Math Taylor Tutorial Homework: Chapter 1

Find the product of the mixed numbers 18 1/4 and 3 2/5.

1241/20 or 62 1/20 irst, multiply the whole numbers (18 and 3) by the denominators of their respective fractions (4 and 5). Add these results to the numerators of their respective fractions (1 and 2), and write the resulting quantities (73 and 17) in the numerators of the improper fractions, keeping the same denominators. Look to see if either numerator can be factored by the denominator of the other fraction. Then multiply the resulting numerators (73 × 17) by their denominators (4 × 5). Divide the numerator by the denominator to express the answer as a mixed number.

Find the product of the mixed numbers 2 4/7 and 8 4/9.

152/7 or 21 5/7 First, multiply the whole numbers (2 and 8) by the denominators of their respective fractions (7 and 9). Add these results to the numerators of their respective fractions (4 and 4), and write the resulting quantities (18 and 76) in the numerators of the improper fractions, keeping the same denominators. Look to see if either numerator can be factored by the denominator of the other fraction (18 ÷ 9 = 2). Then multiply the resulting numerators (2 × 76) by their denominators (7 × 1). Divide the numerator by the denominator to express the answer as a mixed number.

Find the sum of the fractions 3/7 and 1/3

16/21 Because the denominators are different, multiply each denominator by the value that will produce the LCD (7 × 3 = 3 × 7 = 21). Then rewrite each fraction in terms of the LCD by multiplying the numerator by the same factor ((3 × 3)/(7 × 3) and (1 × 7)/(3 × 7)). Finally, add the numerators (9 + 7) to obtain the sum.

Three decreasing doses of a certain medication are administered to a patient. If the doses are 2/3 g, 1/2 g and 1/4 g, how many milligrams of this medication are administered altogether?

17/12 g or 1 5/12 g Because the denominators are different, multiply each denominator by the value that will produce the LCD (3 × 4 = 2 × 6 = 4 × 3 = 12). Then rewrite each fraction in terms of the LCD by multiplying the numerator by the same factor ((2 × 4)/(3 × 4), (1 × 6)/(2 × 6), and (1 × 3)/(4 × 3)). Finally, add the numerators (8 + 6 + 3) to obtain the sum. Divide the numerator by the denominator to express the answer as a mixed number.

A drug is administered as a solution with a concentration of 16 2/3 mg/ml. How much medication does a patient receive with a 3 1/2 ml injection?

175/3 mg or 58 1/3 mg First, multiply the whole numbers (16 and 3) by the denominators of their respective fractions (3 and 2). Add these results to the numerators of their respective fractions (2 and 1), and write the resulting quantities (50 and 7) in the numerators of the improper fractions, keeping the same denominators. Look to see if either numerator can be factored by the denominator of the other fraction (50 ÷ 2 = 25). Then multiply the resulting numerators (25 × 7) by their denominators (3 × 1). Divide the numerator by the denominator to express the answer as a mixed number.

The fraction of an alcohol solution that is water is 18/63 Reduce this fraction to its lowest terms.

2/7 Write the numerator as multiples of prime numbers (18 = 2 × 3 × 3). Write the denominator as multiples of prime numbers (63 = 7 × 3 × 3). Factor out the common terms (3 × 3), and evaluate the remaining terms (2/7).

If a patient weighs 208 1/2 pounds, and the conversion factor to kilograms is 2 1/5 pounds per kilogram, what is the patient's weight expressed in kilograms?

2085/22 kg or 94 17/22 kg

An IV infusion delivers a total of 24 1/2 mg of medication. If it takes 2 1/3 hours for all of the medication to be administered, how much medication is delivered each hour?

21/2 mg/h or 10 1/2 mg/h

A patient drinks 2 1/2 cups of water. Later, the same patient drinks 1 2/3 cups and 3 1/6 cups. What is the total amount of water that the patient drinks?

22/3 cups or 7 1/3 cups First, multiply the whole numbers (2, 1, and 3) by the denominators of their respective fractions (2, 3, and 6). Add these results to the numerators of their respective fractions (1, 2, and 1), and write the resulting quantities (5, 5, and 19) in the numerators of the improper fractions, keeping the same denominators. Because the denominators are different, multiply each denominator by the value that will produce the LCD (2 ´ 3 = 3 × 2 = 6 × 1 = 6). Rewrite each fraction in terms of the LCD by multiplying the numerator by the same factor ((5 × 3)/(2 × 3), (5 × 2)/(3 × 2), and (19 × 1)/(6 × 1)). Finally, add the numerators (15 + 10 + 19) to obtain the sum. Divide the numerator by the denominator to express the answer as a mixed number.

Find the product of the mixed numbers 3 2/3 and 11 1/3

374/9 or 41 5/9 First, multiply the whole numbers (3 and 11) by the denominators of their respective fractions (3 and 3). Add these results to the numerators of their respective fractions (2 and 1), and write the resulting quantities (11 and 34) in the numerators of the improper fractions, keeping the same denominators. Look to see if either numerator can be factored by the denominator of the other fraction. Then multiply the resulting numerators (11 × 34) by their denominators (3 × 3). Divide the numerator by the denominator to express the answer as a mixed number.

A bottle contains 137 tablets, each of which is scored so that it can be divided into two. If a dose consists of 1 1/2 tablets, how many doses does the bottle contain?

274/3 doses or 91 1/3 doses

An IV infusion delivers 5 2/3 mg of medication each minute. How much medication does the patient receive in 8 1/2 minutes?

289/6 mg or 48 1/6 mg First, multiply the whole numbers (5 and 8) by the denominators of their respective fractions (3 and 2). Add these results to the numerators of their respective fractions (2 and 1), and write the resulting quantities (17 and 17) in the numerators of the improper fractions, keeping the same denominators. Look to see if either numerator can be factored by the denominator of the other fraction. Then multiply the resulting numerators (17 × 17) by their denominators (3 × 2). Divide the numerator by the denominator to express the answer as a mixed number.

An iodine solution has a concentration of Picture 94 1/5 g of iodine for every liter of solution. When converted to an improper fraction, this fraction equals

471/5 Multiply the whole number (94) by the denominator (5), add this to the numerator (1), and write this quantity in the numerator of the improper fraction, keeping the same denominator.

Find the quotient for 9 divided by 2 5/6.

54/17 or 3 3/17

Find the quotient for 7 3/5 divided by 3 1/3

57/25 or 2 7/25

Find the sum of the mixed numbers 2 3/5 and 3 4/7

6 6/35 First, multiply the whole numbers (2 and 3) by the denominators of their respective fractions (5 and 7). Add these results to the numerators of their respective fractions (3 and 4), and write the resulting quantities (13 and 25) in the numerators of the improper fractions, keeping the same denominators. Because the denominators are different, multiply each denominator by the value that will produce the LCD (5 × 7 = 7 × 5 = 35). Rewrite each fraction in terms of the LCD by multiplying the numerator by the same factor ((13 × 7)/(5 × 7) and (25 × 5)/(7 × 5)). Finally, add the numerators (91 + 125) to obtain the sum. Divide the numerator by the denominator to express the answer as a mixed number.

A tablet contains 13 1/3 mg of medication. If you give a patient a total of 4 1/2 tablets a day, how many milligrams of medication are given the patient each day?

60 mg First, multiply the whole numbers (13 and 4) by the denominators of their respective fractions (3 and 2). Add these results to the numerators of their respective fractions (1 and 1), and write the resulting quantities (40 and 9) in the numerators of the improper fractions, keeping the same denominators. Look to see if either numerator can be factored by the denominator of the other fraction (40 ÷ 2 = 20; 9 ÷ 3 = 3). Then multiply the resulting numerators (20 × 3) by their denominators (1 × 1).

Find the quotient for 25 1/6 divided by 3/8.

604/9 or 67 1/9

A solution contains 56 ml of an active ingredient for every 80 ml of solution. Reduce the fraction Picture to its lowest terms.

7/10 Write the numerator as multiples of prime numbers (56 = 2 × 2 × 2 × 7). Write the denominator as multiples of prime numbers (80 = 2 × 2 × 2 × 2 × 5). Factor out the common terms (2 × 2 × 2), and evaluate the remaining terms (7/(2 × 5) = 7/10).

The dosage of 65 mg over an 8 hour period may be written as the improper fractionPicture. When converted to a mixed number, this fraction equals 65/8

8 1/8 Divide 65 by 8 to obtain the whole number (8) and fraction (1/8).

During a day, a patient receives 5/4 g of a certain medication. Later that same day, 3/4 g and 1/4 g of the same medication are administered. How many grams of this medication are administered altogether?

9/4 g or 2 1/4 g Because the denominators are the same (4), add the numerators (5 + 3 + 1), and divide the numerator by the denominator to express the answer as a mixed number.

Find the sum of the fractions 7/22 and 9/22

Because the denominators are the same (22), add the numerators (7 + 9), and divide out common factors (2) to simplify the answer.