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7.2B Solve problems (Decimals & Fractions) Adding decimals Ex1: 7 + 3.08 + 4.9 Pay attention to place value. You can give all decimal numbers the same place value by placing zeros to the right of the decimal point (by filling in zeros). Line up the numbers using the ones digits and the decimal points. Add in each place value position. Regroup when needed. 7.00 3.08 +4.90 14.98 Subtracting decimals Ex 2: 40-2.07 Place the larger decimal number on top. Pay attention to place value. Line up the numbers using the ones digits and the decimal points. Subtract in each place value position. Regroup when needed. 40.00 - 2.07 37.93 Multiply decimals To multiply decimals, first multiply the numbers as if they were whole numbers. (place the larger number of digits, not including zeros, on top) Then place the decimal point correctly in the product. To place the decimal point correctly in the product, count the total number of decimal places to the right of TEKSING TOWARD TAKS ©2009 7.2B Solve problems (Decimals & Fractions) the decimal point in the factors. The same number of decimal places should be to the right of the decimal in the product as is the total number of decimal places to the right of the decimal in the factors. Decimal points are not lined up in multiplication as you do in addition and subtraction. Before you multiply decimals, you should round to the nearest whole number and estimate the answer. This is a good way to be certain the decimal point has been correctly placed in the product. Ex 3: 2.8 x 0.785 Whole Number Multiplication 785 x 28 6280 +15700 21980 Divide decimals TEKSING TOWARD TAKS ©2009 Decimal Number Multiplication 0.785 3 decimals x 2.8 1 decimal 6280 4 decimals +15700 21980 = 2.1980 Estimate of Decimal Multiplication 2.8 ≈ 3 0.785 ≈ 1 3x1=3 Since I rounded up, my actual answer is less than 3. To divide a number by a decimal, count 7.2B Solve problems (Decimals & Fractions) the number of decimal places to the right of the decimal point in the divisor. Then move the decimal point to the right that many places in both the divisor and the dividend. Divide as you would for whole numbers. Then place the decimal point in the correct place in the quotient (i.e. over the decimal point in the dividend). Before you divide decimals, you should round to the nearest whole number and estimate the answer. This is a good way to be certain the decimal point has been placed in the correct place in the quotient. Decimal point in answer Ex 4: 2.7 9.18 1 1 2.7 9.18 = 3.4 2.7 9.18 81 0108 108 0 The answer is 3.4. TEKSING TOWARD TAKS ©2009 7.2B Solve problems (Decimals & Fractions) Add /Subtract Fractions If the fractions have the same denominator, add or subtract the numerators and use the same denominator. If the fractions have unlike denominators, rewrite them as equivalent fractions with a common denominator. Then add or subtract the numerators and 3 3 Ex 5: 2 4 8 use the common denominator. Since the Least Common Multiple of 4 and 8 is 8, the common denominator will be 8. For 4: 4, 8, 12, 16 For 8: 8, 16, 24 3 2 6 4 2 8 3 ? 4 8 3 ? 2 2 8 8 3 3 6 3 2 = 2 4 8 8 8 3 1 3 2 2 8 1 8 3 3 6 3 9 2 = 2 2 4 8 8 8 8 9 2 =? 8 1 8 9 8 1 1 8 9 or 1 8 8 8 8 1 2 TEKSING TOWARD TAKS ©2009 9 1 1 2 1 3 8 8 8 7.2B Solve problems (Decimals & Fractions) 1 8 The answer is 3 . 1 7 5 15 Ex 6: 6 Since the Least Common Multiple of 5 and 15 is 15, the common denominator will be 15. For 5: 5, 10, 15, 20 For 15: 15. 30, 45 6 1 3 3 6 6 5 3 15 1 5 15 7 15 15 7 1 7 15 1 15 You can’t subtract 3 from 7, so regroup. 6 3 15 3 18 5 5 15 15 15 15 7 15 The answer is 5 Multiply Fractions 11 . 15 Convert mixed numbers to a fraction by multiplying whole # with the denominator & add numerator, then the answer is put over the denominator. Convert whole numbers to a fraction by putting the # of 1. Simplify a numerator & a denominator if possible. When you multiply fractions, first multiply the numerators to get the numerator of TEKSING TOWARD TAKS ©2009 7.2B Solve problems (Decimals & Fractions) the product. Then multiply the denominators to get the denominator of the product. The fractions do not need a common denominator. Ex 7: 2 3 6 5 5 4 Since 6(5) + 2= 32, then 6 2 32 5 ;5= 5 5 1 32 5 3 5 1 4 Simplify both the numerator 5 & denominator 5 to 1 by dividing each by 5. Simplify both the 32 & 4 by dividing each by 4; then 32 becomes 8 & 4 becomes 1. 32 5 3 8 1 3 24 = 24 5 1 4 1 1 1 1 The answer is 24. Divide Fractions To divide a number by a fraction, multiply the number by the reciprocal of the divisor (i.e. the second fraction). Ex8: 3 33 and 5 5 1 2 the reciprocal of is , 2 1 13 1 33 2 66 then 5 66 = 13 5 5 1 5 -5 16 -15 1 1 The answer is 13 . 5 3 1 6 5 2 TEKSING TOWARD TAKS Since 6(5)+3 = 33, then 6 ©2009 7.2B Solve problems (Decimals & Fractions) TEKSING TOWARD TAKS ©2009