simplify the following 5/8 + -8/9 + 0+ -13/3 + 17/24
The Correct Answer and Explanation is:
Let’s simplify the expression: 58+(−89)+0+(−133)+1724\frac{5}{8} + \left(-\frac{8}{9}\right) + 0 + \left(-\frac{13}{3}\right) + \frac{17}{24}85+(−98)+0+(−313)+2417
Step 1: Identify the fractions and simplify
The given fractions are: 58,−89,0,−133,1724\frac{5}{8}, -\frac{8}{9}, 0, -\frac{13}{3}, \frac{17}{24}85,−98,0,−313,2417
The zero doesn’t affect the sum, so we focus on the fractions: 58,−89,−133,1724\frac{5}{8}, -\frac{8}{9}, -\frac{13}{3}, \frac{17}{24}85,−98,−313,2417
Step 2: Find a common denominator
To add and subtract fractions, we need to express all fractions with the same denominator. The denominators are 8, 9, 3, and 24. The least common denominator (LCD) for these numbers is 72.
Step 3: Convert each fraction to have a denominator of 72
- For 58\frac{5}{8}85:
Multiply the numerator and denominator by 9: 58=5×98×9=4572\frac{5}{8} = \frac{5 \times 9}{8 \times 9} = \frac{45}{72}85=8×95×9=7245 - For −89-\frac{8}{9}−98:
Multiply the numerator and denominator by 8: −89=−8×89×8=−6472-\frac{8}{9} = \frac{-8 \times 8}{9 \times 8} = \frac{-64}{72}−98=9×8−8×8=72−64 - For −133-\frac{13}{3}−313:
Multiply the numerator and denominator by 24: −133=−13×243×24=−31272-\frac{13}{3} = \frac{-13 \times 24}{3 \times 24} = \frac{-312}{72}−313=3×24−13×24=72−312 - For 1724\frac{17}{24}2417:
Multiply the numerator and denominator by 3: 1724=17×324×3=5172\frac{17}{24} = \frac{17 \times 3}{24 \times 3} = \frac{51}{72}2417=24×317×3=7251
Step 4: Add the fractions
Now that we have a common denominator of 72, we can add and subtract the numerators: 4572+−6472+−31272+5172\frac{45}{72} + \frac{-64}{72} + \frac{-312}{72} + \frac{51}{72}7245+72−64+72−312+7251
Add the numerators: 45+(−64)+(−312)+51=45−64−312+51=−28045 + (-64) + (-312) + 51 = 45 – 64 – 312 + 51 = -28045+(−64)+(−312)+51=45−64−312+51=−280
Thus, the sum is: −28072\frac{-280}{72}72−280
Step 5: Simplify the fraction
To simplify −28072\frac{-280}{72}72−280, divide both the numerator and denominator by their greatest common divisor, which is 8: −280÷872÷8=−359\frac{-280 \div 8}{72 \div 8} = \frac{-35}{9}72÷8−280÷8=9−35
Final Answer:
The simplified sum is: −359\boxed{-\frac{35}{9}}−935
Explanation:
To add and subtract fractions, you first find a common denominator. Here, the least common denominator (LCD) was 72. After converting each fraction to have a denominator of 72, the numerators were added and subtracted. The final step was to simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor. The simplified fraction is −359-\frac{35}{9}−935.
