reduce fractions to the lowest terms
9 8/20
10 33/39
11 3/10
12 60/80
13 24/27
14 45/90
15 3/81
16 6/16
9 8/20 = 9 2/5
10 33/39 = 10 11/13
11 3/10 = THIS IS THE LOWEST TERM.
I'll be glad to check your answers for the rest.
http://www.mathsisfun.com/simplifying-fractions.html
15_25
To reduce fractions to the lowest terms, you need to find the greatest common divisor (GCD) of the numerator and the denominator and divide them both by the GCD. Let's reduce each fraction one by one:
1. 9 8/20
The numerator is 9 * 20 + 8 = 188. So the fraction is 188/20.
The GCD of 188 and 20 is 4.
Divide both the numerator and denominator by 4:
188/4 ÷ 20/4 = 47/5.
Therefore, 9 8/20 reduced to the lowest terms is 47/5.
2. 10 33/39
The numerator is 10 * 39 + 33 = 393. So the fraction is 393/39.
The GCD of 393 and 39 is 39.
Divide both the numerator and denominator by 39:
393/39 ÷ 39/39 = 393/1.
Therefore, 10 33/39 reduced to the lowest terms is 393/1.
3. 11 3/10
The numerator is 11 * 10 + 3 = 113. So the fraction is 113/10.
The GCD of 113 and 10 is 1.
Divide both the numerator and denominator by 1:
113/1 ÷ 10/1 = 113/10.
Therefore, 11 3/10 is already in the lowest terms.
4. 12 60/80
The numerator is 12 * 80 + 60 = 1020. So the fraction is 1020/80.
The GCD of 1020 and 80 is 20.
Divide both the numerator and denominator by 20:
1020/20 ÷ 80/20 = 51/4.
Therefore, 12 60/80 reduced to the lowest terms is 51/4.
5. 13 24/27
The numerator is 13 * 27 + 24 = 375. So the fraction is 375/27.
The GCD of 375 and 27 is 3.
Divide both the numerator and denominator by 3:
375/3 ÷ 27/3 = 125/9.
Therefore, 13 24/27 reduced to the lowest terms is 125/9.
6. 14 45/90
The numerator is 14 * 90 + 45 = 1350. So the fraction is 1350/90.
The GCD of 1350 and 90 is 90.
Divide both the numerator and denominator by 90:
1350/90 ÷ 90/90 = 15/1.
Therefore, 14 45/90 reduced to the lowest terms is 15/1.
7. 15 3/81
The numerator is 15 * 81 + 3 = 1218. So the fraction is 1218/81.
The GCD of 1218 and 81 is 81.
Divide both the numerator and denominator by 81:
1218/81 ÷ 81/81 = 14/1.
Therefore, 15 3/81 reduced to the lowest terms is 14/1.
8. 16 6/16
The numerator is 16 * 16 + 6 = 262. So the fraction is 262/16.
The GCD of 262 and 16 is 2.
Divide both the numerator and denominator by 2:
262/2 ÷ 16/2 = 131/8.
Therefore, 16 6/16 reduced to the lowest terms is 131/8.
To reduce fractions to the lowest terms, you need to simplify them by finding the greatest common divisor (GCD) of the numerator and denominator, and then dividing both by the GCD. Here's how you can reduce each of the given fractions to the lowest terms:
1. 9 8/20:
- Convert the mixed number to an improper fraction: 9 8/20 = (9 * 20 + 8) / 20 = 188/20.
- Find the GCD of the numerator (188) and denominator (20). The GCD is 4.
- Divide both the numerator and denominator by the GCD: 188/20 ÷ 4/4 = 47/5.
- Therefore, 9 8/20 simplifies to 47/5.
2. 10 33/39:
- Convert the mixed number to an improper fraction: 10 33/39 = (10 * 39 + 33) / 39 = 393/39.
- Find the GCD of the numerator (393) and denominator (39). The GCD is 39.
- Divide both the numerator and denominator by the GCD: 393/39 ÷ 39/39 = 10/1.
- Therefore, 10 33/39 simplifies to 10/1 or simply 10.
3. 11 3/10:
- Convert the mixed number to an improper fraction: 11 3/10 = (11 * 10 + 3) / 10 = 113/10.
- Find the GCD of the numerator (113) and denominator (10). The GCD is 1.
- Divide both the numerator and denominator by the GCD: 113/10 ÷ 1/1 = 113/10.
- Therefore, 11 3/10 is already in its lowest terms.
4. 12 60/80:
- Convert the mixed number to an improper fraction: 12 60/80 = (12 * 80 + 60) / 80 = 1020/80.
- Find the GCD of the numerator (1020) and denominator (80). The GCD is 20.
- Divide both the numerator and denominator by the GCD: 1020/80 ÷ 20/20 = 51/4.
- Therefore, 12 60/80 simplifies to 51/4.
5. 13 24/27:
- Convert the mixed number to an improper fraction: 13 24/27 = (13 * 27 + 24) / 27 = 375/27.
- Find the GCD of the numerator (375) and denominator (27). The GCD is 3.
- Divide both the numerator and denominator by the GCD: 375/27 ÷ 3/3 = 125/9.
- Therefore, 13 24/27 simplifies to 125/9.
6. 14 45/90:
- Convert the mixed number to an improper fraction: 14 45/90 = (14 * 90 + 45) / 90 = 1325/90.
- Find the GCD of the numerator (1325) and denominator (90). The GCD is 5.
- Divide both the numerator and denominator by the GCD: 1325/90 ÷ 5/5 = 265/18.
- Therefore, 14 45/90 simplifies to 265/18.
7. 15 3/81:
- Convert the mixed number to an improper fraction: 15 3/81 = (15 * 81 + 3) / 81 = 1228/81.
- Find the GCD of the numerator (1228) and denominator (81). The GCD is 1.
- Divide both the numerator and denominator by the GCD: 1228/81 ÷ 1/1 = 1228/81.
- Therefore, 15 3/81 is already in its lowest terms.
8. 16 6/16:
- Convert the mixed number to an improper fraction: 16 6/16 = (16 * 16 + 6) / 16 = 262/16.
- Find the GCD of the numerator (262) and denominator (16). The GCD is 2.
- Divide both the numerator and denominator by the GCD: 262/16 ÷ 2/2 = 131/8.
- Therefore, 16 6/16 simplifies to 131/8.