use multiplication to write three fractions equivalent to each given fraction.
1. 2/3
2. 3/5
3. 5/8
4. 9/10
To write three fractions equivalent to each given fraction using multiplication, follow these steps:
1. Choose any whole number other than zero.
2. Multiply both the numerator and the denominator of the given fraction by the chosen number.
3. Simplify the fraction, if possible.
Let's apply these steps to each of the given fractions:
1. 2/3:
- Choose a whole number, let's say 2.
- Multiply the numerator and the denominator of 2/3 by 2: (2 * 2) / (3 * 2) = 4/6.
- Simplify by dividing the numerator and the denominator by their greatest common divisor, which is 2: 4/6 simplifies to 2/3.
- Another equivalent fraction can be obtained by multiplying by a different number, such as 3: (2 * 3) / (3 * 3) = 6/9. This fraction cannot be simplified any further.
2. 3/5:
- Choose a whole number, let's say 4.
- Multiply the numerator and the denominator of 3/5 by 4: (3 * 4) / (5 * 4) = 12/20.
- Simplify by dividing the numerator and the denominator by their greatest common divisor, which is 4: 12/20 simplifies to 3/5.
- Another equivalent fraction can be obtained by multiplying by a different number, such as 2: (3 * 2) / (5 * 2) = 6/10. This fraction cannot be simplified any further.
3. 5/8:
- Choose a whole number, let's say 3.
- Multiply the numerator and the denominator of 5/8 by 3: (5 * 3) / (8 * 3) = 15/24.
- Simplify by dividing the numerator and the denominator by their greatest common divisor, which is 3: 15/24 simplifies to 5/8.
- Another equivalent fraction can be obtained by multiplying by a different number, such as 2: (5 * 2) / (8 * 2) = 10/16. This fraction cannot be simplified any further.
4. 9/10:
- Choose a whole number, let's say 5.
- Multiply the numerator and the denominator of 9/10 by 5: (9 * 5) / (10 * 5) = 45/50.
- Simplify by dividing the numerator and the denominator by their greatest common divisor, which is 5: 45/50 simplifies to 9/10.
- Another equivalent fraction can be obtained by multiplying by a different number, such as 2: (9 * 2) / (10 * 2) = 18/20. This fraction cannot be simplified any further.
I'll get you started.
2/3 = 4/6 = 6/9 = 8/12
As you can see I multiplied the numerator and denominator by the same numbers.
I'll be glad to check your answers for the other problems.