Title: 3. Addition and subtraction of fractions
Course: Demonstrating STACK (v4.4.7)

Express the following, as a single fraction: \[[value]+[value].\]

Leave your answer in it's lowest terms in the form \(\frac{a}{b}\).
Feedback: The first task in adding fractions is to rewrite each as an equivalent fraction with the same denominators. You can guarantee this by multiplying the two denominators together or find the Lowest Common Multiple (LCM). In this example, \([value]+[value]\), the we need the lowest common multiple of [value] and [value] which is \([value]\). Next re-write the expression in the form: \[\frac{a}[value]+\frac{b}[value].\] To convert a fraction to an equivalent form we must multiply the denominator and numerator by the same number. In this case, multiply the numerator of the first fraction by \([value]\) and the numerator of the second by \([value]\). So we obtain: \[[value]+[value] = \frac[value][value]+\frac[value][value] = \frac[value][value]+\frac[value][value] = \frac[value][value].\] We may need to cancel any common factors in the numerator and denominator to obtain the answer in lowest terms \([value]\).

Express the following, as a single fraction: \[[value]-[value].\]

Leave your answer in it's lowest terms in the form \(\frac{a}{b}\).
Feedback: The first task in subtracting fractions is to rewrite each as an equivalent fraction with the same denominators. You can guarantee this by multiplying the two denominators together or find the Lowest Common Multiple (LCM). In this example, \([value]-[value]\), the we need the lowest common multiple of [value] and [value] which is \([value]\). Next re-write the expression in the form: \[\frac{a}[value]-\frac{b}[value].\] To convert a fraction to an equivalent form we must multiply the denominator and numerator by the same number. In this case, multiply the numerator of the first fraction by \([value]\) and the numerator of the second by \([value]\). So we obtain: \[[value]-[value] = \frac[value][value]-\frac[value][value] = \frac[value][value]-\frac[value][value] = \frac[value][value].\] We may need to cancel any common factors in the numerator and denominator to obtain the answer in lowest terms \([value]\).

Express the following, as a single fraction: \[[value]+[value].\]

Leave your answer in it's lowest terms in the form \(\frac{a}{b}\).
Feedback: In this case the denominators of the fractions are equal so you simply add the numerators to obtain the numerator and the denominator stays the same. The general rule is: \[\frac{a}{b} + \frac{c}{b} = \frac{a+c}{b} \] In this exmaple: \[[value]+[value] = \frac{[value]+[value]}[value] = [value].\]

Express the following, as a single fraction: \[[value]-[value].\]

Leave your answer in it's lowest terms in the form \(\frac{a}{b}\).
Feedback: When the denominators of the fractions are equal you simply subtract the numerators to obtain the numerator and the denominator stays the same. \[\frac{a}{b} - \frac{c}{b} = \frac{a-c}{b}. \] In this exmaple: \[ \frac[value][value] - \frac[value][value] = \frac{[value]-[value]}[value] = [value]. \]

Express the following, as a single fraction: \[[value]+[value].\]

Leave your answer in it's lowest terms in the form \(\frac{a}{b}\).
Feedback: The first task in adding fractions is to rewrite each as an equivalent fraction with the same denominators. You can guarantee this by multiplying the two denominators together or find the Lowest Common Multiple (LCM). In this case the second denominator is a multiple of the first, so the lowest common multiple of [value] and [value] is \([value]\). Next re-write the expression in the form: \[\frac{a}[value]+\frac{b}[value].\] To convert a fraction to an equivalent form we must multiply the denominator and numerator by the same number. In this case, there is nothing to do with the second fraction so we multiply the numerator of the first fraction by \([value]\). We obtain: \[[value]+[value] = \frac[value][value]+[value] = \frac[value][value]+\frac[value][value] = \frac[value][value].\] We may need to cancel any common factors in the numerator and denominator to obtain the answer in lowest terms \([value]\).

Express the following, as a single fraction: \[[value]-[value].\]

Leave your answer in it's lowest terms in the form \(\frac{a}{b}\).
Feedback: The first task in subtracting fractions is to rewrite each as an equivalent fraction with the same denominators. You can guarantee this by multiplying the two denominators together or find the Lowest Common Multiple (LCM). In this case the second denominator is a multiple of the first, so the lowest common multiple of [value] and [value] is \([value]\). Next re-write the expression in the form: \[\frac{a}[value]-\frac{b}[value].\] To convert a fraction to an equivalent form we must multiply the denominator and numerator by the same number. In this case, there is nothing to do with the second fraction so we multiply the numerator of the first fraction by \([value]\). We obtain: \[[value]-[value] = \frac[value][value]-[value] = \frac[value][value]-\frac[value][value] = \frac[value][value].\] We may need to cancel any common factors in the numerator and denominator to obtain the answer in lowest terms \([value]\).