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Sagot :
Sure, let's tackle this problem step-by-step.
### Expression 1: [tex]\( 73.3 \frac{3}{5} + 2 \frac{3}{4} \)[/tex]
1. Convert Mixed Numbers to Improper Fractions or Decimals:
- [tex]\( 73.3 \frac{3}{5} \)[/tex]:
- Here, [tex]\( 73.3 \)[/tex] can be treated as [tex]\( 73 \)[/tex] plus a fractional part.
- [tex]\( \frac{3}{5} \)[/tex] in decimal form is [tex]\( 0.6 \)[/tex].
- Therefore, [tex]\( 73.3 \frac{3}{5} = 73 + 0.6 = 73.6 \)[/tex].
- [tex]\( 2 \frac{3}{4} \)[/tex]:
- Here, we have [tex]\( 2 \)[/tex] plus a fractional part.
- [tex]\( \frac{3}{4} \)[/tex] in decimal form is [tex]\( 0.75 \)[/tex].
- Therefore, [tex]\( 2 \frac{3}{4} = 2 + 0.75 = 2.75 \)[/tex].
2. Perform Addition:
- Now, add the two results together:
[tex]\[ 73.6 + 2.75 = 76.35 \][/tex]
### Expression 2: [tex]\( 74.2 \frac{2}{15} - 1 \frac{2}{3} \)[/tex]
1. Convert Mixed Numbers to Improper Fractions or Decimals:
- [tex]\( 74.2 \frac{2}{15} \)[/tex]:
- Here, [tex]\( 74.2 \)[/tex] can be treated as [tex]\( 74 \)[/tex] plus a fractional part.
- [tex]\( \frac{2}{15} \)[/tex] in decimal form is approximately [tex]\( 0.1333 \)[/tex] (since [tex]\( \frac{2}{15} \approx 0.1333 \)[/tex]).
- Therefore, [tex]\( 74.2 \frac{2}{15} = 74 + 0.1333 = 74.1333 \)[/tex].
- [tex]\( 1 \frac{2}{3} \)[/tex]:
- Here, we have [tex]\( 1 \)[/tex] plus a fractional part.
- [tex]\( \frac{2}{3} \)[/tex] in decimal form is approximately [tex]\( 0.6667 \)[/tex] (since [tex]\( \frac{2}{3} \approx 0.6667 \)[/tex]).
- Therefore, [tex]\( 1 \frac{2}{3} = 1 + 0.6667 = 1.6667 \)[/tex].
2. Perform Subtraction:
- Now, subtract the second result from the first result:
[tex]\[ 74.1333 - 1.6667 = 72.4666 \text{ (rounded to 4 decimal places, it is } 72.4667 \text{)} \][/tex]
### Final Results:
- Expression 1: [tex]\( 73.3 \frac{3}{5} + 2 \frac{3}{4} = 76.35 \)[/tex]
- Expression 2: [tex]\( 74.2 \frac{2}{15} - 1 \frac{2}{3} = 72.4667 \)[/tex]
Thus, the solutions to the given expressions are:
[tex]\[ (76.35, 72.4667) \][/tex]
### Expression 1: [tex]\( 73.3 \frac{3}{5} + 2 \frac{3}{4} \)[/tex]
1. Convert Mixed Numbers to Improper Fractions or Decimals:
- [tex]\( 73.3 \frac{3}{5} \)[/tex]:
- Here, [tex]\( 73.3 \)[/tex] can be treated as [tex]\( 73 \)[/tex] plus a fractional part.
- [tex]\( \frac{3}{5} \)[/tex] in decimal form is [tex]\( 0.6 \)[/tex].
- Therefore, [tex]\( 73.3 \frac{3}{5} = 73 + 0.6 = 73.6 \)[/tex].
- [tex]\( 2 \frac{3}{4} \)[/tex]:
- Here, we have [tex]\( 2 \)[/tex] plus a fractional part.
- [tex]\( \frac{3}{4} \)[/tex] in decimal form is [tex]\( 0.75 \)[/tex].
- Therefore, [tex]\( 2 \frac{3}{4} = 2 + 0.75 = 2.75 \)[/tex].
2. Perform Addition:
- Now, add the two results together:
[tex]\[ 73.6 + 2.75 = 76.35 \][/tex]
### Expression 2: [tex]\( 74.2 \frac{2}{15} - 1 \frac{2}{3} \)[/tex]
1. Convert Mixed Numbers to Improper Fractions or Decimals:
- [tex]\( 74.2 \frac{2}{15} \)[/tex]:
- Here, [tex]\( 74.2 \)[/tex] can be treated as [tex]\( 74 \)[/tex] plus a fractional part.
- [tex]\( \frac{2}{15} \)[/tex] in decimal form is approximately [tex]\( 0.1333 \)[/tex] (since [tex]\( \frac{2}{15} \approx 0.1333 \)[/tex]).
- Therefore, [tex]\( 74.2 \frac{2}{15} = 74 + 0.1333 = 74.1333 \)[/tex].
- [tex]\( 1 \frac{2}{3} \)[/tex]:
- Here, we have [tex]\( 1 \)[/tex] plus a fractional part.
- [tex]\( \frac{2}{3} \)[/tex] in decimal form is approximately [tex]\( 0.6667 \)[/tex] (since [tex]\( \frac{2}{3} \approx 0.6667 \)[/tex]).
- Therefore, [tex]\( 1 \frac{2}{3} = 1 + 0.6667 = 1.6667 \)[/tex].
2. Perform Subtraction:
- Now, subtract the second result from the first result:
[tex]\[ 74.1333 - 1.6667 = 72.4666 \text{ (rounded to 4 decimal places, it is } 72.4667 \text{)} \][/tex]
### Final Results:
- Expression 1: [tex]\( 73.3 \frac{3}{5} + 2 \frac{3}{4} = 76.35 \)[/tex]
- Expression 2: [tex]\( 74.2 \frac{2}{15} - 1 \frac{2}{3} = 72.4667 \)[/tex]
Thus, the solutions to the given expressions are:
[tex]\[ (76.35, 72.4667) \][/tex]
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