying tenths The Word Form is two tenths