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Operations On Fractions-Lesson 1

Operations on Fractions can be simplified by finding the greatest common factor of the numerator and denominator. Fractions can be added or subtracted by finding a common denominator or by converting fractions to equivalent fractions with the same denominator. Mixed numbers are added or subtracted by converting them to equivalent fractions with a common denominator and then adding or subtracting the fractions and whole numbers. Whole numbers can be converted to fractions when subtracting fractions or mixed numbers.

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Mye Beltran
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418 views18 pages

Operations On Fractions-Lesson 1

Operations on Fractions can be simplified by finding the greatest common factor of the numerator and denominator. Fractions can be added or subtracted by finding a common denominator or by converting fractions to equivalent fractions with the same denominator. Mixed numbers are added or subtracted by converting them to equivalent fractions with a common denominator and then adding or subtracting the fractions and whole numbers. Whole numbers can be converted to fractions when subtracting fractions or mixed numbers.

Uploaded by

Mye Beltran
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Operations on Fractions

Recall!
▧ Simplifying Fractions
○ The fraction is in its simplest form,
if the greatest common factor of
the numerator and the
denominator is 1.

2
Simplify the following:
𝟑𝟔 36 ÷ 4 9 9÷3 𝟑
= = =
𝟒𝟖 48 ÷ 4 12 12 ÷ 3 = 𝟒

𝟏𝟕 𝟐
= 17 ÷ 3 = 5 𝑟𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟 2 = 𝟓
𝟑 𝟑

3
Simplify the following:
𝟏𝟐
=𝟒
𝟑

𝟏𝟓
=𝟏
𝟏𝟓

4
1.
Adding and Subtracting
Fractions and Mixed
Numbers
5
Fractions with the Same Denominator
🔑
▧ If the fractions to be added or subtracted
have the same denominator, simply add or
subtract the numerator, then copy the
denominator.

6
Examples:
𝟐 𝟑 2+3 𝟓
+ =
6
=
𝟔 𝟔 𝟔

𝟕 𝟒 7−4 𝟑
− =
10
=
𝟏𝟎 𝟏𝟎 𝟏𝟎

7
Examples:

𝟓 𝟑 𝟕 5−3+7 9 𝟑
− + = = =
𝟓
𝟏𝟓 𝟏𝟓 𝟏𝟓 15 15

8
Fractions with the Different Denominator
🔑
▧ To add or subtract fractions with different
denominators, change them first to
equivalent fractions with the same
denominators.

9
Example 4:
𝟓 𝟐 LCD: 9 x 5 = 45
+ = 5 5 × 5 25
𝟗 𝟓 = =
9 9 × 5 45
25 18 𝟒𝟑 2 2 × 9 18
+ = = =
5 5 × 9 45
45 45 𝟒𝟓

10
Example 5:
𝟗 𝟑 LCD: 10
− = 9 9
𝟏𝟎 𝟓 =
10 10
9 6 𝟑 3 3×2 6
− = = =
5 5 × 2 10
10 10 𝟏𝟎

11
Mixed Numbers
🔑
▧ To add mixed numbers, express the numbers such
that the fractions have common denominator. Add
the fractions, then the whole numbers. Simplify the
answers.
▧ To subtract mixed numbers, express the numbers
such that the fractions have common denominator.
Subtract the fractions, then the whole numbers.
Simplify the answers.

12
Mixed Numbers
🔑
▧ To subtract a mixed number or a fraction from a
whole number, rename first the whole numbers to an
equivalent fraction to the given number, then
subtract.
▧ When subtracting mixed numbers and the fractional
part of the minuend is smaller than the subtrahend,
rename first the minuend.

13
Example 6:
𝟑 𝟐 LCD: 15
𝟑 +𝟔 = 3 9
𝟓 𝟑 3
5
=3
15

2 10
6 =6
3 15

14
Example 7:
𝟐 𝟏 LCD: 6
𝟔 −𝟒 = 2 4
𝟑 𝟐 6 =6
3 6

4 3 𝟏 1 3
4 =4
6 −4 = 𝟐 2 6
6 6 𝟔

15
Example 8:
𝟏 Rename the whole number
𝟖−𝟒 = 3
𝟑 8=7
3

3 1 𝟐
7 −4 = 𝟑
3 3 𝟑

16
Example 9:
𝟏 𝟒 LCD: 15
𝟏𝟐 − 𝟕 = Take 1 from 12 and rename as
15
the add to
5
.
𝟑 𝟓 1 5 20
15 15

12 = 12 = 11
3 15 15
20 12 𝟖
11 − 7 = 𝟒 4 12
15 15 𝟏𝟓 7 =7
5 15

17
Thanks!

18

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