can you please let me know if these are correct:
1. 5 5/6 x 2 4/5 = 16
2. 2/3 divided 3/5 = 1 1/9 or 2/5?
3. 7/12 divided 2/3 = 7/8
4. 3 1/2 divided 3/4 = 4 2/3 or 2 5/7
5. 4 2/3 divided 7 = 2/3
6. 4 1/5 divided 1 2/5 = 3
7. 2/5 x 5/14 = 1//7
8. 2/3 + 1/7 = 17/21 OR 12/21
1) I get 16 1/3
2) Wrong.
3) 4 2/3 is correct.
5) Right
6) Right
7) Right
8) 17/21
1. 5 5/6 x 2 4/5 = 16
35/6 x 14/5= 49/3 = 16 1/3
2. 2/3 divided 3/5 = 1 1/9 or 2/5?
2/3 x 5/3 = 10/9 = 1 1/9
3. 7/12 divided 2/3 = 7/8
7/12 x 3/2 = 21/24 = 7/8
4. 3 1/2 divided 3/4 = 4 2/3 or 2 5/7
7/2 x 4/3 = 28/6 = 4 2/3
5. 4 2/3 divided 7 = 2/3
14/3 x 1/7 = 14/21 = 2/3
6. 4 1/5 divided 1 2/5 = 3
21/5 x 5/7 = 105/35 = 3
7. 2/5 x 5/14 = 1//7
10/70 = 1/7
8. 2/3 + 1/7 = 17/21 OR 12/21
14/21 + 3/21 = 17/21
1. To multiply mixed numbers, you need to convert them to improper fractions first. Here's how you can do it:
5 5/6 = (6 × 5 + 5) / 6 = 35/6
2 4/5 = (5 × 2 + 4) / 5 = 14/5
Now, to multiply these fractions, you can simply multiply the numerators and multiply the denominators:
(35/6) × (14/5) = (35 × 14) / (6 × 5) = 490/30
To simplify the result, you can divide both the numerator and denominator by their greatest common divisor, which is 10:
490/30 = (49/3) ÷ (3/3) = 49/3
So the answer should be 49/3, not 16.
2. To divide fractions, you need to multiply the first fraction by the reciprocal of the second fraction. Here's how you can do it:
2/3 ÷ 3/5 = 2/3 × 5/3
Multiply the numerators and denominators:
(2 × 5) / (3 × 3) = 10/9
The answer should be 10/9, not 1 1/9 or 2/5.
3. To divide fractions, follow the same steps as in the previous example:
7/12 ÷ 2/3 = 7/12 × 3/2
Multiply the numerators and denominators:
(7 × 3) / (12 × 2) = 21/24
To simplify the fraction, divide both the numerator and denominator by their greatest common divisor, which is 3:
21/24 = (7/8) ÷ (8/8) = 7/8
So the answer is 7/8.
4. To divide mixed numbers, convert them to improper fractions:
3 1/2 = (2 × 3 + 1) / 2 = 7/2
3/4 = 3/4
Now divide the fractions:
(7/2) ÷ (3/4) = (7/2) × (4/3)
Multiply the numerators and denominators:
(7 × 4) / (2 × 3) = 28/6
To simplify the fraction, divide both the numerator and denominator by their greatest common divisor, which is 2:
28/6 = (14/3) ÷ (6/6) = 14/3
The answer should be 14/3, not 4 2/3 or 2 5/7.
5. To divide a mixed number by a whole number, convert the mixed number to an improper fraction:
4 2/3 = (3 × 4 + 2) / 3 = 14/3
Now, divide the fractions:
(14/3) ÷ 7 = 14/3 × 1/7
Multiply the numerators and denominators:
(14 × 1) / (3 × 7) = 14/21
The answer is 14/21, which can be further simplified as 2/3.
6. To divide mixed numbers, convert them to improper fractions:
4 1/5 = (5 × 4 + 1) / 5 = 21/5
1 2/5 = (5 × 1 + 2) / 5 = 7/5
Now, divide the fractions:
(21/5) ÷ (7/5) = 21/5 × 5/7
Multiply the numerators and denominators:
(21 × 5) / (5 × 7) = 105/35
To simplify the fraction, divide both the numerator and denominator by their greatest common divisor, which is 35:
105/35 = (3/1) ÷ (35/35) = 3
So the answer is 3.
7. To multiply fractions, simply multiply the numerators and multiply the denominators:
2/5 × 5/14 = (2 × 5) / (5 × 14) = 10/70
To simplify the fraction, divide both the numerator and denominator by their greatest common divisor, which is 10:
10/70 = (1/7) ÷ (7/7) = 1/7
So the correct answer is 1/7, not 1//7.
8. To add fractions, you need to find a common denominator. In this case, the common denominator is 21:
2/3 + 1/7 = (2/3) × (7/7) + (1/7) × (3/3) = 14/21 + 3/21 = 17/21
So the correct answer is 17/21.