Buksis-4.1 Revisi Akhir

4 .1 What are you going to learn? À To identify sentences which are correct À To identify sentences which are wrong À To understand statements À To understand open sentences

Key Terms: • • • • •

Statements Do you ever answer your teacher’s question? If so, how is the answer that you have given? True or false? your

If you answer a question completely,

answer

may

perform

a

sentence.

For

example, “Where do you study?” An example of the answer is “I study at SMP Tanjung Atap”.

correct sentences wrong sentences statements open sentences number sentence

Picture 4.1

Now, study the following sentences. (a) The number of players in a football team is 12. (b) The number of players in a volleyball team is 6. (c) 2 is not a prime number. (d) Surabaya is the capital of East Java. (e) 21 + 15 > 35 (f) –10 > -8 (g) A negative number plus a negative number is a positive number. (e) A prime number is a number that has exactly two Mathematics for Junior High School – Year 7 / 123

factors, i.e. 1 and the number itself. Which sentences are true? Which sentences are false? If a sentence is false, give your reason why.

A true or false sentence is called a statement.

Open Sentences Gift Problem 1. In her birthday party, Ani received some books as a gift from Johan. Lisa said, “the number of the books in Picture 4.2

that gift-box is six pieces”.

What is your opinion about Lisa’s statement? True or false?

2. A fruit seller received a shipment of oranges in a sack, the number of which was unknown. The number of the remaining oranges was 34. The seller said, “the total number of the oranges is 456”. Picture 4.3

Can you

determine the truth-value (True or False) of the seller’s statement? Why?

3. Consider the sentence “A number added by 5 is 12.” Can you determine the truth-value of the sentence?

We cannot determine the truth-value of the

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sentence because the value of “a number” in that sentence has not been determined. Whether it is true or false depends on what “a number” is.

If “a number ” is 7, then the sentence becomes “7 added by 5 is 12”. The truth value of the sentence is true. If “a number ” is 10, then the sentence becomes “10 added by 5 is 12”. The truth value of the sentence is false. If “a number ” is -4, then the sentence becomes “-4 added by 5 is 12”. The truth value of the sentence is false.

Therefore, the sentence “A number added by 5 is 12” is a sentence the truth value of which has not been determined yet. A sentence the truth value of which has not been determined is called an open sentence.

The value of “a number ” in the above sentence has not been determined yet. Mathematically, the value which has not been determined yet is called a variable, symbolized by a letter in lowercase, such as x, y, m or others.

Therefore, the sentence “A number added by 5 is 12” can be symbolized as x + 5 = 12 , or y + 5 = 12 , or

m + 5 = 12.

Thus, the variable of the open

sentence x + 5 = 12 is x. The variable of the open sentence y + 5 = 12 is y, and the variable of the open sentence m + 5 = 12 is m.

Mathematics for Junior High School – Year 7 / 125

Here are some examples of verbal expressions and their mathematical expressions. No. 1 2 3 4 5 6 7 8

Verbal Expressions the sum of a and b the difference between a dan b the square of a the sum of a squared and b squared the difference of a squared and b squared the inverse of a the multiplication of a by b the division of a by b, when b is not zero

Mathematical Expressions a+b a−b a2 a2 + b2 a2 – b2 1 a

a.b a : b, b ≠ 0

The sentence “a certain number is equal to 18 minus 3” can be written in a mathematical expression as t = 18 - 3. The sentence “a certain number minus 8 is larger than 20” can be written in a mathematical expression as m – 8 > 20. 4. Express the following sentences in the form of mathematical expressions. (a) The square of a nonnegative integer is larger than 17. (b) The quotient of a number by 5 equals 7. (c) The opposite of a number multiplied by two is smaller than 13. Although the truth-value of an interrogative sentence and an imperative sentence cannot be determined, they are not open sentences.

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1. Determine whether the following sentences are true or false. If it is false, change the sentence into a true sentence. a. 3 is the multiple of 6 b. Palembang is the capital of Western Sumatra. c.

3 4 < 4 5

d. 4 ( 8 + 2 ) = ( 4 + 2 ) ( 4 + 8 ) e. 27 is not a prime number. o

f. The sum of all three angles in a triangle is 360 .

2. Determine if the following sentences are statements. If it is a declarative sentence, determine whether it is true or false. If it is not a declarative sentence, give your reasons. a. There is no even prime number. b. The GCD of 16 and 32 is 16. c. What is the result of 12 added by 9? d.

6 3 = 8 4

e. Do the exercises. f. Is

1 1 greater than ? 2 4

g. The LCM of 4 and 8 is 32.

3.

Change

each

open

sentence

below

into

a

mathematical expression. a. The difference between a number and 23 is more than 10. b. A number multiplied by two equals 25.

Mathematics for Junior High School – Year 7 / 127

c. The square of a positive integer is more than 20. d. The difference between the square of a number and 2 is 12. 4. Critical Thinking. Is an open sentence a statement? Give your reasons. 5.

Give two examples of open sentences using the

following variables. a) s

d) h

b) u

e) i

c) q

f) z

6. Writing. Give examples of open sentences that can be represented by the following mathematical expressions. a. 200 + x = 500 b. 1000 – y = 300 c. t + 500 = 2000 d. 5r = 4000 e.

x = 2000 6

7.

Make

a

mathematical

sentence

from

the

statements below. a. 25 subtracted from a certain number is 46. b. Father’s age multiplied by 2 is greater than 80. c. After receiving Rp 2,500.00 from Mother, my money becomes Rp10,000.00. d. If Rp 3,000.00 is spent on books, Eva will have Rp 12,000.00 left.

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e. If Fia’s candies are divided for two people, each of them will get 7 candies.

Mathematics for Junior High School – Year 7 / 129

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