1/4+2/3=?
1/2-5/10=?
1/5x1/3=?
1/4 divided by 7/10
1/4 + 2/3 = (3/12) + (8/12) = 11/12
1/2 - 5/10 = (5/10) - (5/10) = 0
1/5 x 1/3 = 1/15
1/4 divided by 7/10 = (1/4) / (7/10) = (1/4) x (10/7) = 10/28 = 5/14
To solve these equations step-by-step:
1) 1/4 + 2/3:
First, find a common denominator. The common denominator for 4 and 3 is 12.
Now, convert each fraction to have a denominator of 12:
1/4 = 3/12 (multiply numerator and denominator by 3)
2/3 = 8/12 (multiply numerator and denominator by 4)
Now, add the fractions:
3/12 + 8/12 = 11/12
Therefore, 1/4 + 2/3 = 11/12.
2) 1/2 - 5/10:
Both fractions already have the same denominator, so you can subtract the numerators directly:
1/2 - 5/10 = 1/2 - 1/2 = 0
Therefore, 1/2 - 5/10 = 0.
3) 1/5 x 1/3:
To multiply fractions, multiply the numerators together and multiply the denominators together:
1/5 x 1/3 = (1 x 1) / (5 x 3) = 1/15
Therefore, 1/5 x 1/3 = 1/15.
4) 1/4 divided by 7/10:
To divide fractions, you invert the second fraction and then multiply:
1/4 divided by 7/10 = 1/4 x 10/7
Simplify the result by canceling out common factors:
1/4 x 10/7 = (1 x 10)/(4 x 7) = 10/28
Therefore, 1/4 divided by 7/10 = 10/28, which can be simplified further if needed.
To solve these arithmetic problems, you need to follow certain steps for each operation. Let's go through each question one by one:
1) 1/4 + 2/3:
To add fractions, you follow these steps:
- Find a common denominator (the least common multiple of the denominators).
- Rewrite each fraction using the common denominator.
- Add the numerators and keep the common denominator.
For 1/4 + 2/3:
Step 1: The least common multiple of 4 and 3 is 12.
Step 2: Rewriting the fractions using the common denominator, we get 3/12 + 8/12.
Step 3: Adding the numerators, we have 3 + 8 = 11. So, the answer is 11/12.
Therefore, 1/4 + 2/3 = 11/12.
2) 1/2 - 5/10:
To subtract fractions, you follow similar steps:
- Find a common denominator.
- Rewrite each fraction using the common denominator.
- Subtract the numerators while keeping the common denominator.
For 1/2 - 5/10:
Step 1: The least common multiple of 2 and 10 is 10.
Step 2: Rewriting the fractions using the common denominator, we get 5/10 - 5/10.
Step 3: Subtracting the numerators, we have 5 - 5 = 0. So, the answer is 0/10.
But, we can simplify this fraction further:
Dividing both the numerator and denominator by their greatest common divisor, which is 5, we get 0/10 = 0/2.
Therefore, 1/2 - 5/10 = 0/2 (or simply 0).
3) 1/5 x 1/3:
To multiply fractions, you multiply the numerators and the denominators together.
For 1/5 x 1/3:
Multiplying the numerators, we get 1 x 1 = 1.
Multiplying the denominators, we get 5 x 3 = 15.
Therefore, 1/5 x 1/3 = 1/15.
4) 1/4 divided by 7/10:
To divide fractions, you multiply the first fraction by the reciprocal of the second fraction.
For 1/4 divided by 7/10:
Multiplying the first fraction by the reciprocal of the second fraction:
1/4 x 10/7.
Then, multiply the numerators: 1 x 10 = 10.
Multiply the denominators: 4 x 7 = 28.
So, the answer is 10/28.
But we can simplify this fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 2:
10/28 = 5/14.
Therefore, 1/4 divided by 7/10 = 5/14.