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Math 7 Q1 Week 4 Lesson 2 edited Aug
Algebra and Trigonometry (MATH 17)
Mindanao State University
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Mathematics
First Quarter
Module 4: Rational Numbers
7
ii
Mathematics – Grade 7 Alternative Delivery Mode Quarter 1 – Module 4: Rational Numbers First Edition, 2021
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For the learner:
Welcome to the Mathematics 7 Alternative Delivery Mode (ADM) Module on Rational Numbers!
The hand is one of the most symbolized part of the human body. It is often used to depict skill, action and purpose. Through our hands we may learn, create and accomplish. Hence, the hand in this learning resource signifies that you as a learner is capable and empowered to successfully achieve the relevant competencies and skills at your own pace and time. Your academic success lies in your own hands!
This module was designed to provide you with fun and meaningful opportunities for guided and independent learning at your own pace and time. You will be enabled to process the contents of the learning resource while being an active learner.
This module has the following parts and corresponding icons:
What I Need to Know This will give you an idea of the skills or competencies you are expected to learn in the module.
What I Know This part includes an activity that aims to check what you already know about the lesson to take. If you get all the answers correct (100%), you may decide to skip this module.
What’s In This is a brief drill or review to help you link the current lesson with the previous one.
What’s New In this portion, the new lesson will be introduced to you in various ways such as a story, a song, a poem, a problem opener, an activity or a situation.
What is It This section provides a brief discussion of the lesson. This aims to help you discover and understand new concepts and skills.
What’s More This comprises activities for independent practice to solidify your understanding and skills of the topic. You may check the answers to the exercises using the Answer Key at the end of the module.
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What I Have Learned This includes questions or blank sentence/paragraph to be filled in toprocess what you learned from the lesson.
What I Can Do This section provides an activity which will help you transfer your new knowledge or skill into real life situations or concerns.
Assessment This is a task which aims to evaluate your level of mastery in achieving the learning competency.
Additional Activities In this portion, another activity will be given to you to enrich your knowledge or skill of the lesson learned. This also tends retention of learned concepts.
Answer Key This contains answers to all activities in the module.
At the end of this module you will also find:
The following are some reminders in using this module:
- Use the module with care. Do not put unnecessary mark/s on any part of the module. Use a separate sheet of paper in answering the exercises.
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We hope that through this material, you will experience meaningful learning and gain deep understanding of the relevant competencies. You can do it!
References This is a list of all sources used in developing this module.
- Write 0 as a fraction in lowest terms.
A. 1225 B. 2450 C. 10048 D. 100048
- Write the appropriate inequality symbol: -2 _____ - 2.
A. > B. < C. ≥ D. ≤
- Which fraction is equal to the decimal 3. 14?
A. 21/50 B. 157/50 C. 311/99 D. 22/
- What is the equivalent fraction form of 0. 55?
A. 5/10 B. 5/9 C. 9/5 D. 10/
- What is the equivalent decimal form of 7/11?
A.0 B. 0 C. 0... D. 0...
- What is the equivalent fraction of 3?
A. 3 1/4 B. 3 8/25 C. 3 32/100 D. 3 2/
- The simplest form of 0 into fraction from is _________.
A. 1/15 B. 3/20 C. 1/5 D. 3/
- What is the equivalent decimal form of 7/14?
A. 0 B. 0 C. 0 D. 0.
- Which fraction is equivalent to 0...?
A. 1/11 B. 4/33 C. 3/25 D. 4/
Lesson
1
Changing Fractions to
Decimals and vice versa
What’s In
Classify the following numbers and place them in its proper column.
1 3
1
18 5
Rational Numbers in Fractional Form
Rational Number in Decimal Form
This lesson will help you revisit mathematical concepts needed to be successful in this module. It covers concepts you learned from elementary years about fractions and decimals.
Think of This! Representation Examples Rational Number is any number that can be written in the form 𝑎𝑏 , where a and b are integers, and b is not equal to 0.
𝑎 𝑏 ⃒ 𝑎 &𝑏 are integers , b ≠ 0 Let a and b be an integer, then a rational number is defined as 𝑎𝑏 , where b is not equal to 0.
6 12 ,
3 4 ,0.
Note: Any rational number can be expressed from fractional form to decimal form and vice versa.
CONVERTING FRACTIONS TO DECIMALS
Converting Fractions to Decimals (with Terminating Decimals) Remember: We can convert fraction to decimal by simply dividing the numerator by the denominator.
Example 1 Example 2
Convert 14 to decimal form. Convert 34 to decimal form.
Solution: Solution:
Note:
Fractions in Examples 1 and 2 produce terminating decimals.
Terminating Decimal - a decimal with finite number of digits.
Examples: 1 2 = 0 ,
1 5 = 0 ,
1 8 = 0.
Converting Fractions to Decimals (with Non-Terminating Decimals)
Example 3 Example 4
Change 13 to decimal form. Change 53 to decimal form.
Therefore, 1 Therefore, 34 = 0. 4 = 0.
