Answer :
Sure, let's go through each problem step-by-step to find the solutions for these subtraction problems.
### 1. [tex]\(\frac{8}{7} - \frac{1}{8} - \frac{3}{4}\)[/tex]
First, we need to find a common denominator for the fractions.
- The denominators are 7, 8, and 4.
- The least common multiple (LCM) of 7, 8, and 4 is 56.
Now, convert each fraction to have the common denominator 56:
- [tex]\(\frac{8}{7} = \frac{8 \times 8}{7 \times 8} = \frac{64}{56}\)[/tex]
- [tex]\(\frac{1}{8} = \frac{1 \times 7}{8 \times 7} = \frac{7}{56}\)[/tex]
- [tex]\(\frac{3}{4} = \frac{3 \times 14}{4 \times 14} = \frac{42}{56}\)[/tex]
Now you can perform the subtraction:
[tex]\[ \frac{64}{56} - \frac{7}{56} - \frac{42}{56} = \frac{64 - 7 - 42}{56} = \frac{15}{56} \][/tex]
In decimal form, [tex]\(\frac{15}{56}\)[/tex] is approximately [tex]\(0.26785714285714285\)[/tex].
### 2. [tex]\(\frac{15}{16} - \frac{1}{4} - \frac{1}{2}\)[/tex]
Next, we also need a common denominator for these fractions.
- The denominators are 16, 4, and 2.
- The least common multiple (LCM) of 16, 4, and 2 is 16.
Now, convert each fraction to have the common denominator 16:
- [tex]\(\frac{15}{16}\)[/tex] is already with denominator 16.
- [tex]\(\frac{1}{4} = \frac{1 \times 4}{4 \times 4} = \frac{4}{16}\)[/tex]
- [tex]\(\frac{1}{2} = \frac{1 \times 8}{2 \times 8} = \frac{8}{16}\)[/tex]
Now you can perform the subtraction:
[tex]\[ \frac{15}{16} - \frac{4}{16} - \frac{8}{16} = \frac{15 - 4 - 8}{16} = \frac{3}{16} \][/tex]
In decimal form, [tex]\(\frac{3}{16}\)[/tex] is [tex]\(0.1875\)[/tex].
### 3. [tex]\(8 \frac{4}{7} - 3 \frac{2}{5} - 1 \frac{1}{10}\)[/tex]
First, convert the mixed numbers into improper fractions.
- [tex]\(8 \frac{4}{7} = \frac{8 \times 7 + 4}{7} = \frac{56 + 4}{7} = \frac{60}{7}\)[/tex]
- [tex]\(3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}\)[/tex]
- [tex]\(1 \frac{1}{10} = \frac{1 \times 10 + 1}{10} = \frac{10 + 1}{10} = \frac{11}{10}\)[/tex]
Now, we need a common denominator for the fractions [tex]\(\frac{60}{7}\)[/tex], [tex]\(\frac{17}{5}\)[/tex], and [tex]\(\frac{11}{10}\)[/tex].
- The denominators are 7, 5, and 10.
- The least common multiple (LCM) of 7, 5, and 10 is 70.
Convert each fraction to have the common denominator 70:
- [tex]\(\frac{60}{7} = \frac{60 \times 10}{7 \times 10} = \frac{600}{70}\)[/tex]
- [tex]\(\frac{17}{5} = \frac{17 \times 14}{5 \times 14} = \frac{238}{70}\)[/tex]
- [tex]\(\frac{11}{10} = \frac{11 \times 7}{10 \times 7} = \frac{77}{70}\)[/tex]
Now you can perform the subtraction:
[tex]\[ \frac{600}{70} - \frac{238}{70} - \frac{77}{70} = \frac{600 - 238 - 77}{70} = \frac{285}{70} = 4 \frac{5}{14} \][/tex]
In decimal form, [tex]\(4 \frac{5}{14}\)[/tex] is approximately [tex]\(4.071428571428571\)[/tex].
So, our final answers are:
1. [tex]\(\frac{15}{56}\)[/tex] or approximately [tex]\(0.26785714285714285\)[/tex]
2. [tex]\(\frac{3}{16}\)[/tex] or [tex]\(0.1875\)[/tex]
3. [tex]\(4 \frac{5}{14}\)[/tex] or approximately [tex]\(4.071428571428571\)[/tex]
### 1. [tex]\(\frac{8}{7} - \frac{1}{8} - \frac{3}{4}\)[/tex]
First, we need to find a common denominator for the fractions.
