Chapter 3 Numeric And Algebraic Expressions
Section 3.0: Review What You Know
Page 115 Exercise 1 Answer
A formula is a rule that uses symbols to relate two or more quantities.
Result
Formula.
Page 115 Exercise 2 Answer
The number 12 is a composite number because it has more than two factors.
Result
Composite number.
Page 115 Exercise 3 Answer
A numerical expression is a mathematical phrase that includes numbers and at least one operation.
Result
Numerical expression.
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Page 115 Exercise 4 Answer
Formula used to find the perimeter P is
P = 2l + 2w,
where l is length and w is width.
In this exercise l is 13cm and w is 13cm.
P = 2 ⋅ 13 + 2 ⋅ 13 = 26 + 26 = 52cm Perimeter of the square is 52cm.
Formula used to find the area A is A = lw, where l is the length and w is the width,and as before l = 13cm and w = 13 A = lw = 13 ⋅ 13 = 169 cm2 Area of the square is 160cm2.
Result
P = 52 cm
A = 169 cm2
Page 115 Exercise 5 Answer
Formula used to find the perimeter P is
P = 2l + 2w,
where l is length and w is width.
In this exercise l is 5 in and w is 21 in. P = 2 ⋅ 5 + 2 ⋅ 21 = 10 + 42 = 52 in Perimeter of the square is 52in.
Formula used to find the area A is A = lw, where l is the length and w is the width, and as before l = 5 in and w = 21 in. A = lw = 5 ⋅ 21 = 105 in2 Area of the square is 105 in2.
Result
P = 52 in
A = 105 in2
Page 115 Exercise 6 Answer
Formula used to find the perimeter P is
P = 2l + 2w,
where l is length and w is width.
In this exercise l is 9m and w is 15m. P = 2 ⋅ 9 + 2 ⋅ 15 = 18 + 30 = 48 m Perimeter of the square is 48m.
Formula used to find the area A is A = lw, where l is the length and w is the width, and as before l = 9m and w = 15m. A = lw = 9 ⋅ 15 = 135 m2 Area of the square is 135m2.
Result
P = 48 m
A = 135 m2
Page 115 Exercise 7 Answer
Multiple is the product of any quantity and an integer.
The first multiple of any number is that number times one, so the first multiple of any number is the number itself. The second multiple of any number is that number times two. […] The n-th multiple of any number is that number times n.
The first five multiples of 8 are:
8 . 1 = 8,
8 . 2 = 16,
8 . 3 = 24,
8 . 4 = 32,
8 . 5 = 40.
Result
The first five multiples of 8 are 8,16,24,32,40.
Page 115 Exercise 8 Answer
Multiple is the product of any quantity and an integer.
The first multiple of any number is that number times one, so the first multiple of any number is the number itself. The second multiple of any number is that number times two. […] The n-th multiple of any number is that number times n.
The first five multiples of 9 are:
9 . 1 = 9,
9 . 2 = 18,
9 . 3 = 27,
9 . 4 = 36,
9 . 5 = 45.
Result
The first five multiples of 9 are 9,18,27,36,45.
Page 115 Exercise 9 Answer
Multiple is the product of any quantity and an integer.
The first multiple of any number is that number times one, so the first multiple of any number is the number itself. The second multiple of any number is that number times two. […] The n-th multiple of any number is that number times n.
The first five multiples of 9 are:
10 . 1 = 10,
10 . 2 = 20,
10 . 3 = 30,
10 . 4 = 40,
10 . 5 = 50.
Result
The first five multiples of 10 are 10,20,30,40,50.
Page 115 Exercise 10 Answer
Multiple is the product of any quantity and an integer.
The first multiple of any number is that number times one, so the first multiple of any number is the number itself. The second multiple of any number is that number times two. […] The n-th multiple of any number is that number times n.
The first five multiples of 6 are:
6 . 1 = 6,
6 . 2 = 12,
6 . 3 = 18,
6 . 4 = 24,
6 . 5 = 30.
Result
The first five multiples of 6 are 6,12,18,24,30.
Page 115 Exercise 11 Answer
Multiple is the product of any quantity and an integer.
The first multiple of any number is that number times one, so the first multiple of any number is the number itself. The second multiple of any number is that number times two. […] The n-th multiple of any number is that number times n.
The first five multiples of 4 are:
4 . 1 = 4,
4 . 2 = 8,
4 . 3 = 12,
4 . 4 = 16,
4 . 5 = 20.
Result
The first five multiples of 4 are 4,8,12,16,20.
Page 115 Exercise 12 Answer
Multiple is the product of any quantity and an integer.
The first multiple of any number is that number times one, so the first multiple of any number is the number itself. The second multiple of any number is that number times two. […] The n-th multiple of any number is that number times n.
The first five multiples of 3 are:
3 . 1 = 3,
3 . 2 = 6,
3 . 3 = 9,
3 . 4 = 12,
3 . 5 = 15.
Result
The first five multiples of 3 are 3,6,9,12,15.
Page 115 Exercise 13 Answer
To find the factors of a number, you need to find all the pairs of numbers that multiply to the number.
To find the factors of 12, we need to find all the pairs of numbers that multiply to 12:
Since 12 ÷ 1 = 12, then 1 × 12 = 12 so 1 and 12 are factors.
Since 12 ÷ 2 = 6, then 2 × 6 = 12 so 2 and 6 are factors.
Since 12 ÷ 3 = 4, then 3 × 4 = 12 so 3 and 4 are factors.
There are no more pairs of numbers that multiply to 12 so the factors of 12 are 1, 2, 3, 4, 6, and 12.
To find the factors of 15, we need to find all the pairs of numbers that multiply to 15:
Since 15 ÷ 1 = 15, then 1 × 15 = 15 so 1 and 15 are factors.
Since 15 ÷ 3 = 5, then 3 × 5 = 15 so 3 and 5 are factors.
There are no more pairs of numbers that multiply to 15 so the factors of 15 are 1, 3, 5, and 15.
Result
To find the factors of a number, you need to find all the pairs of numbers that multiply to the number. The factors of 12 are then 1, 2, 3, 4, 6, and 12 and the factors of 15 are 1, 3, 5, and 15.
To find the factors start dividing by prime numbers. Start with the least prime number which divides 12 and 15. When the remainder is no longer divisble, try the next prime number.
Repeat until the remaining number is a prime itself.
12 ÷ 2 = 6
6 ÷ 2 = 3
Since three is a prime number it is the last factor.
Twelve can be written as a product of prime numbers as following:
12 = 2 × 2 × 3.
15 is not divisible by two so instead start with three.
15 ÷ 3 = 5
Since five is a prime number it is the last factor.
Fifteen can be written as a product of prime numbers as following:
15 = 3 × 5.
Result
Open to see the solution.
Page 115 Exercise 14 Answer
Difference, sum, quotient, and product are all results of arithmetic operations. Difference is the result of subtraction, sum is the result of addition, quotient is the result of division, and product is the result of multiplication.
Result
Difference, sum, quotient, and products are all results of arithmetic operations.