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Sagot :
Answer:
To solve "three and three-fourths less than ten and two-thirds," you need to subtract the two fractions:
1. Convert "three and three-fourths" to an improper fraction: \( 3 \frac{3}{4} = \frac{15}{4} \).
2. Convert "ten and two-thirds" to an improper fraction: \( 10 \frac{2}{3} = \frac{32}{3} \).
To subtract these, find a common denominator (which is 12):
- \( \frac{15}{4} = \frac{45}{12} \)
- \( \frac{32}{3} = \frac{128}{12} \)
Now subtract \( \frac{45}{12} \) from \( \frac{128}{12} \):
\[ \frac{128}{12} - \frac{45}{12} = \frac{83}{12} \]
Convert \( \frac{83}{12} \) back to a mixed number: \( 6 \frac{11}{12} \).
So, the result is \( 6 \frac{11}{12} \).
Step-by-step explanation:
same lng yung nasa pic at yung type ko
Step 1: Convert Mixed Numbers to Improper Fractions
First, convert both mixed numbers to improper fractions.
[tex] \( 3 \frac{3}{4} \):
\[ 3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} [/tex]
[tex] \( 10 \frac{2}{3} \):
\[ 10 \frac{2}{3} = \frac{10 \times 3 + 2}{3} = \frac{30 + 2}{3} = \frac{32}{3} [/tex]
Step 2: Find the Difference
[tex]\frac{32}{3} - \frac{15}{4}[/tex]
Step 3: Common Denominator
To subtract these fractions, find a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
Convert both fractions to have a denominator of 12:
[tex]\frac{32}{3} = \frac{32 \times 4}{3 \times 4} = \frac{128}{12}[/tex]
[tex]\frac{15}{4} = \frac{15 \times 3}{4 \times 3} = \frac{45}{12}[/tex]
Step 4: Subtract the Fractions
Now subtract the fractions:
[tex]\frac{128}{12} - \frac{45}{12} = \frac{128 - 45}{12} = \frac{83}{12}[/tex]
Step 5: Simplify if Necessary
### Final Answer
To express it in mixed number form:
[tex]\frac{83}{12} = 6 \frac{11}{12}[/tex]
[tex] \( 10 \frac{2}{3} \) \: is \: \( 6 \frac{11}{12} \) \: more \: than \: \( 3 \frac{3}{4} \).[/tex]
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