I need help with these
1. 1 7/8 + 1/9
2. 5 2/11 -3 2/18
3. 8 2/17 x 1 15/17
4. 2/9 + 4/9
5. -5/6 + 4/18
6. 11 5/9 + 10 1/3
7. -1/5 + (-3/7)
7/8- 1/2. estimate
Sure! I can help you with those math problems. Let's solve them step by step:
1. To add fractions, we first need to find a common denominator. The least common multiple (LCM) of 8 and 9 is 72. So, we need to convert both fractions to have a denominator of 72.
Convert 1 7/8 to an improper fraction: 1 7/8 = 15/8
Convert 1/9 to a fraction with a denominator of 72: 1/9 = 8/72
Now, we can add the fractions: 15/8 + 8/72
To add fractions, we need to have the same denominator. So, let's convert 15/8 to a fraction with a denominator of 72 by multiplying the numerator and denominator by 9: 15/8 = 135/72
Now, we can add: 135/72 + 8/72 = 143/72
The sum of 1 7/8 + 1/9 is 143/72.
2. Similar to the previous question, we first find a common denominator. The LCM of 11 and 18 is 198. So, we convert both mixed numbers to improper fractions with a denominator of 198.
Convert 5 2/11 to an improper fraction: 5 2/11 = 57/11
Convert 3 2/18 to an improper fraction: 3 2/18 = 56/18
Now, we can subtract the fractions: 57/11 - 56/18
To subtract fractions, we need to have the same denominator. So, let's convert 57/11 to a fraction with a denominator of 198 by multiplying the numerator and denominator by 18: 57/11 = 342/66
Now, we can subtract: 342/66 - 56/18 = (342*3 - 56*11)/(66*3) = 966/198
The difference of 5 2/11 - 3 2/18 is 966/198.
3. For multiplication of mixed numbers, we can convert both mixed numbers to improper fractions and then multiply.
Convert 8 2/17 to an improper fraction: 8 2/17 = 146/17
Convert 1 15/17 to an improper fraction: 1 15/17 = 32/17
Now, we can multiply the fractions: 146/17 * 32/17
To multiply fractions, we simply multiply the numerators together and the denominators together: (146 * 32)/(17 * 17) = 4672/289
The product of 8 2/17 x 1 15/17 is 4672/289.
4. We add fractions by combining the numerators over a common denominator. In this case, the denominators are already the same, so we can simply add the numerators.
2/9 + 4/9 = (2 + 4)/9 = 6/9
However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (which is 3 in this case): 6/9 = 2/3
The sum of 2/9 + 4/9 is 2/3.
5. Similar to the previous question, we add fractions by combining the numerators over a common denominator. In this case, the denominators are different, so we need to find a common denominator.
The least common multiple (LCM) of 6 and 18 is 18. So, we need to convert both fractions to have a denominator of 18.
Convert -5/6 to a fraction with a denominator of 18: -5/6 = -15/18
Convert 4/18 to a fraction with a denominator of 18: 4/18 = 2/9
Now, we can add the fractions: -15/18 + 2/9
To add fractions, we need to have the same denominator. So, let's convert -15/18 to a fraction with a denominator of 18 by multiplying the numerator and denominator by 2: -15/18 = -30/36
Now, we can add: -30/36 + 2/9 = (-30 + 8)/36 = -22/36
However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (which is 2 in this case): -22/36 = -11/18
The sum of -5/6 + 4/18 is -11/18.
6. To add mixed numbers, we first add the whole numbers together and then add the fractions together.
11 + 10 = 21
For the fractions, we need to find a common denominator. The least common multiple (LCM) of 9 and 3 is 9. So, we need to convert both fractions to have a denominator of 9.
Convert 5/9 to a fraction with a denominator of 9: 5/9
Convert 1/3 to a fraction with a denominator of 9: 1/3 * 3/3 = 3/9
Now, we can add the fractions: 5/9 + 3/9 = 8/9
The sum of 11 5/9 + 10 1/3 is 21 8/9.
7. To add or subtract fractions with different signs, we find a common denominator and then perform the operation.
The least common multiple (LCM) of 5 and 7 is 35. So, we need to convert both fractions to have a denominator of 35.
Convert -1/5 to a fraction with a denominator of 35: -1/5 = -7/35
Convert -3/7 to a fraction with a denominator of 35: -3/7 * 5/5 = -15/35
Now, we can add the fractions: -7/35 + (-15/35) = -22/35
The sum of -1/5 + (-3/7) is -22/35.
I hope this helps! Let me know if you have any other questions.
I'll get you started with the first two.
1. 1 7/8 + 1/9
1 7/8 is almost 2. 1/9 is almost nothing. Add the two together and you get about 2.
2. 5 2/11 -3 2/18
5 2/11 = 5
3 2/18 = 3
Take 3 from 5 and you get about 2.
I'll be glad to check your answers to the other problems.