Question

5 which equation is true when $k = \frac{7}{4}$? a $1\frac{1}{5} - k = 0$ b $0.4 + k = \frac{9}{4}$ c $\frac{4}{7}k = 3$ d $k + \frac{5}{4} = 3$

Explanation:

Step1: Check Option A

Substitute \( k = \frac{7}{4} \) into \( 1\frac{1}{5}-k \). First, convert \( 1\frac{1}{5} \) to improper fraction: \( 1\frac{1}{5}=\frac{6}{5} \). Then \( \frac{6}{5}-\frac{7}{4}=\frac{24 - 35}{20}=-\frac{11}{20}
eq0 \). So A is false.

Step2: Check Option B

Substitute \( k = \frac{7}{4} \) into \( 0.4 + k \). Convert \( 0.4 \) to fraction: \( 0.4=\frac{2}{5} \). Then \( \frac{2}{5}+\frac{7}{4}=\frac{8 + 35}{20}=\frac{43}{20}=2.15 \), and \( \frac{9}{4}=2.25 \). Wait, miscalculation: \( \frac{2}{5}+\frac{7}{4}=\frac{8 + 35}{20}=\frac{43}{20}=2.15 \), \( \frac{9}{4}=2.25 \). Wait, no, let's recalculate: \( 0.4=\frac{2}{5} \), \( \frac{2}{5}+\frac{7}{4}=\frac{8 + 35}{20}=\frac{43}{20}=2.15 \), \( \frac{9}{4}=2.25 \). Wait, maybe I made a mistake. Wait, \( k=\frac{7}{4}=1.75 \), \( 0.4 + 1.75 = 2.15 \), \( \frac{9}{4}=2.25 \). No, that's not equal. Wait, maybe Option D? Wait, let's check Option D.

Step3: Check Option D

Substitute \( k=\frac{7}{4} \) into \( k+\frac{5}{4} \). \( \frac{7}{4}+\frac{5}{4}=\frac{12}{4}=3 \). So this equals 3. Let's confirm other options.

Step4: Check Option C

Substitute \( k = \frac{7}{4} \) into \( \frac{4}{7}k \). \( \frac{4}{7}\times\frac{7}{4}=1
eq3 \). So C is false.

Step5: Recheck Option B

Wait, \( 0.4=\frac{2}{5} \), \( \frac{2}{5}+\frac{7}{4}=\frac{8 + 35}{20}=\frac{43}{20}=2.15 \), \( \frac{9}{4}=2.25 \). Not equal. Option D: \( \frac{7}{4}+\frac{5}{4}=\frac{12}{4}=3 \), which matches the right - hand side. So D is true.

Answer:

D. \( k+\frac{5}{4}=3 \)