Question

1. four friends are working together to paint a barn for one of their uncles. the table gives the fractional part of the job done by each of the four: maureen $\frac{1}{6}$, hank $\frac{3}{8}$, betsy $\frac{5}{24}$, carl $\frac{1}{4}$

a. who did most of the work?
b. find the difference in the portions done by hank and betsy.
c. find the portion of the work done by carl and maureen.
d. show that the sum of the four fractions is 1.

Explanation:

Part a

Step1: Convert to common denominator

Convert all fractions to 24 denominator:
$\frac{1}{6} = \frac{4}{24}$, $\frac{3}{8} = \frac{9}{24}$, $\frac{5}{24} = \frac{5}{24}$, $\frac{1}{4} = \frac{6}{24}$

Step2: Compare numerators

Largest numerator is 9, so $\frac{3}{8}$ is biggest.

Part b

Step1: Identify fractions to subtract

Hank: $\frac{3}{8}$, Betsy: $\frac{5}{24}$

Step2: Convert to common denominator

$\frac{3}{8} = \frac{9}{24}$

Step3: Subtract the fractions

$\frac{9}{24} - \frac{5}{24} = \frac{4}{24} = \frac{1}{6}$

Part c

Step1: Identify fractions to add

Carl: $\frac{1}{4}$, Maureen: $\frac{1}{6}$

Step2: Convert to common denominator

$\frac{1}{4} = \frac{3}{12}$, $\frac{1}{6} = \frac{2}{12}$

Step3: Add the fractions

$\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$

Part d

Step1: List all fractions

$\frac{1}{6}, \frac{3}{8}, \frac{5}{24}, \frac{1}{4}$

Step2: Convert to common denominator

$\frac{4}{24}, \frac{9}{24}, \frac{5}{24}, \frac{6}{24}$

Step3: Sum the fractions

$\frac{4+9+5+6}{24} = \frac{24}{24} = 1$

Answer:

a. Hank
b. $\frac{1}{6}$
c. $\frac{5}{12}$
d. The sum of the four fractions equals 1, as shown above.