Question 1
A decimal number is a modified way of expressing a fraction. A fraction shows a number as a part of a whole figure. For example, 2/3 means when a quantity is divided into 3 equal parts we have to take 2 parts of it. When this fraction is expressed in terms of fractions of 10, 100, 100 it becomes a decimal fraction. For example we can write 2/5 as 4/10. Thus 4/10 is decimal fraction. We can write 4/10 as 0.4 . This is a decimal number. In a similar way we can write 13 9/100 as 13.09.
Question 2
PEMDAS stands for Parenthesis, Exponential, Multiplication, Division, Addition and Subtraction. This is the order in which a mathematical expression has to simplified. Let us take an example:
2+5*9/3+2(9-4) -3(5-2)
We solve this in the following steps:
=2+5*3+2*5-3*3
=2+15+10-9
=27-9
=18
Question 3
Addition, Subtraction, Multiplication and division of fractions are demonstrated below:
Addition:
We convert the fractions to be added into like fractions that is with common denominators and then we add them:
4/5 + ¾ = 16/20 + 15/20 = 31/20 = 111/20
Subtraction:
In this case also we convert the fractions into like fractions and then subtract the numerators:
3/7 – 1/8 = 24/56 – 7/56 = 17/56
Multiplication:
We multiply the numerators of the fractions and write it as the numerator of the product and we multiply the denominator and write it as the denominator of the product:
4/7*5/12 = 4*5/7*12 = 20/84 = 5/21
Division:
In case of division we find the reciprocal of the divisor and then multiply the dividend and the reciprocal of the divisor:
9/11/8/9 = 9/11*9/8 =81/88
Let us find an example of how we use fraction in everyday life
A child plans to spend 1/3 of his pocket money of $225 in buying snacks, 3/5 on toys. What fraction is left?
Part spent: 1/3 + 3/5 = 14/15
Part left = 1/15
Amount left: 1/15 of $225 = $15
Question 4
Order of operations refers to the order in which we have to silve a mathematical expression. The order is expressed as BODMAS: Bracket OF Division Multiplication Addition and Subtraction .
Example:
24(4*6-3*2)+24/(2*3)-1/3of12
In this case we are going to solve the brackets first such as;
24(24-6)+24/6 – 1/3of12
=24*18 + 24/6 -1/3 of 12
Next we solve the of
24*18 + 24/6 -4
Then we do the division
24*18 + 4 -4
Then we solve the multiplication problem:
360 + 4 – 4
Now we add
364 -4
Finally we do the subtraction:
360
Thus we have followed the order to simplify the mathematical expression to find the final answer as 360.
References
Bansal, R. (2008). Middle School Mathematics Book 6. New Delhi: Selina.
Bansal, R. (2008). Middle School Mathematics Book 7. New Delhi: 2008.
