Multiplication of Literals
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
(ii) x times y
(iii) m times 100
(iv) The product of 8 and m.
(v) The product of m and n.
(vi) The product of x and 25.
(vii) Multiply p and 5.
(viii) Multiply a and b.
(ix) Multiply 17 and z.
(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?
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?
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
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.
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.
● Literal Numbers