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.
Examples of Multiplication of Literals
1. Write
each of the following phrases using numbers, literals and the basic
operations of addition, subtraction and multiplication:
(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 )
(xiii) p times the sum of 10 and y.
Answer: p(10 + y )
(xiv) 5 times a is subtract from b
Answer: b – 5a.
(xv) x times k is subtract from 10
Answer: 10 – xk.
(xvi) 10 more than thrice a number y.
Answer: Here we have,
(xvii)Thrice a number y = 3y.
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.
Properties of Multiplication of Literals
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