Answer :
To solve [tex]\( 3 \frac{3}{4} - 1 \frac{2}{3} \)[/tex], follow these steps:
1. Convert Mixed Numbers to Improper Fractions:
- For [tex]\( 3 \frac{3}{4} \)[/tex]:
- Multiply the whole number (3) by the denominator (4) and add the numerator (3).
- This gives [tex]\((3 \times 4) + 3 = 15\)[/tex].
- So, [tex]\(3 \frac{3}{4}\)[/tex] converts to the improper fraction [tex]\(\frac{15}{4}\)[/tex].
- For [tex]\( 1 \frac{2}{3} \)[/tex]:
- Multiply the whole number (1) by the denominator (3) and add the numerator (2).
- This gives [tex]\((1 \times 3) + 2 = 5\)[/tex].
- So, [tex]\(1 \frac{2}{3}\)[/tex] converts to the improper fraction [tex]\(\frac{5}{3}\)[/tex].
2. Find a Common Denominator:
- The denominators are 4 and 3. The least common multiple of 4 and 3 is 12.
3. Convert to Equivalent Fractions with Common Denominator:
- Convert [tex]\(\frac{15}{4}\)[/tex] to a fraction with a denominator of 12:
- Multiply both the numerator and denominator by 3:
- [tex]\(\frac{15 \times 3}{4 \times 3} = \frac{45}{12}\)[/tex].
- Convert [tex]\(\frac{5}{3}\)[/tex] to a fraction with a denominator of 12:
- Multiply both the numerator and denominator by 4:
- [tex]\(\frac{5 \times 4}{3 \times 4} = \frac{20}{12}\)[/tex].
4. Subtract the Fractions:
- Before deletion: We subtract the numerators while keeping the common denominator:
- [tex]\( \frac{45}{12} - \frac{20}{12} = \frac{25}{12} \)[/tex].
5. Convert the Result to a Mixed Number:
- Divide the numerator (25) by the denominator (12) to find the whole number part:
- [tex]\(25 \div 12 = 2\)[/tex] remainder 1.
- The remainder is the numerator of the fractional part, with 12 as the denominator:
- [tex]\(2 \frac{1}{12}\)[/tex].
So, [tex]\(3 \frac{3}{4} - 1 \frac{2}{3} = 2 \frac{1}{12}\)[/tex].
1. Convert Mixed Numbers to Improper Fractions:
- For [tex]\( 3 \frac{3}{4} \)[/tex]:
- Multiply the whole number (3) by the denominator (4) and add the numerator (3).
- This gives [tex]\((3 \times 4) + 3 = 15\)[/tex].
- So, [tex]\(3 \frac{3}{4}\)[/tex] converts to the improper fraction [tex]\(\frac{15}{4}\)[/tex].
- For [tex]\( 1 \frac{2}{3} \)[/tex]:
- Multiply the whole number (1) by the denominator (3) and add the numerator (2).
- This gives [tex]\((1 \times 3) + 2 = 5\)[/tex].
- So, [tex]\(1 \frac{2}{3}\)[/tex] converts to the improper fraction [tex]\(\frac{5}{3}\)[/tex].
2. Find a Common Denominator:
- The denominators are 4 and 3. The least common multiple of 4 and 3 is 12.
3. Convert to Equivalent Fractions with Common Denominator:
- Convert [tex]\(\frac{15}{4}\)[/tex] to a fraction with a denominator of 12:
- Multiply both the numerator and denominator by 3:
- [tex]\(\frac{15 \times 3}{4 \times 3} = \frac{45}{12}\)[/tex].
- Convert [tex]\(\frac{5}{3}\)[/tex] to a fraction with a denominator of 12:
- Multiply both the numerator and denominator by 4:
- [tex]\(\frac{5 \times 4}{3 \times 4} = \frac{20}{12}\)[/tex].
4. Subtract the Fractions:
- Before deletion: We subtract the numerators while keeping the common denominator:
- [tex]\( \frac{45}{12} - \frac{20}{12} = \frac{25}{12} \)[/tex].
5. Convert the Result to a Mixed Number:
- Divide the numerator (25) by the denominator (12) to find the whole number part:
- [tex]\(25 \div 12 = 2\)[/tex] remainder 1.
- The remainder is the numerator of the fractional part, with 12 as the denominator:
- [tex]\(2 \frac{1}{12}\)[/tex].
So, [tex]\(3 \frac{3}{4} - 1 \frac{2}{3} = 2 \frac{1}{12}\)[/tex].
