By Stephen L Slavin
Read or Download Math essentials : conquer fractions, decimals, and percentages--get the right answer every time! PDF
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Extra info for Math essentials : conquer fractions, decimals, and percentages--get the right answer every time!
Example text
1 5 + 2 5 + 2 5 =1 2. 1 9 + 2 9 + 3 9 = 6 9 = 2 3 3. 1 8 + 1 8 + 2 8 + 2 8 = 6 8 = 3 4 4 2 = 2. ADDING FRACTIONS 4. 2 12 + 3 12 + 1 12 + 2 12 = 8 12 = 2 3 5. 1 20 + 3 20 + 2 20 + 4 20 + 1 20 = 11 20 6. 2 50 + 3 50 + 7 50 + 4 50 + 8 50 = 24 50 = 12 25 Did you reduce all your fractions to their lowest possible terms? If you left problem 1 at 55 , is it wrong? No, but by convention we always reduce our fractions as much as possible. Indeed, there are mathematicians who can’t go to sleep at night unless they’re sure that every fraction has been reduced to its lowest possible terms.
3 10 12. 3 8 + + 2 5 = 3 10 5 12 = 3×3 8×3 + = 2×2 5×2 + 3 12 + 4 12 = 7 12 1 6 = 3 6 = 1 2 = 2 12 + 3 12 = 5 12 = 5 20 + 8 20 = 13 20 + = 3 10 + 4 10 = 7 10 5×2 12 × 2 = 9 24 + 10 24 = 19 24 In problem 9, if you did it the way I did it below, it’s okay. By not finding the lowest common denominator, you needed to do an extra step— which doesn’t matter if you ended up with the right answer. 1 6 46 + 1 4 = 1×4 6×4 + 1×6 4×6 = 4 24 + 6 24 = 10 24 = 5 12 ADDING FRACTIONS ADDING SEVERAL FRACTIONS TOGETHER So far we’ve been adding two fractions.
17 20 – 9 20 = 4. 5 12 – 2 12 = 5. 17 19 – 4 19 = 6. 9 10 – 4 10 = Solutions 1. 3 5 – 2 5 = 1 5 2. 8 9 – 1 9 = 7 9 3. 17 20 – 9 20 = 8 20 = 2 5 4. 5 12 – 2 12 = 3 12 = 1 4 5. 17 19 – 4 19 = 13 19 6. 9 10 – 4 10 = 5 10 = 1 2 SUBTRACTING FRACTIONS WITH UNLIKE DENOMINATORS Let’s step back for a minute and take stock. When we added fractions with different denominators, we found their common denominators and added. We do the same thing, then, when we do subtraction with fractions having different denominators.