If 6.3 of a =1.17 of b, then what is a:b ?

Options

A. `13:70`
B. `91:7`
C. `7:130`
D. `13:7`

Answer

To solve the problem where \( 6.3a = 1.17b \) and we need to find the ratio \( a:b \), we can follow these steps:

### Step 1: Write the equation
We start with the equation given in the problem:
\[ 6.3a = 1.17b \]

### Step 2: Rearrange the equation
To find the ratio \( a:b \), we can rearrange the equation to express \( a \) in terms of \( b \):
\[ a = \frac{1.17b}{6.3} \]

### Step 3: Express the ratio \( a:b \)
Now we can express the ratio \( a:b \) as:
\[ a:b = \frac{1.17b}{6.3}:b \]

### Step 4: Simplify the ratio
We can simplify the ratio by dividing both terms by \( b \):
\[ a:b = \frac{1.17}{6.3}:1 \]

### Step 5: Calculate the numerical values
Now we need to calculate \( \frac{1.17}{6.3} \):
\[ \frac{1.17}{6.3} = \frac{117}{630} \]

### Step 6: Simplify the fraction
To simplify \( \frac{117}{630} \), we can find the greatest common divisor (GCD) of 117 and 630. The GCD is 21:
\[ \frac{117 \div 21}{630 \div 21} = \frac{5.5714}{30} \]

### Step 7: Convert to ratio form
Now we can express the simplified ratio:
\[ a:b = \frac{117}{630} = \frac{39}{210} = \frac{13}{70} \]

### Final Answer
Thus, the ratio \( a:b \) is:
\[ a:b = 13:70 \]