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A step-by-step guide on how to subtract fractions and mixed numbers, including the use of fraction bars, finding the LCD, and borrowing. It covers both like and unlike denominators, as well as subtracting mixed fractions from whole numbers.
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Study the subtraction problems below. When subtracting fractions with unlike denominators, express the fractions into equivalent fractions with the same denominator, then subtract.
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
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
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.
Borrow (7 = 6 + 1 = )
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.