- The denominators are 7, 8, and 4.
- The least common multiple (LCM) of 7, 8, and 4 is 56.
Now, convert each fraction to have the common denominator 56:
- [tex]\(\frac{8}{7} = \frac{8 \times 8}{7 \times 8} = \frac{64}{56}\)[/tex]
- [tex]\(\frac{1}{8} = \frac{1 \times 7}{8 \times 7} = \frac{7}{56}\)[/tex]
- [tex]\(\frac{3}{4} = \frac{3 \times 14}{4 \times 14} = \frac{42}{56}\)[/tex]
Now you can perform the subtraction:
[tex]\[ \frac{64}{56} - \frac{7}{56} - \frac{42}{56} = \frac{64 - 7 - 42}{56} = \frac{15}{56} \][/tex]
In decimal form, [tex]\(\frac{15}{56}\)[/tex] is approximately [tex]\(0.26785714285714285\)[/tex].
### 2. [tex]\(\frac{15}{16} - \frac{1}{4} - \frac{1}{2}\)[/tex]
Next, we also need a common denominator for these fractions.
- The denominators are 16, 4, and 2.
- The least common multiple (LCM) of 16, 4, and 2 is 16.
Now, convert each fraction to have the common denominator 16:
- [tex]\(\frac{15}{16}\)[/tex] is already with denominator 16.
- [tex]\(\frac{1}{4} = \frac{1 \times 4}{4 \times 4} = \frac{4}{16}\)[/tex]
- [tex]\(\frac{1}{2} = \frac{1 \times 8}{2 \times 8} = \frac{8}{16}\)[/tex]
Now you can perform the subtraction:
[tex]\[ \frac{15}{16} - \frac{4}{16} - \frac{8}{16} = \frac{15 - 4 - 8}{16} = \frac{3}{16} \][/tex]
In decimal form, [tex]\(\frac{3}{16}\)[/tex] is [tex]\(0.1875\)[/tex].
### 3. [tex]\(8 \frac{4}{7} - 3 \frac{2}{5} - 1 \frac{1}{10}\)[/tex]
First, convert the mixed numbers into improper fractions.
- [tex]\(8 \frac{4}{7} = \frac{8 \times 7 + 4}{7} = \frac{56 + 4}{7} = \frac{60}{7}\)[/tex]
- [tex]\(3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}\)[/tex]
- [tex]\(1 \frac{1}{10} = \frac{1 \times 10 + 1}{10} = \frac{10 + 1}{10} = \frac{11}{10}\)[/tex]
Now, we need a common denominator for the fractions [tex]\(\frac{60}{7}\)[/tex], [tex]\(\frac{17}{5}\)[/tex], and [tex]\(\frac{11}{10}\)[/tex].
- The denominators are 7, 5, and 10.
- The least common multiple (LCM) of 7, 5, and 10 is 70.
Convert each fraction to have the common denominator 70:
- [tex]\(\frac{60}{7} = \frac{60 \times 10}{7 \times 10} = \frac{600}{70}\)[/tex]
- [tex]\(\frac{17}{5} = \frac{17 \times 14}{5 \times 14} = \frac{238}{70}\)[/tex]
- [tex]\(\frac{11}{10} = \frac{11 \times 7}{10 \times 7} = \frac{77}{70}\)[/tex]
Now you can perform the subtraction:
[tex]\[ \frac{600}{70} - \frac{238}{70} - \frac{77}{70} = \frac{600 - 238 - 77}{70} = \frac{285}{70} = 4 \frac{5}{14} \][/tex]
In decimal form, [tex]\(4 \frac{5}{14}\)[/tex] is approximately [tex]\(4.071428571428571\)[/tex].
So, our final answers are:
1. [tex]\(\frac{15}{56}\)[/tex] or approximately [tex]\(0.26785714285714285\)[/tex]
2. [tex]\(\frac{3}{16}\)[/tex] or [tex]\(0.1875\)[/tex]
3. [tex]\(4 \frac{5}{14}\)[/tex] or approximately [tex]\(4.071428571428571\)[/tex]
