# Number Sense and Equations

2 1/3 - 1 1/4

Use at least one of the following three methods of subtracting these fractions:

(1) subtract the whole numbers and the fractional components separately, and then add the results

(2) convert the two numbers to their decimal equivalents, and then subtract the decimal equivalents

(3) convert any mixed numbers to improper fractions, and then subtract the fractions.

### Comments for Number Sense and Equations

 Sep 18, 2011 Subtract Mixed Numbers by: Staff ------------------------------------------------------------ Part II Convert the fraction 7/3 to a fraction with a denominator of 12 (the LCM) To accomplish this, multiply the fraction 7/3 by another fraction: 4/4. Note that 4/4 = 1, so you are actually multiplying by 1. The decimal value of the fraction 7/3 will not change. = (7/3)*(4/4) When multiplying two fractions, multiply the numerators together, and multiply the denominators together. = (7*4)/(3*4) = (28)/(12) = 28/12 7/3 = 28/12 Convert the fraction 5/4 to a fraction with a denominator of 12 (the LCM) To accomplish this, multiply the fraction 5/4 by another fraction: 3/3. Note that 3/3 = 1, so you are actually multiplying by 1. The decimal value of the fraction 5/4 will not change. = (5/4)*(3/3) = (5*3)/(4*3) = (15)/(12) = 15/12 5/4 = 15/12 Since the two fractions now have the same denominator, they can be easily subtracted. (Remember, only the numerators are subtracted. The denominator of 12 remains the same) Original problem 2 ⅓ - 1 ¼ Mixed numbers converted to improper fractions = 7/3 - 5/4 Improper fractions converted to fractions with the same denominator = 28/12 - 15/12 Subtract numerators = (28 - 15)/12 = 13/12 This fraction cannot be reduced, but it can be converted into a mixed number. To convert 13/12 to a mixed number, divide 13 by 12 = 13 ÷ 12 = 1, remainder 1 = 1 1/12 The final answer is: 1 1/12 (or 13/12 or ≈1.0833333) Check the answer with a calculator: 2 ⅓ - 1 ¼ = ????? = 2.333333… - 1.25 ≈ 1.0833333 Since 1.0833333 is the same answer obtained by converting 1 1/12 to its decimal equivalent, the answer of 1 1/12 is correct. Thanks for writing. Staff www.solving-math-problems.com

 Sep 18, 2011 Subtract Mixed Numbers by: Staff Part I The question: 2 1/3 - 1 1/4 The answer: 2 ⅓ - 1 ¼ = ????? There are three widely used methods of subtracting these fractions: (1) subtract the whole numbers and the fractional components separately, and then add the results (2 - 1) + (⅓ - ¼); (2) convert the two numbers to their decimal equivalents, and then subtract the decimal equivalents (2.3333 … - 1.25); (3) convert any mixed numbers to improper fractions, and then subtract the fractions. I’m going to demonstrate the third method. Begin by converting the mixed number 2 ⅓ into an improper fraction. (2*3 + 1 = 7, so the improper fraction will be 7/3) 2 ⅓ = 7/3 Next, convert the mixed number 1 ¼ into an improper fraction. (1*4 + 1 = 5, so the improper fraction will be 5/4) 1 ¼ = 5/4 Subtract the improper fractions 2 ⅓ - 1 ¼ = 7/3 - 5/4 These fractions cannot be subtracted directly unless the denominators of both fractions are the same. To convert both fractions to the same denominator, find the LCM (the least common multiple of the original denominators). 1st fraction: 7/3 1st fraction denominator: 3 Multiplies of 3: 3, 6, 9, 12, 15, 20 2nd fraction: 5/4 2nd fraction denominator: 4 Multiplies of 4: 4, 8, 12, 16, 20, 24 The least common multiple (LCM) is the smallest number which appears in both the multiples of 3 and the multiples of 4 The LCM = 12 ------------------------------------------------------------