Converting Repeating or Non-terminating Decimal into Fraction
To convert non- terminating decimal fractional Form, perform the steps below:
Example 1 Example 2 Change the 0... to fraction form.
Change 1... to fraction form.
(1) Let n be your given decimal number
Step 1: Let n = 0...
Step 1: Let n = 1... (2) Multiply the equation by a power of 10 depending on the place value of the given decimal.
Step 2: Multiply n by 10. (10) (n = 0...) 10 n = 3...
Step 2: Multiply n by 10. (10) (n = 1...) 10 n = 16...
(3) Subtract the first equation to the new equation to obtain a whole number as difference.
Step 3: 10n = 3...
- n =0... 9n = 3
Step 3: 10n = 16...
- n = 1... 9n = 15 (4) Find the value of n by applying the multiplication property of equality (MPE).
(1 9 )(9𝑛) = 3(1 9 )
Step 4:
n = 39 = 39
(1 9 )(9𝑛) = 15(1 9 )
Step 4:
n = 159 = 53
(5) Finalize your answer.
Step 5:
Therefore,
0... = 39 or 13
Step 5:
Therefore,
1... = 39 or 13
Converting Terminating Decimal Form into Fractional Form
To convert terminating decimal to fractional form, do the following steps:
Example 1 Example 2
Change 0 to Fraction.
Change 0 to Fraction
(1) Let n be your given decimal number.
Step 1: Let n = 0.
Step1: Let n = 0.
(2) Multiply the equation by a power of 10 depending on the place value of the given decimal
Step 2: Multiply the equation by 10.
(10) ( n = 0) 10 n = 3
Step 2: Multiply the equation by 100. (100) ( n = 0) 100 n = 75
(3) Find the value of n in a fraction.
Step 3: Find the value of n 1 10 (10𝑛) = 3(
1 10 ) n = 103
Step 3: Find the value of n 1 100 (100𝑛) = (75)
1 100 n = 10075 = 34
(4) Finalize your answer. Step 4: Therefore, 0 = 3 10
Step 4:
Therefore, 0 = 10075 = 34
What I Have Learned
Fill in the blanks to complete the paragraph. Number 1 is done for you.
The word (1)Rational is derived from the word (2)________ which means (3). A rational number is any number that can be written in the form (4)_ where a and b are (5)_________ and the denominator is not equal to (6). Rational numbers can be a (7)_ or (8)____________. Decimal numbers could be (9)or , (10).
What I Can Do
Answer the given problems. Express your answers in its simplest form.
If there are 62 boys out of 100 Grade 7 students, how do you express this in fractional form? What is its decimal form?
A Hummingbird’s egg weighs 0 ounce. Express this as a fraction in simplest form.
Directions: Read the questions carefully. Choose the letter of the correct answer.
- The word ratio means _________.
A. difference B. product C. quotient D. sum
- The following numbers are rational EXCEPT
A. 3 B. 1... C. 12 D. 0
- Which of the following are terminating decimals?
A. 0 C. 1... B. 0... D. 3...
- Which of the following is the equivalent of 34?
A. 0 B. 0 C. 0 D. 1.
- Write the appropriate inequality symbol between: -2 ___ 2.
A. > B. < C. ≥ D. ≤
- Which of the following decimal numbers is the smallest?
A. 0 B. 0 C. 0 D. 0.
- Rational number is any number that can be written in the form _________.
A. 𝑎𝑏 B. a + b C. ab D. a – b
- Which of the following is the equivalent fraction of 0 in lowest terms?
A. 13 B. 14 C. 12 D. 34
- It is a number that repeats itself.
A. addend C. repetend B. augend D. repeated
- Write the appropriate symbol: 1. 25 _______ 1.
A. > B. < C. ≥ D. ≤
- A line that is used to order or arrange rational numbers.
A. Horizontal line C. Slanting line B. Number line D. Vertical line
####### Assessment
Activity: Do as indicated.
Name 10 rational numbers that are greater than -1 but less than 1 and arrange them from least to greatest on the real number line.
A unit fraction is a fraction that has a numerator of 1. The four greatest unit fractions that are terminating decimals are 12 , 13 , 14 , 15. Express each fraction as a decimal number. Write your answers in your Mathematics notebook.
####### Additional Activities
####### Answer Key
What I know 1. A 2. C 3. B 4. B 5. A 6. C 7. A 8. D 9. B
B
D
B
B
C
B
Assessment
C
B
A
C
B
A
A
D
C
A
B
A
C
B
B
What’s More Lesson 1: A. ¾ , 0, 0, 3, 0.
B.
2/5 0 TD 9/20 0 TD 1/6 0... NTD 8/11 0... NTD 4/9 0... NTD
What I Can Do 1. 62/100 or 31/ = 0. 2. 0 = 13/
Additional Activities 1. Answer may vary 2. 0, 0..., 0, 0.
What’s New
- C
- D
- B
- A
- E
Math 7 Q1 Week 4 Lesson 2 edited Aug
Course: Algebra and Trigonometry (MATH 17)
University: Mindanao State University
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