Learning Mathematical Concepts Assignment Sample

Understanding of Concepts- Task 1

A prime number is a number that is more noteworthy than 1 that cannot be made by duplicating other whole numbers. These numbers can only be multiplied by themselves and 1. For example, the below given are a few numbers that are prime numbers:

• 2
• 3
• 5
• 7
• 11
• 13
• 17
• 19
• 23….

The numbers that are made out of these prime numbers are called composite numbers.

For example- if we multiply a prime number to a prime number we get a composite number. Like:

2*2=4

In this case, 2 is a prime number while 4 is a composite number.

Prime Factorisation is the method used to find a solution to multiplying two prime numbers and getting a single original number.

By Multiplying:

Prime factorisation of 90?

Solution: 90= 9*10

Prime factors: 3*3*2*5

Understanding of Concepts- Task 2

For multiplication of two fractional numbers, we must multiply the numerator of the first number with the numerator of the second number and the same shall be done with the denominator.

We are taught that when we are confronted with a troublesome inquiry, for example, 3/5 ÷ 4/7, we should reverse the second part and then multiply (reciprocal).

It would positively appear to be more instinctual just to partition the numerator of the first fractional number by the numerator of the second and afterwards correspondingly to isolate one denominator by the other. Would this instinctive strategy for tackling the difficult work? Not exclusively is the appropriate response "yes," utilizing this technique for isolating the fractional numbers really reveals some insight into why we are taught to do reciprocal of the other number and then multiply.

Let’s try 35÷47 as an example.

While we are aware of the fact that the number 1 is an identity number so we are not supposed the multiply the first fractional number’s division with the element 1, therefore, we multiply the number by 4/4.

To be serious, the solution remains the same when we reciprocate the fractional number and multiply subsequently.

However, the intuitive method requires a lot more work to achieve the same results.

Let us study about the next method.

Dividend Divisor Method

After dividing the numerator of the first number with the numerator of the second number, i.e dividing 3 with 4 we need to multiply 3 with the denominator of the second number i.e. 3 multiplied with 7. Now, this would be applicable in the case of the denominator as well. We multiply the first fractional number with the reciprocal of the second number is just a shortcut!

Understanding of Concepts- Task 3

In mathematics, a fraction is a value, which defines the part of a whole. In other words, the fraction is a ratio of two numbers. Whereas, the decimal is a number, whose whole number part and the fractional part are separated by a decimal point. The decimal number can be classified into different types, such as terminating and non-terminating decimals, repeating and non-repeating decimals. While solving many mathematical problems, the conversion of decimal to the fractional value is preferred, as we can easily simplify the fractional values. In this article, we are going to discuss how to convert repeating decimals to fractions in an easy way.

Terminating and Non-Terminating Decimals

· A terminating decimal is a decimal that has an end digit. It is a decimal, which has a finite number of digits (or terms). Example: 0.15, 0.86, etc.

· Non-terminating decimals are the one that does not have an end term. It has an infinite number of terms. Example: 0.5444444….., 0.1111111….., etc.

Repeating and Non-Repeating Decimals

· Repeating decimals are the one, which has a set of terms in decimal to be repeated uniformly. Example: 0.666666…., 0.123123…., etc.

· Non-repeating decimals are the one that does have repeated terms.

Repeating Decimals to Fraction Conversion

Let us now learn the conversion of repeating decimals into the fractional form. Now, we are going to discuss the two different cases of the repeating fraction.

Case 1: Fraction of type 0.abcd¯¯¯¯¯¯¯¯¯¯

The formula to convert this type of repeating decimal to a fraction is given by:

abcd¯¯¯¯¯¯¯¯¯¯ = Repeated term / Number of 9’s for the repeated term

Example 1:

Convert 0.7¯¯¯ to the fractional form.

Solution:

Here, the number of repeated term is 7 only. Thus the number of times 9 to be repeated in the denominator is only once.

0.7¯¯¯=79

Case 2: Fraction of type 0.ab..cd¯¯¯¯¯

The formula to convert this type of repeating decimal to the fraction is given by:

0.ab..cd¯¯¯¯¯=(ab….cd…..)–ab……Number of time 9′s the repeating term followed by the number of times 0′s for the non−repeated terms.

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