Math problems involving addition, subtraction, multiplication, and division of whole numbers are much easier to compute compared to fractions, decimals, and radicals. Whole numbers start from zero to infinity, with no fractions and decimals. They are sometimes called natural numbers. Counting numbers are also whole numbers, but exclude zero. To operate with whole numbers, always take note of the digits’ place value.
Examples:
When adding 50,560 and 175 vertically, align 560 and 175. The same reminder is applicable when subtracting.
When multiplying 1234 by 56 manually, always start multiplying from the ones place value to the tens and higher place values.
When dividing, always check your answer by multiplying the quotient (your answer) with the divisor (the smaller of the two numbers), and see if you get the dividend (the bigger number). If so, your division was executed correctly.
When referring to both positive and negative whole numbers, the term integer is used. The numbers 100, 435, –5 and –77 are integers, while 99 ½ and –3.25 are not.
To add integers with like (the same) signs, use the usual method of adding numbers and affix the common sign to the result:
Adding positive integers: 9 + 7 = 16 Adding negative integers: -9 + –7 = –16
To add integers with unlike (different) signs, subtract the smaller integer from the bigger integer and affix the sign of the larger integer to the result:
Small positive integer + larger negative integer: 7 + (–9) = –2 Large positive integer + smaller negative integer: 9 + (–7) = 2
Subtracting integers sometimes sounds confusing. There is one general rule, however, that applies to all cases of subtracting integers:
Rule: Change the sign of the subtrahend and proceed to addition (following the previous rules for adding integers).
Examples:
Large positive integer – smaller negative integer: 9 – 7 = 9 + (–7) = 2
Small positive integer - larger negative integer: 7 – 9 = 7 + (–9) = –2
Positive integer – negative integer: 7 – (–9) = 7 + 9 = 16
Negative integer – positive integer: –7 - (–9) = –7 + 9 = 2
Fractions, decimals, and percentages are other ways of representing numbers that are not whole numbers or integers. A fraction represents part of a whole and is written with a numerator (the part) over a denominator (the whole). The fraction ⅔ refers to 2 parts of a whole, which is made up of 3 parts. This concept of fractions is similar to decimals and percentages.
The fraction ⅔, for instance, can be expressed as decimal by dividing 2 by 3. The result is 0.67, which is the decimal equivalent of ⅔. Take note that we only used 2 decimal places or rounded to the nearest hundredths. Should the question specify 3 decimal places, the correct result should be 0.667.
To express ⅔ or 0.67 as percentage, do the following:
To add or subtract fractions, make sure that they have a common denominator. If they don’t, then determine the least common denominator (LCD) first.
To multiply fractions, multiply numerators first, then multiply denominators next. Reduce the resulting fraction to its lowest form.
To divide fractions, take the reciprocal of the divisor and proceed to multiplication.
Mathematical operations involving decimals are simpler and more similar to operations involving whole numbers, except that there is the decimal point to consider.
When adding vertically and doing subtraction, make sure that the decimal points are aligned.
When multiplying, count the number of decimal places in the factors because this will determine the number of places in the product. To multiply 1.05 by 5.25, multiply as you would whole numbers:
Then count the number of places in both factors (there are four decimal places). Move four decimal places to the left in the result of 55125, and you get 5.5125, the correct answer.
Percentages can be added and subtracted as they are:
Percentages are seldom multiplied or multiplied, but if a question asks for such operation, it will be easier to convert them into decimal or fraction forms first before proceeding to multiplication or division.