Subtracting Fractions

Grade 9 Applied MathematicsM. M. Couturier

Subtracting Fractions

• Like in addition, fractions can only be subtracted when the denominators are identical. Hence the first step in subtracting fractions is simply to ask: “Are the denominators the same?”

Subtracting Fractions

• Let us take the following example:

• 2 - 2• 3 5

• The denominators are not the same; one is 3 and the other is 5.

Subtracting Fractions

• If they are not the same, we must make them the same WITHOUT changing the number. The second step is therefore to multiply the fractions by 1, such that the denominators become equal.

Subtracting Fractions

• We essentially want to find the lowest common denominator. In this case, 3x5 = 15.

• 2 - 2• 3 5

Subtracting Fractions

• We will therefore multiply (2/3) by (5/5). Recall that (5/5) = 1, hence we are not changing the number. We will also multiply (2/5) by (3/3). Also note that (3/3) = 1 so we are, again, not changing the number.

Subtracting Fractions

• What effect does this have: • (5)(2) - (2)(3)

(5)(3) (5)(3)

• becomes: • 10 - 6

15 15

Subtracting Fractions

• 10 - 6 15 15

• Now that the denominators are the same we can subtract the numerators.

• 4 15

Subtracting Fractions

• Let’s do another example: • 2 - 1

3 4 • Here, the lowest common is 4x3=12.

So we will multiply each fraction by 1.

Subtracting Fractions

• What effect does this have: • (4)(2) - (1)(3)

(4)(3) (4)(3)

• becomes: • 8 - 3

12 12

Subtracting Fractions

• 8 - 3 12 12

• Hence, • 5

12

Subtracting Fractions

• ... and another • 3 - 1

5 10 • In this case, the lowest common

denominator is 10 because 2x5 = 10, so 10 does not need to be modified in any way.

Subtracting Fractions

• What effect does this have: • (2)(3) - 1

(2)(5) 10• 6 - 1

10 10• 5 or ½

10

THE BLUEPRINT

• The following will work for ALL subtractions of proper fractions.

THE BLUEPRINT • Let us recall our strand in algebra:• a - c

b d• The lowest common denominator is

therefore bd; hence, • (d)(a) - (c)(b)

(d)(b) (d)(b)

THE BLUEPRINT • ad - bc

bd bd• ad - bc

bd

WWW • Let us visit the world wide web:

• http://www.math.com/school/subject1/practice/S1U4L3/S1U4L3Pract.html

WWW • Let us visit the world wide web:

• http://www.aaamath.com/fra57b-subfractld.html

WWW • Let us visit the world wide web:

• http://www.aaamath.com/fra66l-subfracud.html

WWW • For those who need visuals:

http://www.visualfractions.com/subtract.htm