Express 1/10: 1/15 in simplest form. Please give step by step explanation.
The Correct Answer and Explanation is:
The given expression is:110:115\frac{1}{10} : \frac{1}{15}101:151
The colon “:” represents division. So, the expression can be rewritten as:110÷115\frac{1}{10} \div \frac{1}{15}101÷151
Step 1: Apply the rule for dividing fractions
When dividing fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 115\frac{1}{15}151 is 151\frac{15}{1}115. Thus:110÷115=110×151\frac{1}{10} \div \frac{1}{15} = \frac{1}{10} \times \frac{15}{1}101÷151=101×115
Step 2: Multiply the fractions
Multiply the numerators:1×15=151 \times 15 = 151×15=15
Multiply the denominators:10×1=1010 \times 1 = 1010×1=10
Thus, the product is:1510\frac{15}{10}1015
Step 3: Simplify the fraction
Both numerator and denominator can be divided by 5, which is their greatest common divisor (GCD):15÷510÷5=32\frac{15 \div 5}{10 \div 5} = \frac{3}{2}10÷515÷5=23
Thus, the simplest form of the expression is:32\frac{3}{2}23
Explanation:
The problem involves dividing two fractions. Division of fractions follows a simple rule: multiply the first fraction by the reciprocal of the second. This operation transforms the division into multiplication, which simplifies the calculation process.
After applying this rule, the multiplication of numerators and denominators leads to a new fraction, 1510\frac{15}{10}1015. Simplification of this fraction requires finding the greatest common divisor of the numerator and denominator. The number 5 evenly divides both 15 and 10, producing the simplified fraction 32\frac{3}{2}23.
This final fraction, 32\frac{3}{2}23, is an improper fraction since the numerator is larger than the denominator. It can also be expressed as a mixed number, 1121 \frac{1}{2}121, but in this problem, the fraction 32\frac{3}{2}23 represents the simplest form of the given expression. Simplifying fractions helps present answers in their most reduced and understandable form, making them easier to interpret in mathematical contexts.
