Download MATH - 7 MODULE QUARTER 1 WEEK 1 and more Study notes Mathematics in PDF only on Docsity!
St. Catherineās College
6019 Carcar City, Cebu
BASIC EDUCATION DEPARTMENT
School Year 2020 ā 2021
MATHEMATICS ā 7 LEARNING MODULE Quarter 1 ā Most Essential Learning Competency (MELCS) ā Week 5 In this week, the learners are going to perform operations on rational numbers.
MR. ALVIN T. UBAS
Learning Targets The Grade 7 learners can:
1. express rational numbers from fraction form to decimal form and vice versa.
2. perform operations on fractions (addition and subtraction)
3. perform operations on fractions (multiplication and division)
4. perform operations on rational numbers.
Key Concepts
ļ· Fractions and Decimals
ļ· Powers and Roots
Learnerā s Name
No part of this module may be reproduced in any form or by any means without any
Module Writer/Teacher
Name: Grade & Section: Date Received: FRACTIONS AND DECIMALS Lesson Proper What are fractions? A fraction represents a part if a whole. It is written as
a
b
Where: a ā numerator ā that tells us how many equal parts are being taken from the whole. b ā denominator ā that tells us how many equal parts the whole is to be divided. Example: A circle is being divided into four (4) equal parts. Three shaded parts are being taken from the whole. In fraction, we represent;
= 3 equal parts are being taken Āæ the whole Āæ
4 equal parts that represents thewhole
No part of this module may be reproduced in any form or by any means without any This module covers important operations of God, author of all truth; send Your Holy Spirit upon us; that we may be inspired to know You; and in knowing You, we may love you better; and in loving You Better, we may serve You the most. All this we ask, through Christ out Lord. Amen. The Introductory Prayer: Make the sign of the cross before and after the prayer. SESSION 1 LEARNING TARGET LEARNING ACTIVITIES By the end of the session, you will be able say , express rational numbers from fraction form to decimal form and vice versa. EXTRA MATH The horizontal line that divides the numerator and denominator is called as Fraction Bar ā
a
b
MORE EXAMPLES:
1.
ā 123 Ć· 124
2.
ā 1 Ć· 2
3.
ā 4 Ć· 2
P a g e | 4 CONVERTING DECIMAL TO FRACTION To convert a Decimal to a Fraction follow these steps:
- Write down the decimal divided by 1, like this: ā
- Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
- Simplify (or reduce) the fraction. Examples No part of this module may be reproduced in any form or by any means without any
MATH
When there is a whole number part, put the whole number aside and bring it back at the end: No part of this module may be reproduced in any form or by any means without any
Let us check your Enrichment Activity. Direction: Use the answer key below and do not forget to remind yourself that ā Honesty is the Best Policy ā. A. Express each fraction as a decimal. Use two (2) decimal places for your final answer. Show your solutionsā¦ B. Express each decimal as a fraction. Show your solutionsā¦ No part of this module may be reproduced in any form or by any means without any
ASSESSMENT
OPERATIONS OF FRACTIONS
INTRODUCTION
What are fractions? A fraction represents a part of a whole and it is written as
a
b
. The concept of fraction involves four (4) operations;
- Adding Fractions,
- Subtracting Fractions,
- Multiplying Fractions, and
- Dividing Fractions. LESSON PROPER No part of this module may be reproduced in any form or by any means without any
AGREEMENT
Now that you have already learned important concepts in expressin rational numbers from fraction form to decimal form and vice versa, your next task is to refresh your ideas about types and operations of fractions. God blessā¦ SESSION 2 LEARNING TARGET By the end of the session, you will be able say , I can perform operations of fractions. LEARNING ACTIVITIES
Step 2 : Make the denominators the same by finding the Least Common Multiple (LCM) of their denominators. This step is exactly the same as finding the Least Common Denominator (LCD). Step 3: Rewrite each fraction into its equivalent fraction with a denominator which is equal to the Least Common Multiple that you found in step #2. Step 4: Now, add or subtract the ānewā fractions from step #3. Always reduce the answer to its lowest terms. Example 1 Example 2 Given: Add. Step 1: The two fractions have denominators that are not equal. We need to make them equal by finding their Least Common Multiple that will serve as their Least Common Denominator (LCD). Step 2: Start by listing the multiples of each denominator, and identify the least number that is common to both of them. Step 3: The first fraction already has a denominator equal to the LCM = 15, and so we will leave it alone. The second fraction requires some adjusting to make its denominator equal to 15. Do that by multiplying its numerator and denominator by the number 3. Step 4: Once their denominators are equal, add the fractions by adding their numerators and then copying the common denominator. Given: Add Step 1: We canāt add the two fractions just yet because they have different denominators, namely 5 and 9. Begin by listing their multiples and pick the smallest number that is common to both. This will become their common denominator. Step 2: Start by listing the multiples of each denominator, and identify the least number that is common to both of them Step 3: Now, convert each fraction to an equivalent fraction with the LCM as its denominator, then proceed with regular addition. Step 4: Add and always look for the opportunity to reduce the answer to its lowest term. Example 3 Example 4 Given: Add Given: Subtract No part of this module may be reproduced in any form or by any means without any
