Class VII Mathematics Algorithms for multiplication and division

Class VII Mathematics Algorithms for multiplication and division in fractions/decimals Source: NCERT Text Book Class VII By Mr. Srikanta Kumar Das, TGT(Maths) Demonstration Multipurpose School(R. I. E. , NCERT), Bhubaneswar

Multiplication of a fraction by a whole number is same as 3 times OR

Similarly, we will find that Thus, to multiply a whole number with a fraction, we multiply the whole number with the numerator of the fraction, keeping the denominator same.

Multiplication of a fraction with another fraction. The whole was divided in 6(2 x 3) parts and 1(1 x 1) part was taken out.

In case of numerator other than 1 in one of the fractions.

Pictorially � By taking 5 circles,

We multiply two fractions as Product of numerators Product of denominators

Division of a whole number by a fraction. � 1÷ (2 halves in 1) 1 1 12, s are there 1

Following the same pattern, We are taking the reciprocal. Division of a fraction by a whole number. � Based on earlier observations

Multiplication of decimal numbers. � 0. 1× 0. 1= 1 dot out of 100=1/100=0. 01

0. 2× 0. 3=2/10× 3/10 � 2/10 of 3/10=6/100=0. 06 � 6 dots out of 100( can been shown pictorially) � Here number of digits to the right of decimal is 2. Same for 0. 1 x 0. 1=0. 01 � From this patterns we can say, � Multiply numbers by neglecting decimal points, then put decimal point in the product by counting number of digits from the right.

Multiplication of decimal number by 10, 100 …. . . � 1. 76 x 10= So we say, when a decimal number is multiplied by 10, 100 or 1000…. . , the digits in the product are 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 0 s over one.

Division by 10, 100…. . . See the pattern 31. 5÷ 10=3. 15 31. 5÷ 100=0. 315 So we can say that, while dividing a number by 10, 100…. . , 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 0 s over one.

Division of a decimal number by a whole number. 19. 5÷ 5=3. 9 12. 96÷ 4=3. 29 We can also do in this fashion. Divide neglecting decimal points. Put decimal after division by counting no of digits from the right.

Division of a decimal number by another decimal number. We are shifting decimal point to the right. By shifting decimal, can be written as

Or the simple method is to convert decimal numbers into fractional numbers and work out by applying the rules learnt for fractions. �Assessment � Q 1. Shade 2/3 of the triangles in the box.

� Q 2. 2/3 x _____ = 10/30. Q 3. How many 1/4 s are there in 2? � Q 4. 5 X 4/7 means _______ times 4/7. � Q 5. Express 15 mm in cm, m, and km. � Q 6. Find � Q 7. Find: 10. 05 X 1. 05 � Q 8. Find: 7÷ 3. 5 � Q 9. Find 2. 73÷ 1. 3 � Q 10. Lipika plants 4 saplings in a row, in her garden. The distance between two adjacent saplings is ¾ m. Find the distance between the first and the last sapling.