Question

2 salvador added up on a number line to find \\(\frac{4}{5} - \frac{5}{10}\\). use equivalent fractions and an addition equation to show how salvador found the difference. \\(\frac{4}{5}\\) \\(-\frac{5}{10}\\) — curriculum associates, llc copying is not permitted. lesson 13 subtractio

Explanation:

Step1: Find equivalent fraction

To subtract \(\frac{4}{5}\) and \(\frac{5}{10}\), we first find an equivalent fraction for \(\frac{4}{5}\) with denominator 10. Multiply numerator and denominator of \(\frac{4}{5}\) by 2: \(\frac{4\times2}{5\times2}=\frac{8}{10}\)

Step2: Subtract the fractions

Now we have \(\frac{8}{10}-\frac{5}{10}\). To show the addition equation (related to subtraction as \(a - b = c\) implies \(b + c = a\)), we know that \(\frac{5}{10}+x=\frac{8}{10}\), so \(x = \frac{8}{10}-\frac{5}{10}=\frac{3}{10}\). The subtraction equation is \(\frac{8}{10}-\frac{5}{10}=\frac{3}{10}\) and the addition equation is \(\frac{5}{10}+\frac{3}{10}=\frac{8}{10}\) (which is equivalent to \(\frac{4}{5}\)).

Answer:

Subtraction: \(\frac{4}{5}-\frac{5}{10}=\frac{8}{10}-\frac{5}{10}=\frac{3}{10}\); Addition: \(\frac{5}{10}+\frac{3}{10}=\frac{8}{10}=\frac{4}{5}\)