Tag Archives: Subtracting
When it comes to performance of mental math subtraction, excelling is not a matter of chance but rather of choice. The student must aspire to be good at it and find means through which to achieve this end. There are simple things which if overlooked can derail you from this goal and by exploring them; it becomes easy to learn how to solve these equations. Almost all errors that occur in subtraction involve the step where one has to borrow and carry digits. As such, if these mistakes are to be completely eliminated, then the aspect of borrowing and carrying has to be completed eliminated.
Zero is the easiest number to subtract is the easiest number to subtract. This is for the simple reason it does not require borrowing. As such, when carrying out mental math subtraction, it is advisable to end the second number with a zero. Consider the following examples:
- If 2 is added to 28, the answer is 30. Subtracting 30 from 53 mentally is also easy. The answer is 23. However, this has 2 units that are too small and as such, implies that more has been taken away from the problem.
- To compensate on this, the 2 should be added to the answer. Therefore that will be 23 + 2 = 25
- As such, to ensure that 53-28 is carried out efficiently mentally the equation should be 53 – 30 + 2 =25.
Though there are students who might find this hard, the algebra behind it is quiet simple and straightforward. One should start with a – b then proceed to add another number n to the b which gives translates to a -b +n. this therefore means that the number is large by the n fraction. To compensate for this, one has to subtract n from the final answer and this delivers an equation like this: (a – b + n) – n. Note that n – n = 0. As such, this means that the mental math subtraction was carried out without necessarily having to borrow.
By using this method, 90% of the subtractions you have to deal with mentally are solved and needless to say with so much ease. This is especially true when handling some of those small subtractions that people come across on a daily basis. Though this is the case, it is important to state that for other complex subtractions, it might be considered efficient to use borrowing and carrying techniques.
All students need the ability to mentally calculate math because it is important for them, especially so for those students who are blind or visually impaired. Quite a number of strategies in the calculation of mental math are available and students can learn this starting from when they begin to count and deal with simple numbers. One of the most important things for the students to understand before they start manipulating these numbers in their minds is the concept of complements. These complements also known as partners of numbers are useful in aspects such as addition, subtraction, multiplication and division.
There are four basic approaches that teachers can use to help the students get the mental math strategies. One of these is decomposing numbers, which involves breaking down of different numbers into simple units that can be easily recomposed. The other approaches is making numbers easier to work with, substituting numbers and compensating.
When it comes to addition, the students can use some of the strategies such as adjusting numbers to make it easier for them to add. When handling large numbers, the students can simplify their addition by adding tens’ first, hundreds next and so on. They can also use the additive principle, doubles and facts for numbers that are up to 10 as well as derive other facts from these additions, for example, 3+2 is 1 less from 3+3. In adding nine, the students need to keep in mind that the digit of the sum is one less from the value of the number added to it.
In subtraction, there are a number of strategies that students can use. Using the concept of complements, they can start subtracting the partners of numbers up to 10; continue to numbers from 20 and subtracting two digit numbers from 100 before moving to other larger numbers. The other strategy is to subtract numbers from smaller units that are closer to the subtrahend and then adding the remaining portion, for example, 9-3 can be done as 9-6 then adding the remainder, which is 3.
For multiplication, children will need to know that multiplication is continued addition and use this concept in finding answers. Associative properties of the factors in this calculation and the doubles are also important. Division requires the concept of partners. The students will also be required to deal with larger units within the factors and add the progressive products. These concepts are very useful in ensuring that the students find their way around mental math.