Question

add the mixed numbers. enter your answers.
$1\frac{4}{5} + 4\frac{4}{7} = 1\frac{?}{35} + 4\frac{?}{35}$
$= 5\frac{?}{35}$

Explanation:

Step1: Find common denominator

The denominators are 5 and 7. The least common denominator (LCD) of 5 and 7 is \(5\times7 = 35\). To convert \(\frac{4}{5}\) to a fraction with denominator 35, multiply numerator and denominator by 7: \(\frac{4\times7}{5\times7}=\frac{28}{35}\).

Step2: Convert second fraction

To convert \(\frac{4}{7}\) to a fraction with denominator 35, multiply numerator and denominator by 5: \(\frac{4\times5}{7\times5}=\frac{20}{35}\).

Step3: Add the fractions

Now we have \(1\frac{28}{35}+4\frac{20}{35}\). Add the whole numbers: \(1 + 4=5\). Add the fractions: \(\frac{28}{35}+\frac{20}{35}=\frac{28 + 20}{35}=\frac{48}{35}\). But we can write this as a mixed number: \(5\frac{48}{35}\)? Wait, no, wait. Wait, actually, when adding mixed numbers, we add whole numbers and fractions separately. Wait, \(1\frac{28}{35}+4\frac{20}{35}=(1 + 4)+(\frac{28}{35}+\frac{20}{35})=5+\frac{48}{35}\). But \(\frac{48}{35}=1\frac{13}{35}\), so \(5 + 1\frac{13}{35}=6\frac{13}{35}\)? Wait, no, maybe I made a mistake. Wait, the problem is showing \(1\frac{?}{35}+4\frac{?}{35}=5\frac{?}{35}\). Wait, maybe the problem is just asking for the numerators when converting to 35 denominator, then adding the fractions. Let's re - do:

First, convert \(\frac{4}{5}\) to 35 denominator: \(\frac{4}{5}=\frac{4\times7}{5\times7}=\frac{28}{35}\), so first? is 28.

Second, convert \(\frac{4}{7}\) to 35 denominator: \(\frac{4}{7}=\frac{4\times5}{7\times5}=\frac{20}{35}\), so second? is 20.

Then, add the fractions: \(\frac{28}{35}+\frac{20}{35}=\frac{28 + 20}{35}=\frac{48}{35}\), so the third? is 48.

Answer:

First? : 28, Second? : 20, Third? : 48