How many thirds are there in $2 \frac{4}{12}$?
Answer (2)
There are 7 thirds in the mixed number 2 12 4 . This is determined by converting the mixed number to an improper fraction and dividing it by 3 1 . Following these steps shows that the total is 7 thirds.
;
Convert the mixed number 2 12 4 to an improper fraction: 2 12 4 = 2 3 1 = 3 7 .
Divide the improper fraction 3 7 by 3 1 to find the number of thirds.
Perform the division: 3 7 ÷ 3 1 = 3 7 × 3 = 7 .
State the final answer: There are 7 thirds in 2 12 4 .
Explanation
Convert mixed number to improper fraction We need to find out how many thirds are in the mixed number 2 12 4 . First, let's convert the mixed number into an improper fraction.
Simplify the fraction To convert 2 12 4 to an improper fraction, we first simplify the fraction part: 12 4 = 3 1 . So, the mixed number becomes 2 3 1 .
Convert to improper fraction Now, convert 2 3 1 to an improper fraction. Multiply the whole number (2) by the denominator (3) and add the numerator (1): 2 × 3 + 1 = 6 + 1 = 7 . Place this result over the original denominator (3). So, 2 3 1 = 3 7 .
Divide by one third Now we need to find how many thirds ( 3 1 ) are in 3 7 . This is the same as dividing 3 7 by 3 1 .
Calculate the division Dividing 3 7 by 3 1 is the same as multiplying 3 7 by the reciprocal of 3 1 , which is 3. So, 3 7 ÷ 3 1 = 3 7 × 3 = 3 7 × 3 = 7 .
Final Answer Therefore, there are 7 thirds in 2 12 4 .
Examples
Understanding fractions is crucial in everyday situations, such as cooking. Imagine you are following a recipe that calls for 2 12 4 cups of flour, but your measuring cup is only marked in thirds of a cup. By knowing that 2 12 4 cups is equal to 7 thirds of a cup, you can easily measure out the correct amount using your cup marked in thirds. This ensures your recipe turns out perfectly!
