Subtract. Express your answer in simplest form or lowest terms, if needed. Write your answers on your answer sheet. 1.) 7/9 – 1/3 = 2.) 3/4 – 1/2 = 3.) 7/9 – 2/5 =
The Correct Answer and Explanation is:
1) 79−13\frac{7}{9} – \frac{1}{3}97−31
To subtract these fractions, we need a common denominator.
The least common denominator (LCD) of 9 and 3 is 9.
Convert 13\frac{1}{3}31 to have a denominator of 9:13=39\frac{1}{3} = \frac{3}{9}31=93
Now subtract:79−39=49\frac{7}{9} – \frac{3}{9} = \frac{4}{9}97−93=94
Answer: 49\frac{4}{9}94
2) 34−12\frac{3}{4} – \frac{1}{2}43−21
The least common denominator of 4 and 2 is 4.
Convert 12\frac{1}{2}21 to have a denominator of 4:12=24\frac{1}{2} = \frac{2}{4}21=42
Now subtract:34−24=14\frac{3}{4} – \frac{2}{4} = \frac{1}{4}43−42=41
Answer: 14\frac{1}{4}41
3) 79−25\frac{7}{9} – \frac{2}{5}97−52
Here, we need to find a common denominator for 9 and 5.
The least common denominator of 9 and 5 is 45.
Convert both fractions to have a denominator of 45:79=3545,25=1845\frac{7}{9} = \frac{35}{45}, \quad \frac{2}{5} = \frac{18}{45}97=4535,52=4518
Now subtract:3545−1845=1745\frac{35}{45} – \frac{18}{45} = \frac{17}{45}4535−4518=4517
Answer: 1745\frac{17}{45}4517
Explanation Summary
Subtracting fractions involves three main steps: finding a common denominator, rewriting the fractions with the common denominator, and then subtracting the numerators while keeping the denominator the same.
In the first problem, the denominators were 9 and 3. Since 9 is a multiple of 3, we converted 13\frac{1}{3}31 into 39\frac{3}{9}93. This allowed us to subtract the two fractions easily. After subtraction, we got 49\frac{4}{9}94, which is already in its simplest form.
The second problem involved the fractions 34\frac{3}{4}43 and 12\frac{1}{2}21. The least common denominator of 4 and 2 is 4. Rewriting 12\frac{1}{2}21 as 24\frac{2}{4}42, we subtracted the numerators and kept the denominator. This gave us 14\frac{1}{4}41, which does not need to be simplified.
In the third problem, the denominators 9 and 5 do not share common factors, so the least common denominator is their product, 45. We rewrote both fractions with a denominator of 45. The first became 3545\frac{35}{45}4535, and the second 1845\frac{18}{45}4518. Subtracting the numerators gives 1745\frac{17}{45}4517, which is already simplified because 17 and 45 share no common factors other than 1.
In each case, the key skills involved were identifying the least common denominator, converting the fractions accurately, and subtracting the numerators. Simplifying the result when necessary ensures the final answer is in its lowest terms.
