Houghton Mifflin Math: Grade 4

Math Background

Adjusting the Quotient: When Students Ask

  • What are the different ways to divide?
    You can use many different strategies to find the answer to a division problem. One strategy is to use repeated subtraction. To find 123 ÷ 36, think: How many groups of 36 are there in 123? Start with 123. Subtract 36 repeatedly. Count how many times you subtracted: 123 − 36 = 87 (1); 87 − 36 = 51 (2); 51 − 36 = 15 (3); 15 < 36. There are 3 groups of 36 in 123 with 15 left over. Therefore, 123 ÷ 36 = 3 R15.

    Another strategy is to use what is sometimes called long division. The algorithm for long division is estimate, multiply, subtract, bring down, and repeat as needed. To find 123 ÷ 36, start with the estimate 120 ÷ 40 = 3. Then use this estimate to help you place the first digit in the quotient of the division algorithm.

    width=”93″ height=”71″ alt=”long division: 123 divided by 36 = 3 with a remainder of 15″ />

    One other way to divide is to use what is sometimes called short division. This method is very useful when dividing by a one-digit number. The short division method requires you to do the estimation, multiplication, and subtraction steps mentally.

    short division: 1,378 divided by 3. first position 13 divided by 3 = 4 with a remainder of 1

    Think: 13 ÷ 3 = 4; 4 × 3 = 12; 13 – 12 = 1

    Place the 1 next to the 7.

    short division: 1,378 divided by 3. second position 17 divided by 3 = 5 with a remainder of 2

    Think: 17 ÷ 3 = 5; 5 × 3 = 15; 17 – 15 = 2

    Place the 1 next to the 7.

    short division: 1,378 divided by 3. third position 28 divided by 3 = 9 with a remainder of 2

    Think: 28 ÷ 3 = 9; 9 × 3 = 27; 28 – 27 = 1

    Place the 1 next to the 7.

  • How do I know where to place the first digit in the quotient?
    There are a couple of ways to decide where to place the first digit in the quotient. You can use an estimate. To find 389 ÷ 19, first estimate 400 ÷ 20 = 20. Knowing that 389 ÷ 19 is about 20, or 2 tens, helps you know where to place the first digit when finding the actual quotient.

    400 ÷ 20 = 20

    So, 389 ÷ 19 us about 20, or 2 tens.

    short division: 389 divided by 19.

    The first digit in the quotient should be placed above the 8 in 389.

    Another way to decide where to place the first digit is to make some comparisons.

    389 divided by 19 with the 19 and the 3 highlighted in red 19 > 3. There are not enough hundreds.
    389 divided by 19 with the 19 and the 3 and 8 highlighted in red 19 < 38. There are not enough tens.
  • Place the first digit of the quotient, 2, in the tens place.
  • How can I check my answer in division?
    If you multiply the divisor by the quotient and then add the remainder, the result should equal the dividend. You can do this with paper and pencil or with a calculator. For example: 231 ÷ 6 = 38R3; 6 x 38 = 228 and 228 + 3 = 231.

    You can also use a calculator to divide, then you can compare the two answers. However, you must remember that quotients are given only in decimal form on most calculators. Therefore, you must multiply the whole number portion of the quotient by the divisor, take that answer and subtract it from the dividend to get the correct remainder. For example: 231 ÷ 6 = 38.5; 38 x 6 = 228 and 231 − 228 = 3; therefore 231 ÷ 6 = 38.5, is the same as 231 ÷ 6 = 38 R3.

  • How can I decide whether the number I choose for the first digit in the quotient needs to be greater or lesser?
    When the number being subtracted is greater than the number being subtracted from, adjust the quotient to a lesser number. When the answer to the subtraction is greater than the divisor, adjust the quotient to a greater number.


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How do you check the quotient from a division problem?


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Do it backwards. Multiply the quotient by the divisor. If that total equals the dividend, the original problem was correct.
36 divided by 9 = 4
4 times 9 = 36

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found this useful

Why can you write a division problem as a fraction?

when you are writing a division problem as a fraction u take the remainder of your problem and make it the numerator and make the number you are dividing by the denominator

10 long division problems?

divison is when you basicly want to make an number smaller by cuting it into equal parts.

Check for correctness in division math?

ok well here’s the thing all u need to do is divide the quotient(the ancwer) multiplied by the divisor(multiplied by the number ur dividing with)it should give u the divident.(divident=the biger number u are dividing).
are u doing long division or short? well…i will write both..
short division t (MORE)

In a division problem what is the number into which the diviser goes?

