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(1) \( \frac{1}{80}-\frac{2}{5}= \) (1) \( \frac{7}{8}-\frac{3}{6}= \) (19) \( \frac{51}{15}-\frac{3}{5}= \) (14) \( \frac{15}{20}-\frac{1}{2}= \)

Ask by Martinez Simpson. in the United States
Feb 18,2025

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Tutor-Verified Answer

Answer

The answers are: 1. –31/80 2. 3/8 3. 14/5 4. 1/4

Solution

Let’s solve each subtraction step by step. 1. 1/80 – 2/5 • Write 2/5 with denominator 80: 2/5 = (2×16)/(5×16) = 32/80 • Subtract: 1/80 – 32/80 = (1 – 32)/80 = –31/80 2. 7/8 – 3/6 • Notice 3/6 simplifies to 1/2. • To subtract 7/8 − 1/2, write 1/2 with denominator 8: 1/2 = 4/8 • Subtract: 7/8 – 4/8 = (7 – 4)/8 = 3/8 3. 51/15 – 3/5 • Write 3/5 with denominator 15: 3/5 = (3×3)/(5×3) = 9/15 • Subtract: 51/15 – 9/15 = (51 – 9)/15 = 42/15 • Simplify by dividing numerator and denominator by 3: 42÷3/15÷3 = 14/5 4. 15/20 – 1/2 • First simplify 15/20 to 3/4 (divide numerator and denominator by 5). • Write 1/2 with denominator 4: 1/2 = 2/4 • Subtract: 3/4 – 2/4 = (3 – 2)/4 = 1/4 Thus, the answers are: 1. –31/80 2. 3/8 3. 14/5 4. 1/4

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Bonus Knowledge

To solve the first equation, start by finding a common denominator for \( \frac{1}{80} \) and \( \frac{2}{5} \). The common denominator is 80, so \( \frac{2}{5} \) equals \( \frac{32}{80} \). Therefore, \[ \frac{1}{80}-\frac{32}{80}=\frac{1-32}{80}=\frac{-31}{80}. \] For the second equation, the two fractions are \( \frac{7}{8} \) and \( \frac{3}{6} \). Since \( \frac{3}{6} \) simplifies to \( \frac{1}{2} \) (with a common denominator of 8), you can rewrite it as \( \frac{7}{8} - \frac{4}{8} = \frac{3}{8} \). In the third equation, convert \( \frac{3}{5} \) to have a common denominator with \( \frac{51}{15} \). Rewrite \( \frac{3}{5} \) as \( \frac{9}{15} \). This gives us \[ \frac{51}{15} - \frac{9}{15} = \frac{42}{15}. \] For the last calculation, since \( \frac{1}{2} \) equals \( \frac{10}{20} \), you can see that \[ \frac{15}{20} - \frac{10}{20} = \frac{5}{20}. \] Finally, \( \frac{5}{20} \) simplifies to \( \frac{1}{4} \). So the final answers are: 1. \( \frac{1}{80}-\frac{2}{5} = \frac{-31}{80} \) 2. \( \frac{7}{8}-\frac{3}{6} = \frac{3}{8} \) 3. \( \frac{51}{15}-\frac{3}{5} = \frac{42}{15} \) 4. \( \frac{15}{20}-\frac{1}{2} = \frac{1}{4} \)

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