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SUBTRACTING FRACTIONS AND MIXED NUMBERS
To find the difference of fractions, we subtract. We will first explore
subtracting fractions using fraction bars for fractions with like and unlike
denominators. Using fraction bars helps us to understand the meaning of
subtraction of fractions. We will then practice subtracting fractions with
paper and pencil.
Next we’ll look at subtracting mixed fractions using fraction bars and then
practice subtracting mixed fractions with paper and pencil.
Sometimes we must borrow to subtract mixed fractions. To borrow we will
first look at subtracting mixed fractions from whole numbers using fraction
bars and then practice subtracting mixed fractions from whole numbers with
paper and pencil.
On some occasions the mixed fraction from which that we are subtracting
includes a fraction that is smaller than the mixed fraction we are
subtracting. To understand this borrowing process, we will first look at
subtracting mixed fractions with borrowing using fraction bars and then
practice subtracting mixed fractions with borrowing with paper and pencil.
Subtracting Fractions Using Fraction Bars
Study the subtraction problems below. When subtracting fractions with unlike denominators, express the fractions into equivalent fractions with the same denominator, then subtract.
Subtracting Fractions
Example 1 : Find 11/12 – 5/12. Simplify, if necessary.
Thus, 11/12 – 5/12 = 1/2.
Example 2 : Find 7/8 – 5/6. Simplify, if necessary.
Thus, 7/8 – 5/6 = 1/24.
÷ =
= or say 6 divides into 24,4 times, 5 4 = 20.
= or say 8 divides into 24, 3 times, 7 3 = 21.
Find the LCD of 8 & 6.
List multiples of 8 8 = {8, 16, 24 , 32 ...} List multiples of 6 6 = {6, 12, 18, 24 , 30 ...}
The LCD is the first common factor in both sets.
LCD = 24
Subtracting Mixed Fractions Using Fraction Bars
Study the two subtraction problems below. To subtract fractions with unlike denominators, express the fractions into equivalent fractions with the same denominator.
1 8
1 8
1 8
1 8
1 8
1 8
1 8
1 8
1 8
1 8
1 8
1 8
Subtracting Mixed Fractions from Whole Numbers
Using Fraction Bars
Study the subtraction problem below. To subtract a mixed fraction from a whole number, express the whole number as 1 less and the rename the 1 as a fraction equivalent to one , and has the same denominator as the mixed number.
Subtracting Mixed Fractions from Whole Numbers
Borrow (7 = 6 + 1 = )
Find
Subtracting Mixed Fractions with Borrowing
Example 1 : Find 9 3/8 – 4 7/8. Simplify, if necessary.
Thus, 9 3/8 – 4 7/8 = 4 1/2.
Example 2 : Find 5 5/12 – 2 11/18. Simplify, if necessary.
Thus, 5 5/12 – 2 11/18 = 2 29/36.
reduces to
Borrow
A shortcut to find the numerator, 11 in , is to add the 3 + 8, in and write it over 8.
= or say 12 divides into 36, 3 times, 5 3 = 15.
Find the LCD of 12 & 18. List multiples of 18 18 = {18, 36 , 54 ...} List multiples of 12 12 = {12, 24, 36 , 48 ...} The LCD is the first common factor in both sets.
LCD = 36
Borrow
= or say 18 divides into 36, 2 times, 11 2 = 22.
A shortcut to find the numerator, 51, in , is to add the 15 + 36, in and write it over 36.
