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Answer :
We want to add the mixed numbers
[tex]$$
1\frac{1}{8} \quad \text{and} \quad 1\frac{4}{5}.
$$[/tex]
Step 1. Convert the fractional parts to an equivalent fraction with a common denominator.
A common denominator for [tex]$8$[/tex] and [tex]$5$[/tex] is [tex]$40$[/tex]. We convert each fractional part as follows:
- For [tex]$\frac{1}{8}$[/tex]:
[tex]$$
\frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40}.
$$[/tex]
- For [tex]$\frac{4}{5}$[/tex]:
[tex]$$
\frac{4}{5} = \frac{4 \times 8}{5 \times 8} = \frac{32}{40}.
$$[/tex]
Step 2. Rewrite the mixed numbers with the new fractional parts.
Now the mixed numbers become:
[tex]$$
1\frac{1}{8} = 1\frac{5}{40} \quad \text{and} \quad 1\frac{4}{5} = 1\frac{32}{40}.
$$[/tex]
Step 3. Add the whole parts and the fractional parts separately.
- The whole number parts are [tex]$1$[/tex] and [tex]$1$[/tex], so:
[tex]$$
1 + 1 = 2.
$$[/tex]
- The fractional parts are [tex]$\frac{5}{40}$[/tex] and [tex]$\frac{32}{40}$[/tex]:
[tex]$$
\frac{5}{40} + \frac{32}{40} = \frac{5+32}{40} = \frac{37}{40}.
$$[/tex]
Step 4. Combine the sum of the whole parts and the fractional parts.
The result is:
[tex]$$
2\frac{37}{40}.
$$[/tex]
Thus, the missing numerator in the expression
[tex]$$
2\frac{\square}{40}
$$[/tex]
is [tex]$37$[/tex].
[tex]$$
1\frac{1}{8} \quad \text{and} \quad 1\frac{4}{5}.
$$[/tex]
Step 1. Convert the fractional parts to an equivalent fraction with a common denominator.
A common denominator for [tex]$8$[/tex] and [tex]$5$[/tex] is [tex]$40$[/tex]. We convert each fractional part as follows:
- For [tex]$\frac{1}{8}$[/tex]:
[tex]$$
\frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40}.
$$[/tex]
- For [tex]$\frac{4}{5}$[/tex]:
[tex]$$
\frac{4}{5} = \frac{4 \times 8}{5 \times 8} = \frac{32}{40}.
$$[/tex]
Step 2. Rewrite the mixed numbers with the new fractional parts.
Now the mixed numbers become:
[tex]$$
1\frac{1}{8} = 1\frac{5}{40} \quad \text{and} \quad 1\frac{4}{5} = 1\frac{32}{40}.
$$[/tex]
Step 3. Add the whole parts and the fractional parts separately.
- The whole number parts are [tex]$1$[/tex] and [tex]$1$[/tex], so:
[tex]$$
1 + 1 = 2.
$$[/tex]
- The fractional parts are [tex]$\frac{5}{40}$[/tex] and [tex]$\frac{32}{40}$[/tex]:
[tex]$$
\frac{5}{40} + \frac{32}{40} = \frac{5+32}{40} = \frac{37}{40}.
$$[/tex]
Step 4. Combine the sum of the whole parts and the fractional parts.
The result is:
[tex]$$
2\frac{37}{40}.
$$[/tex]
Thus, the missing numerator in the expression
[tex]$$
2\frac{\square}{40}
$$[/tex]
is [tex]$37$[/tex].
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