Division problems ask how many copies of something we can have if we distribute a number equally. For instance, say that you bought a large pizza with 8 slices for a family of 4. To calculate how many slices each person gets, we use division:
8 / 4 = 2.
But what if there were 3 people instead? Obviously, everyone could still have two slices, but that would leave two in the box. Now, the question is whether we want to keep them for later or cut them into smaller pieces. And that's where the quotient and remainder come in handy.
As said in the above section, the result of division is called the quotient. However, not all numbers are divisible by one another (like 4 divided by 3 or 25 divided by 2). In such cases, we can distribute as much as possible until we leave the last few, the non-divisible parts: that's the remainder.
In the pizza example above, an 8-slice pizza given to 3 people gives 2 slices each with a remainder of 2. Other examples would be, say, 4 divided by 3, giving 1 with a remainder 1, or 25 divided by 2, giving 12 with a remainder 1. Symbolically, we write the result of such division in math by separating the quotient and remainder by a capital R (see below).
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8 / 3 = 2 R 2
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4 / 3 = 1 R 1
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25 / 2 = 12 R 1
We can also use this notation when the dividend in math problems is smaller than the divisor:
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2 / 3 = 0 R 2
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17 / 20 = 0 R 17
Or when the numbers are divisible by one another, like 12 divided by 4:
However, we need to be careful with remainders when dealing with negative numbers. As a rule, we define the remainder in mathematics as a positive number smaller than the absolute value of the divisor. Nevertheless, some applications (especially computer sciences) allow negative remainders. To satisfy both parties, Omni's integer division calculator presents both possibilities, and so if you use the calculator to find the quotient of, say, -4 divided by 3 or 25 divided by -2, you'll get two results:
(-4) / 3 = -1 R (-1) = -2 R 2
25 / (-2) = -13 R (-1)= -12 R 1
Lastly, let's mention that we sometimes want to tackle division problems without mentioning the remainder. If we recall the example with an 8-slice pizza for 3 people, this would mean cutting the 2 remaining slices into smaller pieces to finish it. Mathematically speaking, this translates to a fractional quotient.
8 / 3 = 2⅔ ≈ 2.666.
In essence, everyone gets two full pizza slices and another two-thirds of a slice. No remainders here. If needed, make sure to check our fraction to decimal converter.
As you can see, you can use our calculator to find the quotient, whichever form you need. Quite a tool, wouldn't you say? So let's finish off with some clear instructions on how to operate it.
Answer
Explanation
Based on the given conditions, formulate:
Multiply both sides of the equation by the common denominator:
Reduce the fraction:
Calculate the product or quotient:
Rearrange unknown terms to the left side of the equation:
Calculate the sum or difference:
get the result:
Answer:
Get the answer to your homework problem.
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We don’t have your requested question, but here is a suggested video that might help.
If the quotient of a number and 4 is added to $\frac{1}{2},$ the result is $\frac{3}{4} .$ Find the number.
X / 2 + 8 = 33 (original problem) x / 2 = 25 (subtract 8 from both sides) x = 50 (multiply both sides by 2)
Sonia P.
1 Expert Answer
We have a number that's divided by 4, and then we add 3. That totals 24. So what we need to do now is isolate n. All you need to do is first subtract 3 from both sides: All you need to do now is multiply both sides by 4 for your final answer.