If you have a dividing box thingy, the divisor is on the outside and the dividend is in the inside..
Or like.
in the expression = 7, 2 is the divisor.

What is a problem that is solved by interpreting a quotient in division?

Tina needs 36 flowers for her next project. The flowers are sold in bunches of 5. How many bunches will she need?.

How can you check if a number is divisible by 6?

To check for divisibility by 6 you need to check for divisibility by 2 and by 3. Divisibility by 2: If the number ends with a 0, 2, 4, 6 or 8 it is divisible by 2. If it is not then it is not divisible by 2 and so cannot be divisible by 6. Divisibility by 6: If the digital root is divisible by (MORE)

Explain how to check the quotient from a division problem?

You multiply the http://wiki.answers.com/Q/How_do_you_check_the_quotient_from_a_division_problem# my the divisor. If it equals the quoitent you are right. If your problem has a remainder then after multipling the dividend by the divisor, you add the remainder. For example… if you had 100/2(100 d (MORE)

What is the answer to division problems?

A division is a dividend divided by the divisor to give the quotient ; this is written as: quotient = dividend ÷ divisor .
A division can also be expressed as the divisor divided into a dividend to give the quotient ; this is written as: …………….. quotient …. (MORE)

The sum is 20 the quotient is 9 how do you work that problem?

The question is looking for 2 numbers that satisfy both expressions. Try using trial and error. What number sums equal 20? 1+19, 2+18, 3+17 etc. What is the quotient of each set of numbers? 19/1=19, 18/2=9 Your answer is 18 and 2 because it satisfies both expressions. 18+2=20 and 18/2=9.

How do you check a division problem?

Multiply the answer to the problem by the number that you are dividing by. (e.g. 18/2=9 Check it with 9*2=18).

In a division problem what happens to the quotient when the dividend increases?

help me people i need to know for homework please help me with this question please answer this question so i can be done with homework and be free please please please please please please please please please please please please please please please please please. 😀

What is the quotient in division?

The quotient is the answer to a division problem. For example, in 8 divided by 2 = 4, the quotient is 4. angle2222222:it is the answer to the division qeusiton

How do you check if division answer is right?

Take the answer of the division problem and multiply it by one of the numbers. It should equal the OTHER number..
a/b = c.
c * b = a OR c * a = b

If a division answer is a quotient then what is a multiplication answer?

The result of multiplication is the ” product “, regardless of what the result of division is called.

What is three plus the quotient of eight and four written as a problem?

(8/4) + 3=5 .
Another answer: .
above is incorrect. it would be 3+ (8*4)

Explain how to check a division problem when it has a remainder?

Multiply the quotient times the dividend and then add on the remainder to the product.

What is a long division problem that has a 2 digit divisor a five digit divedend and a quotient of 308?

There are a huge number of answers to that question. Here are a few: .
10,164 divided by 33 = 308 .
15,092 divided by 49 = 308 .
16,632 divided by 54 = 308 .
21,252 divided by 69 = 308 .
23,100 divided by 75 = 308 .
25,564 divided by 83 = 308 .
30,492 divided by 99 = 308

How do you check the quotient from a multiplication problem?

When numbers are divided, the result is called the quotient. When numbers are multiplied, the result is called the product. To check the result of a multiplication problem, divide the result (the product) by one of the multipliers. The quotient will be the other multiplier. EXAMPLE : To verify tha (MORE)

How can you use multiplication to check if a quotient is correct?

If you multiply the divisor by the quotient you should get the original number. For example, if I want to check 10/2 =5. I multiply the divisor 2 by the quotient 5 and check to see if it gives me back my original number, 10. 2*5 =10 so 5 was the correct quotient. Alternatively if you divide the o (MORE)

What websites answer division problems?

We don’t give out website on this website. But you can ask for answers to division problems here and also askfor explanations for how they were done.

How can you use multiplication to check a quotient?

For example: 28 divided by 4 You think the answer is 7. Use multiplication to check. Use the quotient (7) and multiply with the divisor (4 the one outside of the house. 7 x 4 = 28. The quotient 7 is correct.

In complete division divisor and quotient are of dividend.?

Divisor is the number you’re dividing (the number on top). Dividend is the number it’s being divided by (the number on the bottom) The quotient is the answer.

What are the problems in division?

The biggest problem in division comes with computers. Most of us have probably experienced programs malfunctioning or even crashing due to “Divide by zero error” even though this error message might not be presented. We can not divide any number with zero. A second “problem” is division where (MORE)

How to check division problems?

