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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