Let's match each addition operation to its correct sum step-by-step.
1. Matching pairs involving whole numbers and fractions:
- For the expression [tex]\( -24 \frac{5}{9} + 30 \frac{7}{9} \)[/tex]:
Calculate the sum of the whole numbers and fractions:
[tex]\( -24 + 30 = 6 \)[/tex] and [tex]\( \frac{5}{9} + \frac{7}{9} = \frac{12}{9} = 1 \frac{3}{9} \)[/tex].
Combining these, we get [tex]\( 6 + 1 \frac{3}{9} = 6 \cdot 1 \frac{3}{9} \)[/tex].
So, the result that matches [tex]\( -24 \frac{5}{9} + 30 \frac{7}{9} \)[/tex] is [tex]\( 6 \frac{1}{9} \)[/tex].
- For the expression [tex]\( 45 \frac{2}{9} + 39 \frac{3}{9} \)[/tex]:
Calculate the sum of the whole numbers and fractions:
[tex]\( 45 + 39 = 84 \)[/tex] and [tex]\( \frac{2}{9} + \frac{3}{9} = \frac{5}{9} \)[/tex].
Combining these, we get [tex]\( 84 \frac{0}{9} \)[/tex].
So, the result that matches [tex]\( 45 \frac{2}{9} + 39 \frac{3}{9} \)[/tex] is [tex]\( 84 \frac{0}{9} \)[/tex].
2. Matching pairs involving decimal numbers:
- For the expression [tex]\( 28.98 + (-52.22) \)[/tex]:
Calculating the sum:
[tex]\( 28.98 + (-52.22) = -23.24 \)[/tex].
So, the result that matches [tex]\( 28.98 + (-52.22) \)[/tex] is [tex]\( -23.24 \)[/tex].
- For the expression [tex]\( 56.75 + 75.12 \)[/tex]:
Calculating the sum:
[tex]\( 56.75 + 75.12 = 131.87 \)[/tex].
So, the result that matches [tex]\( 56.75 + 75.12 \)[/tex] is [tex]\( 131.87 \)[/tex].
Here are the correctly matched pairs:
1. [tex]\( -24 \frac{5}{9} + 30 \frac{7}{9} \)[/tex] → [tex]\( 6 \frac{1}{9} \)[/tex]
2. [tex]\( 45 \frac{2}{9} + 39 \frac{3}{9} \)[/tex] → [tex]\( 84 \frac{0}{9} \)[/tex]
3. [tex]\( 28.98 + (-52.22) \)[/tex] → [tex]\( -23.24 \)[/tex]
4. [tex]\( 56.75 + 75.12 \)[/tex] → [tex]\( 131.87 \)[/tex]
