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Write two fractions between each of the following pairs:

a. [tex]\(\frac{2}{3}, \frac{4}{5}\)[/tex]
b. [tex]\(\frac{7}{9}, \frac{10}{23}\)[/tex]
c. [tex]\(\frac{1}{5}, 1\)[/tex]
d. [tex]\(1 \frac{3}{7}, 5 \frac{5}{8}\)[/tex]
e. [tex]\(1 \frac{1}{3}, 2 \frac{1}{2}\)[/tex]
f. [tex]\(5 \frac{1}{5}, 5 \frac{1}{10}\)[/tex]



Answer :

GinnyAnswer
Certainly! Let's identify two fractions between each pair of given fractions step-by-step.

### a. Between [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex]

1. Convert [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex] to fractions with a common denominator (optional).
2. Calculate fractions between these two.
3. The resulting two fractions are:
[tex]\[ \frac{22}{45} \quad \text{and} \quad \frac{44}{45} \][/tex]

### b. Between [tex]\(\frac{7}{9}\)[/tex] and [tex]\(\frac{10}{23}\)[/tex]

1. Convert [tex]\(\frac{7}{9}\)[/tex] and [tex]\(\frac{10}{23}\)[/tex] to fractions with a common denominator (optional).
2. Calculate fractions between these two.
3. The resulting two fractions are:
[tex]\[ \frac{251}{621} \quad \text{and} \quad \frac{502}{621} \][/tex]

### c. Between [tex]\(\frac{1}{5}\)[/tex] and [tex]\(1 \frac{1}{5}\)[/tex] (which is [tex]\(\frac{6}{5}\)[/tex])

1. Convert [tex]\(\frac{1}{5}\)[/tex] and [tex]\(\frac{6}{5}\)[/tex] to fractions with a common denominator (optional).
2. Calculate fractions between these two.
3. The resulting two fractions are:
[tex]\[ \frac{7}{15} \quad \text{and} \quad \frac{14}{15} \][/tex]

### d. Between [tex]\(1 \frac{3}{7}\)[/tex] (which is [tex]\(\frac{10}{7}\)[/tex]) and [tex]\(5 \frac{5}{8}\)[/tex] (which is [tex]\(\frac{45}{8}\)[/tex])

1. Convert [tex]\(1 \frac{3}{7}\)[/tex] and [tex]\(5 \frac{5}{8}\)[/tex] to improper fractions: [tex]\(\frac{10}{7}\)[/tex] and [tex]\(\frac{45}{8}\)[/tex].
2. Calculate fractions between these two.
3. The resulting two fractions are:
[tex]\[ \frac{395}{168} \quad \text{and} \quad \frac{395}{84} \][/tex]

### e. Between [tex]\(1 \frac{1}{3}\)[/tex] (which is [tex]\(\frac{4}{3}\)[/tex]) and [tex]\(2 \frac{1}{2}\)[/tex] (which is [tex]\(\frac{5}{2}\)[/tex])

1. Convert [tex]\(1 \frac{1}{3}\)[/tex] and [tex]\(2 \frac{1}{2}\)[/tex] to improper fractions: [tex]\(\frac{4}{3}\)[/tex] and [tex]\(\frac{5}{2}\)[/tex].
2. Calculate fractions between these two.
3. The resulting two fractions are:
[tex]\[ \frac{23}{18} \quad \text{and} \quad \frac{23}{9} \][/tex]

### f. Between [tex]\(5 \frac{1}{5}\)[/tex] (which is [tex]\(\frac{26}{5}\)[/tex]) and [tex]\(5 \frac{1}{10}\)[/tex] (which is [tex]\(\frac{51}{10}\)[/tex])

1. Convert [tex]\(5 \frac{1}{5}\)[/tex] and [tex]\(5 \frac{1}{10}\)[/tex] to improper fractions: [tex]\(\frac{26}{5}\)[/tex] and [tex]\(\frac{51}{10}\)[/tex].
2. Calculate fractions between these two.
3. The resulting two fractions are:
[tex]\[ \frac{103}{30} \quad \text{and} \quad \frac{103}{15} \][/tex]

These are the two fractions between each of the given pairs.

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