Work backwards with multiplication. For example 15 divided by 5 = 3 so… multiply 3 time 5 if it = the first number, then BINGO

Why is division used to solve a problem?

Division is used to find out how many times a caeratin quantity, goes into another quantity. It is basically the opposite of multiplication. It is to find the second quantity, that when multiplied by the first, would give you the total quantity. Hope that helps!

How do you check addition with division?

You don’t. You can check addition with subtraction or subtraction with addition, since subtraction is the opposite of addition. Similary, you can check division with multiplication, or vice versa.

How do you do partial quotients for division for fifth grade?

to do this is that you do the simple steps for example divide mulitiply subtract bring down

How do you check the answer to a decimal division question?

Multiply the quotient by the divisor to result in the dividend. If dividend/divisor=quotient, then dividend=quotient x divisor

How can you use addition to check division?

Well, the normal way to check a division problem is with multiplication… if you divide 21 by 7 and come up with three, then you check that by multiplying 7 and 3, to get 21. But if you’re on an abacus or something, I suppose you could say, “I came up with a result of three, which means three seven (MORE)

Why can you use multiplication to check your answ er to a division problem?

Because – if you multiply your answer by one of the original numbers you should get the other number. For example – take the sum 1024 divided by 64 – The answer is 16. You can confirm that by multiplying 16 by 64, and you get the original number 1024

What is a remainder and how are they used in division problem?

If you are talking about a remainder its like whats left over after a problem for ex.l f divided by 2 equels 2 because 2×2 =4 and we are trying to get to 5 so the awnser is 2 remainder 1 because there is 1 left over so the awnser should like lile 2R1

How can you use multiplication to check quotient?

You can use multiplication to check a quotient because, if you think about it, division is like algebra with multiplication. Lets say you have the problem 49/7 49/7 is 7, right? So you check by taking the answer (7) and the divisor (7) and multiply it to check. Does 7×7=49? Yes, it does! The (MORE)

What is the names of the numbers in a division problem?

example 32/4=8 32 is the dividend / is the division symbol 4 is the divisor 8 is the answer or the quotient

Why you can use multiplication to check a division problem?

multiplication is the Inverseoperation .
of division so it could be used to check my work

Do you have to check if 221 is divisible by 6?

It is easy to see if 221 is divisible by 6. The number 6 is even and 221 is not. An even number cannot evenly divide an odd number . You get: 36.8333333… recurring A handy rule is: Any number is divisible by 6 if it is divisible by both 2 and 3.

How do you find the quotient and then check your answer?

quotient is the answer to a division problem so after dividing, to check your answer, you need to take the quotient and multiply it to one of the given numbers.

How do you check the problem to a division problem?

Multiply the answer to the problem by the number that you are dividing by. (e.g. 18/2=9 Check it with 9*2=18)

How do you check if a number is divisible by 88?

If a number is divisible by both 8 and 11, it will be divisible by 88.

Why is the answer for a division problem a quotient?

The word “quotient” comes from the Latin quotiens whichmeans “how many times” and indicates how many times a number goesinto another.

How do you check the correctness of a division answer that has no remainder?

a/b=c, if and only if c*b=a. This means that if some number, which is represented here by a, is divided by some other number, which is represented here by b, to get a quotient, which is represented here by c, then c multiplied by b should equal a. Using the correct terms for a division, the quotie (MORE)

How can you estimate the quotient help you check your answer for reasonableness?

Suppose at some point in your life you wanted to know the answer of 29 divided by 14. If you can estimate in your head that 30 divided by 15 is 2, you would expect the answer to be somewhere around two. Since 14 is a little less than half, you would expect the answer to be a little bit more than two (MORE)

How can you use mutiplication to check quotient?

To use multiplication to check the quotient, you multiply the quotient by the divisor given! For instance: 6 / 2 = 3 Then, to check that 3 is the quotient of 6 and 2, multiply 3 by 2 to get 3 x 2 = 6.

What is the quotient of 3 division by 24 is?

A quotient is the number of times a lesser number can go into a larger number. Therefore, 24 / 3 = 8 (giving 8 as the quotient).

How can you use multiplication to check a division?

Always remember that multiplication is the inverse/opposite of division, so they can be used to check each other. For example: Let’s say the problem is 120 / 6. Whatever you think is your answer, you can multiple by 6 and that result should be 120. Is 120 / 6 = 10? No. The quick check is 10 * (MORE)

How do you check the answer to a division question?

