Multiplication of literals obeys all operation of multiplication of numbers. In arithmetic, we studied multiplication as the repeated addition.



For example, 5 + 5 + 5 + 5 is called 4 times 5 and it is written as 4 × 5.

Similarly, if a is a literal, then a + a + a + a is 4 times a and is written as 4 × a.

Sometimes, the sign of multiplication is confused with the letter x. To avoid such as confusion we omit the sign of multiplication between a number and a literal or between two literals.

Thus, when there is no sign between a literal and a number of two literals, it is understand that the two are multiplied.

Thus, y + y + y + y + y = 5 × y = 5y

Similarly, the product of literals a and b is written as ab.It should be noted that the product of the type y × 4 is not written as y4. Conventionally, we written it as 4y.


For example :

Write each of the following phrases using numbers, literals and the basic operations of addition, subtraction and multiplication:

1. (i) 10 times a

Answer: 10a


(ii) x times y

Answer: xy


(iii) m times 100

Answer: 100m


(iv) The product of 8 and m.

Answer: 8m


(v) The product of m and n.

Answer: mn


(vi) The product of x and 25.

Answer: 25x


(vii) Multiply p and 5.

Answer: 5p


(viii) Multiply a and b.

Answer: ab


(ix) Multiply 17 and z.

Answer: 17z


(x) 4 times x added to y .

Answer: 4x + y


(xi) m times k added to 5 .

Answer: mk + 5


(xii) 5 times the sum of x and y.

Answer: 5(x + y )


(xii) p times the sum of 10 and y.

Answer: p(10 + y )


(xiii) 5 times a is subtract from b

Answer: b – 5a.


(xiii) x times k is subtract from 10

Answer: 10 – xk.


(xiv) 10 more than thrice a number y.

Answer: Here we have,
Thrice a number y = 3y.

Therefore, 10 more than thrice a number y = 3y + 10


2. John covers x centimeters in one step. How many centimeters does he cover in 9 steps?

Solution:

We have,
Distance covered in one step = x centimetres

Therefore, Distance covered in 9 steps = (9 times x ) centimetres.

= 9 centimeters.


3. Mark spend $ x daily and saves $ y per week. What is his income after 3 weeks?

Solution:

We know that,
1 week = 7 days.

Therefore, 3 weeks = (7 × 3) days = 21 days.

Mark spends $ x daily.

Therefore, amount spent by Mark in 3 weeks = $ (3 times y) = $ 3y

Now,
Income = Expenditure + Savings

Therefore, Mark's income after 3 weeks = sum of $ 21x and $ 3y

= $ (21x + 3y)


4. The score of Jessica in Mathematics is 35 more than thrice of her score in Science. If she scored x marks in Science, determine her score in Mathematics.

Solution:

We have,
Score in Science = x

Thrice of score in Science = 3x

Therefore, 35 more than two third of score in Science = 3x + 35

Hence, score in Mathematics = 3x + 35.