what is the smallest to greatest of these fractions 3/5,7/8,8/10,2/4
http://www.mathsisfun.com/numbers/common-denominator.html
The common denominator is 40
3/5 = 24/40
7/8 = 35/40
8/10 = 32/40
2/4 = 20/40
Arrange these fractions in order of their numerators.
To arrange the given fractions from smallest to greatest, you can compare their values.
Let's start with the fractions provided:
Fraction 1: 3/5
Fraction 2: 7/8
Fraction 3: 8/10 (or simplifying it, 4/5)
Fraction 4: 2/4 (or simplifying it, 1/2)
To compare these fractions, we can either find a common denominator or convert them to decimals.
Method 1: Finding a common denominator
To find the common denominator, we need to find the least common multiple (LCM) of the denominators. In this case, the denominators are 5, 8, 5, and 2. The LCM of these numbers is 40.
Now, let's convert the fractions to have a denominator of 40:
Fraction 1: (3/5) × (8/8) = 24/40
Fraction 2: (7/8) × (5/5) = 35/40
Fraction 3: (4/5) × (8/8) = 32/40
Fraction 4: (1/2) × (20/20) = 20/40
Now that all the fractions have the same denominator, we can compare them:
20/40 < 24/40 < 32/40 < 35/40
Therefore, the fractions from smallest to greatest are:
1. 1/2
2. 3/5
3. 4/5
4. 7/8
Method 2: Converting to decimals
Another way to compare these fractions is by converting them to decimals using division.
Fraction 1: 3/5 = 0.6
Fraction 2: 7/8 = 0.875
Fraction 3: 8/10 (or 4/5) = 0.8
Fraction 4: 2/4 (or 1/2) = 0.5
Now that the fractions are converted to decimals, we can compare them:
0.5 < 0.6 < 0.8 < 0.875
Therefore, the fractions from smallest to greatest are:
1. 1/2
2. 3/5
3. 4/5
4. 7/8
To arrange fractions from smallest to greatest, we need to find a common denominator and compare the numerators.
Step 1: Find a common denominator.
To compare fractions, we need a common denominator. In this case, we can see that the denominators are already related. The denominators are: 5, 8, 10, and 4. Now, let's check if there is a common multiple of these denominators.
Multiples of 5: 5, 10, 15, 20, 25, ...
Multiples of 8: 8, 16, 24, 32, ...
Multiples of 10: 10, 20, 30, 40, ...
Multiples of 4: 4, 8, 12, 16, 20, ...
From the list of multiples, we can see that the first common denominator is 40.
Step 2: Convert all fractions to have a denominator of 40.
To convert fractions to a common denominator of 40, we multiply the numerator and denominator of each fraction by the appropriate factor:
3/5 * 8/8 = 24/40
7/8 * 5/5 = 35/40
8/10 * 4/4 = 32/40
2/4 * 10/10 = 20/40
Now, our fractions become:
24/40, 35/40, 32/40, and 20/40.
Step 3: Arrange the fractions from smallest to greatest.
Comparing the numerators of these fractions, we can now arrange them in ascending order:
20/40, 24/40, 32/40, 35/40
So, the fractions in order from smallest to greatest are: 20/40, 24/40, 32/40, 35/40.
However, we can simplify these fractions further:
20/40 simplifies to 1/2.
24/40 simplifies to 3/5.
32/40 simplifies to 4/5.
35/40 simplifies to 7/8.
So, the simplified fractions in order from smallest to greatest are: 1/2, 3/5, 4/5, 7/8.