To check the answer to a division question, multply the divisor(the number that is being divided into the dividend) and thequotient (the answer). If there is a remainder, add the remainderto the answer. If the number matches the dividend, your answer tothe division problem is correct.

How do you get a formula when checking a division problem?

You use the second number of the dividend and divide it by youamount of numbers in your divisor

How do you check multiplication using division?

You could divide the answer into the larger number of the problem.The answer should be the remaining number (multiplicand).

How do you check the correctness of a division answer that has no reminder?

Divisions will not have a remainder if the divisor is a factor ofthe number. eg 6/2=3

How use multiplication to check the answer to a division problem?

Dividend divided by divisor equals quotient. If you multiply the quotient by the divisor, you should get thedividend. 18/9 = 2 2 x 9 = 18 Just reverse your steps.

Is quotient a division word or a multiplication word?

It is a division word. The quotient is the result you get when youdivide a number (dividend) by another number (divisor).
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    Kids Math

    Division Basics

    What is division?



    Division is breaking a number up into an equal number of parts.



    Example:



    20 divided by 4 = ?



    If you take 20 things and put them into four equal sized groups, there will be 5 things in each group. The answer is 5.







    20 divided by 4 = 5.



    Signs for Division



    There are a number of signs that people may use to indicate division. The most common one is ÷, but the backslash / is also used. Sometimes people will write one number on top of another with a line between them. This is also called a fraction.



    Example signs for “a divided by b”:



    a ÷ b

    a/b

    a

    b


    Dividend, Divisor, and Quotient



    Each part of a division equation has a name. The three main names are the dividend, the divisor, and the quotient.

    • Dividend – The dividend is the number you are dividing up
    • Divisor – The divisor is the number you are dividing by
    • Quotient – The quotient is the answer

    Dividend ÷ Divisor = Quotient



    Example:



    In the problem 20 ÷ 4 = 5



    Dividend = 20

    Divisor = 4

    Quotient = 5



    Special Cases



    There are three special cases to consider when dividing.



    1) Dividing by 1: When dividing something by 1, the answer is the original number. In other words, if the divisor is 1 then the quotient equals the dividend.



    Examples:



    20 ÷ 1 = 20

    14.7 ÷ 1 = 14.7



    2) Dividing by 0: You cannot divide a number by 0. The answer to this question is undefined.



    3) Dividend equals Divisor: If the dividend and the divisor are the same number (and not 0), then the answer is always 1.



    Examples:



    20 ÷ 20 = 1

    14.7 ÷ 14.7 = 1


    Remainder



    If the answer to a division problem is not a whole number, the “leftovers” are called the remainder.



    For example, if you were to try and divide 20 by 3 you would discover that 3 does not divide evenly into 20. The closest numbers to 20 that 3 can divide into are 18 and 21. You pick the closest number that 3 divides into that is smaller than 20. That is 18.



    18 divided by 3 = 6, but there are still some leftovers. 20 -18 = 2. There are 2 remaining.



    We write the remainder after an “r” in the answer.



    20 ÷ 3 = 6 r 2



    Examples:



    12 ÷ 5 = 2 r 2

    23 ÷ 4 = 5 r 3

    18 ÷ 7 = 2 r 4



    Division is the Opposite of Multiplication



    Another way to think of division is as the opposite of multiplication. Taking the first example on this page:



    20 ÷ 4 = 5



    You can do the reverse, replacing the = with a x sign and the ÷ with an equal sign:



    5 x 4 = 20



    Examples:



    12 ÷ 4 = 3

    3 x 4 = 12



    21 ÷ 3 = 7

    7 x 3 = 21



    Using multiplication is a great way to check your division work and get better scores on your math tests!



    Advanced Kids Math Subjects


    Multiplication

    Intro to Multiplication

    Long Multiplication

    Multiplication Tips and Tricks



    Division

    Intro to Division

    Long Division

    Division Tips and Tricks



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    Equivalent Fractions

    Simplifying and Reducing Fractions

    Adding and Subtracting Fractions

    Multiplying and Dividing Fractions



    Decimals

    Decimals Place Value

    Adding and Subtracting Decimals

    Multiplying and Dividing Decimals

    Statistics

    Mean, Median, Mode, and Range

    Picture Graphs



    Algebra

    Order of Operations

    Exponents

    Ratios

    Ratios, Fractions, and Percentages



    Geometry

    Polygons

    Quadrilaterals

    Triangles

    Pythagorean Theorem

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    Misc

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    Roman Numerals

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