Question

kareem is finding the sum of \\(\frac{3}{20}\\) and \\(\frac{5}{4}\\). his work is shown. \\(\frac{3}{20} + \frac{5}{4} = \frac{3}{20} + \frac{5}{20} = \frac{8}{20}\\) is kareem’s work correct? a yes. \\(\frac{3}{20} + \frac{5}{4} = \frac{8}{20}\\). b no, because 20 is not a common denominator for \\(\frac{3}{20}\\) and \\(\frac{5}{4}\\). c no, because \\(\frac{5}{4}\\) is not equivalent to \\(\frac{5}{20}\\). d no, because \\(\frac{3}{20} + \frac{5}{20}\\) does not equal \\(\frac{8}{20}\\).

Explanation:

Step1: Recall fraction addition rule

To add fractions, we need a common denominator. For \(\frac{3}{20}\) and \(\frac{5}{4}\), we convert \(\frac{5}{4}\) to a fraction with denominator 20. Multiply numerator and denominator of \(\frac{5}{4}\) by 5: \(\frac{5\times5}{4\times5}=\frac{25}{20}\), not \(\frac{5}{20}\).

Step2: Analyze Kareem's work

Kareem wrote \(\frac{3}{20}+\frac{5}{4}=\frac{3}{20}+\frac{5}{20}\), which is wrong because \(\frac{5}{4}
eq\frac{5}{20}\). Then he added to get \(\frac{8}{20}\), but the correct addition should be \(\frac{3}{20}+\frac{25}{20}=\frac{28}{20}\). So his work is incorrect because \(\frac{5}{4}\) is not equivalent to \(\frac{5}{20}\), which matches option C.

Answer:

C. No, because \(\frac{5}{4}\) is not equivalent to \(\frac{5}{20}\).