Question

practical math cp
directions: find the sum or difference of the mixed numbers. please keep your answer as a simplified
fraction. (hint: you must convert the mixed numbers to improper fractions! magic c! if necessary, you will
need common denominators.)

1. $2\frac{1}{5} + 19\frac{2}{5}$ (3 points)

a.) $\frac{108}{5}$
b.) $\frac{21}{5}$
c.) $\frac{17}{5}$
d.) $\frac{2}{5}$

1. $21\frac{4}{5} - 19\frac{1}{5}$ (3 points)

a) $2\frac{3}{0}$
b.) $2\frac{3}{5}$
c.) $40\frac{3}{5}$
d.) $40\frac{5}{5}$

1. $11\frac{1}{7} + 9\frac{3}{21}$ (5 points)

1. $33\frac{1}{2} - 8\frac{2}{5}$ (5 points)

Explanation:

Question 33:

Step1: Convert mixed numbers to improper fractions

For \(2\frac{1}{5}\), multiply the whole number (2) by the denominator (5) and add the numerator (1): \(2\times5 + 1 = 11\), so \(2\frac{1}{5}=\frac{11}{5}\).
For \(19\frac{2}{5}\), multiply 19 by 5 and add 2: \(19\times5 + 2 = 97\), so \(19\frac{2}{5}=\frac{97}{5}\).

Step2: Add the improper fractions

Since the denominators are the same, add the numerators: \(\frac{11}{5}+\frac{97}{5}=\frac{11 + 97}{5}=\frac{108}{5}\).

Step1: Subtract the mixed numbers (or convert to improper fractions)

Since the fractions have the same denominator, we can subtract the whole numbers and the fractions separately.
Whole numbers: \(21 - 19 = 2\).
Fractions: \(\frac{4}{5}-\frac{1}{5}=\frac{4 - 1}{5}=\frac{3}{5}\).

Step2: Combine the results

Combine the whole number and the fraction: \(2+\frac{3}{5}=2\frac{3}{5}\).

Step1: Convert mixed numbers to improper fractions (or adjust denominators)

For \(11\frac{1}{7}\), convert to improper fraction: \(11\times7 + 1 = 78\), so \(11\frac{1}{7}=\frac{78}{7}\).
For \(9\frac{3}{21}\), simplify the fraction: \(\frac{3}{21}=\frac{1}{7}\), so \(9\frac{3}{21}=9\frac{1}{7}\). Convert to improper fraction: \(9\times7 + 1 = 64\), so \(9\frac{1}{7}=\frac{64}{7}\).

Step2: Add the improper fractions

Add the numerators (denominators are the same): \(\frac{78}{7}+\frac{64}{7}=\frac{78 + 64}{7}=\frac{142}{7}\).

Step3: Convert back to mixed number

Divide 142 by 7: \(7\times20 = 140\), so \(142\div7 = 20\) with a remainder of 2. Thus, \(\frac{142}{7}=20\frac{2}{7}\).

Answer:

a) \(\frac{108}{5}\)

Question 34: