Multiplication and Division Of Decimal Fractions

Mathematics deals with various arithmetic functions and calculations, including integers, decimals and fractions. Multiplication and division come amongst the four primary functions in mathematics, which guide other functions. Multiplication and division of integers seem a lot easier, be it multiplication and division word problems, than multiplication and division of fractions.

What is a fraction?

We all know that an integer is either a positive or a whole negative number, which does not include fractions. But what are fractions? Well, fractions are numbers that are expressed in terms of a quotient, with a numerator and denominator. It usually is used to represent a part of the whole thing. For example, three out of 8 kids liked the new chocolate; numerically, it can be represented as 3/8. Where 3 is the numerator, and 10 is the denominator. Multiplication and division of fractions can be a little tricky, but one can make it easier with practice.

Decimal fractions:

Now that we understand fractions better let us understand what decimal fractions are. Decimal fractions are numbers whose bottom number or the denominator is ten or in the higher powers of 10, like 100,1000,10000. For example, 23/100 or 23/1000. To make multiplication and division easier, we can write these numbers, fractions, by putting the decimal point. For example, 23/100 can be written as 0.23, and 23/1000 can be expressed as 0.023. Remember, the number of zeros after the first digit is the number of digits you need to leave from your decimal point.

Multiplication of fractions is somewhat easy; one multiplies the top numbers and multiplies the bottom numbers.

35 * 417 = 1285

Now, when it is possible, you can reduce fractions by cancelling out the common factors. 

For example,

35 * 415 = 1275= 425 (common factor 3)

If one is unsure what cancels out considering the common factor, you could always factor out the numerator and denominator and then cancel out the common factors. 

Division of fractions

Multiplication and division of fractions almost follow similar steps, though there is one extra step to be added while dividing fractions. This extra step is to flip the 2nd fraction and then multiply. Flipping the fraction means finding its reciprocal. After finding the reciprocal of the 2nd fraction, you multiply the first one by the reciprocal of the 2nd one. 

e.g.:

Simplify 35 ÷ 94

To proceed,

First, flip the 2nd fraction hence we will be getting 49,

Now multiply the first fraction with the reciprocal of the second fraction.

35 * 49

Cancelling out the common factors, we get our answer as:

415 

Multiplication and division of word problems could be a challenge for fractions. We need to determine the numerator and denominator from the word problem given. As mentioned earlier, the numerator will be a part of the whole, which will be the denominator.

Conclusion

Multiplication and division, be it of fractions, whole numbers, mixed fractions, is not daunting if you pay attention to the required details and solve each step thoroughly before moving to the next one. One needs to keep in mind if they are to divide a fraction, follow the same steps as multiplication, but first take the reciprocal of the second fraction. With practice and consistency, one will be able to understand this concept very easily.