We have learnt about the fractions. fractions included proper, improper and mixed fractions as well as their addition and subtraction. Also studied comparison of fractions, equivalent fractions, representation of fractions on the number line and ordering of fractions.
We have also learnt decimals included, their comparison, their representation on the number line and their addition and subtraction.
How Well Have You Learnt About Fractions?
A proper fraction is a fraction that represents a part of a whole. E.g. 7/4, 8/4
An improper fraction is a combination of whole and a proper fraction. 7/4.
To multiply a whole number with a proper or an improper fraction, we multiply the whole number with the numerator of the fraction, keeping the denominator same.
To multiply a mixed fraction to a whole number, first convert the mixed fraction to an improper fraction and then multiply.
Multiply two fractions as Product of Numerators/Product of Denominators when two proper fractions are multiplied, the product is less than each of the fractions. Or, we say the value of the product of two proper fractions is smaller than each of the two fractions.
The product of two improper fractions is greater than each of the two fractions.
The value of the product of two improper fractions is more than each of the two fractions.
We are required to divide a whole number by a fraction or a fraction by another fraction.
The non-zero numbers whose product with each other is 1, are called the reciprocals of each other.
To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction.
While dividing a whole number by a mixed fraction, first convert the mixed fraction into improper fraction and then solve it.
We have learnt about decimal numbers in previous class, how 10th, 100th or 1000nds places of the fractions and integers.
1/100 = 0.01
1/10 = 0.1
1/1000 = 0.001
While multiplying 2.5 and 1.25, you will first multiply 25 and 125. For placing the decimal in the product obtained, you will count 1 + 2 = 3 (Why?) digits starting from the rightmost digit.
Thus, 2.5 x 1.25 = 3.225
When a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
The division of a decimal number by 10, 100 and 1000.
3/10 = 0.3
3/100 =0.03
3/1000 = 0.003
301/100 = 3.01
While dividing a number by 10, 100 or 1000, the digits of the number and the quotient are same but the decimal point in the quotient shifts to the left by as many places as there are zeros over 1.
2.38 ÷ 10 = 0.238, 2.38 ÷ 100 = 0.0238, 2.38 ÷ 1000 = 0.00238