Multiply and reduce to simplest form.
1 and two-thirds times 4 and one-fifth
(1 point)
Responses
4 and two-fifteenths
Image with alt text: 4 and two-fifteenths
1 and eleven-fifteenths
Image with alt text: 1 and eleven-fifteenths
7
7
5 and thirteen-fifteenths
5 and thirteen-fifteenths
To multiply and reduce to the simplest form of 1 and two-thirds times 4 and one-fifth, follow these steps:
Step 1: Convert the mixed numbers to improper fractions:
1 and two-thirds = (1 × 3 + 2) / 3 = 5/3
4 and one-fifth = (4 × 5 + 1) / 5 = 21/5
Step 2: Multiply the fractions:
(5/3) × (21/5) = (5 × 21) / (3 × 5) = 105/15
Step 3: Simplify the fraction to its simplest form:
105/15 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 15.
105 ÷ 15 = 7 and 15 ÷ 15 = 1
So, the simplified fraction is 7/1, which is equal to 7.
Therefore, the product of 1 and two-thirds times 4 and one-fifth is equal to 7.
To multiply and reduce the given fractions to the simplest form, follow these steps:
Step 1: Convert the mixed numbers to improper fractions.
- 1 and two-thirds can be written as (1 * 3 + 2) / 3 = 5 / 3.
- 4 and one-fifth can be written as (4 * 5 + 1) / 5 = 21 / 5.
Step 2: Multiply the two fractions.
Multiply the numerators (top numbers) together: 5 * 21 = 105.
Multiply the denominators (bottom numbers) together: 3 * 5 = 15.
So, the result is 105 / 15.
Step 3: Reduce the fraction to its simplest form.
Find the greatest common divisor (GCD) of the numerator (105) and the denominator (15).
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105.
The factors of 15 are 1, 3, 5, 15.
The GCD of 105 and 15 is 15.
Divide both the numerator and denominator by the GCD (15):
105 / 15 = 7 / 1.
The result is 7.
Therefore, the product of 1 and two-thirds times 4 and one-fifth is 7.