Add with Unlike Denominators Practice
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Question
Use the image to answer the question.
An illustration shows 2 bars. The first bar is divided vertically into 4 equal parts, and 3 parts are shaded. The second bar is divided vertically into 6 equal parts, and 5 parts are shaded.
Add the fractions from the picture provided to create a mixed number.
(1 point)
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To add fractions with unlike denominators, we need to find a common denominator. In this case, the common denominator is the least common multiple of 4 and 6, which is 12.
To convert the first fraction into twelfths, we need to multiply both the numerator and denominator by 3:
3/4 is equivalent to (3*3)/(4*3) = 9/12.
To convert the second fraction into twelfths, we need to multiply both the numerator and denominator by 2:
5/6 is equivalent to (5*2)/(6*2) = 10/12.
Now we can add the fractions:
9/12 + 10/12 = 19/12.
Since the numerator is greater than the denominator, we have an improper fraction. To convert it into a mixed number, we divide the numerator by the denominator:
19 divided by 12 is 1 with a remainder of 7.
Therefore, the mixed number is 1 7/12.
To add fractions with unlike denominators, we first need to find a common denominator. In this case, the common denominator would be 12 (the least common multiple of 4 and 6).
To convert the fractions to have a denominator of 12, we can multiply the numerator and denominator of the first fraction by 3 (to get 12 as the new denominator), and we can multiply the numerator and denominator of the second fraction by 2 (to get 12 as the new denominator).
After converting the fractions, the first fraction becomes 9/12 (3 parts shaded out of 4), and the second fraction becomes 10/12 (5 parts shaded out of 6).
Now, we can add the fractions:
9/12 + 10/12 = 19/12
Since the numerator is greater than the denominator in this case, we can simplify the fraction to a mixed number by dividing the numerator by the denominator:
19 ÷ 12 = 1 remainder 7
Therefore, the mixed number is 1 and 7/12.
To add fractions with unlike denominators, you need to find a common denominator. The common denominator is the smallest number that both denominators can divide evenly into. In this case, the denominators are 4 and 6.
To find a common denominator, you can multiply the two denominators together. In this case, 4 multiplied by 6 is 24.
Next, you need to convert the fractions so they have the same denominator. To do this, you need to find the equivalent fractions for each fraction that have the common denominator of 24.
For the first fraction, which has a denominator of 4, you can multiply both the numerator and the denominator by 6 to get an equivalent fraction with a denominator of 24. So, (3/4) multiplied by (6/6) is equal to (18/24).
For the second fraction, which has a denominator of 6, you can multiply both the numerator and the denominator by 4 to get an equivalent fraction with a denominator of 24. So, (5/6) multiplied by (4/4) is equal to (20/24).
Now that both fractions have the same denominator, you can simply add the numerators together. (18/24) + (20/24) is equal to (38/24).
To convert this improper fraction to a mixed number, you need to divide the numerator by the denominator. 38 divided by 24 is equal to 1 with a remainder of 14. So the mixed number is 1 14/24.