Solving Math Grade 7 Pages 34, 35

=> Check more 7th-grade math solutions here: 7th-grade math solutions

- Solving 7th Grade Math on page 32 in the Connect Knowledge Book Volume 1 - Exercise 6: Irrational Numbers. Square root of a numerical value
- Solving 7th Grade Math on page 45 in the Creative Horizon Book Volume 1 - Exercise at the end of chapter 2
- Solving 7th Grade Math on page 47 in the Kite Book Volume 1 - Exercise 3. Absolute value of a real number

Solving Math Grade 7 Pages 34, 35

Exercise 65 (Math Grade 7 Page 34)
Explain why the following fractions can be written as finite decimals and then write them in that form:

Solution:
8=2³, 5 = 5, 20 = 2² . 5, and 125 = 5³ all have no prime factors other than 2 and 5, so they can be written as finite decimals. Result:

Exercise 66 (Math Grade 7 Page 34)
Explain why the following fractions can be written as infinite repeating decimals and then write them in that form:

Solution:
The given fractions, all with positive denominators, are as follows:
6 = 2.3; 11 = 1.11; 9 = 3 . 3; 18 = 2.3²
Since they all contain prime factors other than 2 and 5, they can be written as infinite repeating decimals.
The result is:

Exercise 67 (Math Grade 7 Page 34)
Given:

Fill in the question mark with a single-digit prime number so that A can be written as a finite decimal. How many such numbers can be filled in?
Solution:
Fill in the question mark with the prime numbers with a single digit 2, 3, 5, 7.

Among them:
4 has the prime factor 2
2 has the prime factor 2
10 has the prime factors 2, 5
14 has the prime factors 2, 7 different from 2, 5
=> There are 3 numbers that can be written as finite decimals:

Therefore, you can fill in three numbers: 2, 3, 5.
Exercise 68 (Math Grade 7 Page 34)
a) Among the following fractions, which ones can be written as finite decimals, and which ones can be written as infinite repeating decimals. Explain.

b) Write the fractions below as finite decimals or infinite repeating decimals (write in a concise form with the cycle in parentheses).
Solution:
a) Simplify the fractions

Examining by denominators:
8=2³
20=2².5
11=11
22=2.11
12=2².3
5=5
+ The denominators with no prime factors other than 2 and 5 are 8, 20, 5, so these fractions will be written as finite decimals as follows:

+ The denominators containing prime factors other than 2 and 5 are 11,22,12, so these fractions will be written as infinite repeating decimals as follows:

Exercise 69 (Math Book 7 page 34)
Utilize parentheses to clarify the recurring decimal cycles in the following divisions:
a) 8.5:3
b) 18.7:6
c) 58:11
d) 14.2:3.33
Solution
a) 8.5 : 3 = 2.8(3) => the cycle of the recurring decimal is 3.

Exercise 71 (Math Book 7 page 35)
Express the fractions  1/99; 1/999 in decimal form.
1/99 = 0.(0,1)
1/999 = 0.(001)
Exercise 72 (Math Book 7 page 35)
Are the following numbers equal?
0.(31) ; 0.3(13)
Solution:
0.(31) = 0.3131313...
0.3(13)= 0.3131313...
=> 0.(31)−0.3(13) = 0.3131313... − 0.3131313... = 0
So, 0.(31) = 0.3(13)

Detailed solutions for exercises on pages 119, 120 in Math Book 7 Volume 1 have been provided for your reference and preparation to enhance your understanding of Grade 7 Mathematics.

In addition to the covered material, you can prepare and explore the solutions for exercises on pages 114, 115 in Math Book 7 Volume 1 to grasp the concepts within the Grade 7 Math curriculum.

In this lesson, you will master the synthesis of theoretical knowledge and the process of solving exercises on Finite Decimal Numbers. The topic of recurring decimal numbers will be elaborated with examples and step-by-step instructions for specific exercises on pages 34 and 35 of Math Book 7. The detailed solutions and guidance make solving these exercises easier, aligning closely with the curriculum. Feel free to refer to the material to optimize your learning.

In the upcoming lesson, we will explore the techniques for rounding numbers. Please refer to the material and apply it to your studies for the best results.

Guidance for solving exercises on pages 34, 35 of Math Book 7 Volume 1 in the section on Grade 7 math exercises. Students can review the solutions for exercises on pages 34, 35 of Math Book 7 Volume 2 from the previous lesson or preview the guidance for solving exercises on pages 36, 37, 38 of Math Book 7 Volume 1 to excel in Grade 7 Math.