Solution: Since the denominators 11 and 13 are both prime numbers, the least common denominator will be their product. Convert the current denominators of the two fractions into the LCD, and proceed with regular addition. Solution: To subtract these fractions with unequal denominators is very similar to addition. Make their denominators equal using the concept of least common multiple. Then subtract their numerators accordingly. Rewrite each fraction to its equivalent fraction with a denominator equal to the LCM = 30 , then subtract their numerators. Make sure to reduce your answer to the lowest term. No part of this module may be reproduced in any form or by any means without any
4) (ā^3
4 8)^ (
Checking Activity Directions: Check your own output and do not forget to remind yourself that āHonesty is the Best Policyā. Use the flipped answer key below. A. Add each given set of Fractions and express your final answer to its lowest term. Show your solutionsā¦ B. Subtract each given set of Fractions and express your final answer to its lowest term. Show your solutionsā¦
- 1
- (^) 7)
- (^) 8) Note: Observe that there are items having negative sign, you can use the idea of adding and subtracting integers from previous sessions. No part of this module may be reproduced in any form or by any means without any written permission from St. Catherineās College, Carcar City, Cebu
ASSESSMENT
AGREEMENT
Now that you have already learned important concepts in adding and subtracting fractions, your next task is to refresh your leassons learned about multiplying and dividing integers. God blessā¦
MULTIPLYING FRACTIONS
LESSON PROPER
To multiply fractions is as easy as following the 3 suggested steps below. Itās understood that no fraction can have a denominator of zero ā 0 ā because it will be an undefined term. Steps in Multiplying Fractions Given two fractions with nonzero denominators: Step 1: Multiply the numerators. This will be the numerator of the ānewā fraction. Step 2: Multiply the denominators. Step 3: Simplify the resulting fraction by reducing it to the lowest term, if needed. Example 1 Example 2 Given: multiply Solution: Step 1: Multiply the numerators of the fractions. Step 2: Similarly, multiply the denominators together. Given: multiply Solution: Step 1: Multiply the numerators of the fractions. Step 2: Multiply the denominators. Step 3: Simplify No part of this module may be reproduced in any form or by any means without any
SESSION 3 LEARNING TARGET
By the end of the session, you will be able say , I can perform operations of fractions. LEARNING ACTIVITIES
Example 1 Example 2 Given: divide Solution Step 1: The reciprocal of the divisor (second fraction) is Step 2: Multiply the dividend (first fraction) to the reciprocal of the divisor. Step 3: This is our final answer because the resulting fraction is already in its lowest term! Given: divide Solution Step 1: The reciprocal of the divisor (second fraction) is Step 2: Multiply the dividend (first fraction) to the reciprocal of the divisor. Step 3: Simplify to its lowest term. A. Multiply each given set of Fractions and express your final answer to its lowest term. Show your solutionsā¦ B. Divide each given set of Fractions and express your final answer to its lowest term. Show your solutionsā¦
No part of this module may be reproduced in any form or by any means without any
ENRICHMENT ACTIVITY
Checking Activity Directions: Check your own output and do not forget to remind yourself that āHonesty is the Best Policyā. Use the flipped answer key below. A. Multiply each given set of Fractions and express your final answer to its lowest term. Show your solutionsā¦ B. Divide each given set of Fractions and express your final answer to its lowest term. Show your solutionsā¦
No part of this module may be reproduced in any form or by any means without any written permission from St. Catherineās College, Carcar City, Cebu
ASSESSMENT
AGREEMENT
Now that you have already learned important concepts in multiplying and
THE CLOSING PRAYER
āGod is our refuge and strength, an ever-present help in trouble. Therefore, we will not fear, though the earth give way and the mountains fall into the heart of the sea...ā āPsalm 46:1-2 (NIV) End of Module 2 No part of this module may be reproduced in any form or by any means without any Signature of Learner over Printed Name/ Date Signature of Parent over Printed Name / Date Reference List Chua, Sy Tan, Rodriguez, Ubarro, Glorial, Kotah, Soaring 21st^ Century Mathematics : Phoenix www.chilimath.com www.mathisfun.com https://www.kutasoftware.com/freeipa.html
