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Sagot :
Answer:
The three pieces of lace are [tex]\begin{aligned}\frac{13}{14}\end{aligned}[/tex] meters.
Step-by-step explanation:
There are different sizes of lace. In fact, there are three sizes. The problem is asking us to combine all the sizes, thus, we are to add the measurements to find how long the pieces of lace together.
The measurements are in fraction form. There are different types of fractions and there are different techniques in adding them.
Different Types of Fractions
- Similar Fractions
- Dissimilar Fractions
- Improper Fractions
- Proper Fractions
- Mixed Numbers
Similar fractions are fractions that have the same denominator.
Dissimilar fractions are the opposite of similar fractions. These are fractions that don't have the same denominator.
Improper fractions are fractions whose numerator is bigger than its denominator.
Proper fractions are the opposite of improper fractions. These are fractions whose numerator is less than the denominator.
Mixed numbers are a whole number and a fraction put together.
Solution
We can add the two fractions, [tex]\begin{aligned}\frac{1}{7}\end{aligned}[/tex] and [tex]\begin{aligned}\frac{3}{7}\end{aligned}[/tex], since there are similar fractions. To add them, simply copy the denominator, then add the numerators.
[tex]\begin{aligned}\frac{1}{7}+\frac{3}{7}&=\frac{1+3}{7}=\frac{4}{7}\end{aligned}[/tex]
We will then add the result to [tex]\begin{aligned}\frac{5}{14}\end{aligned}[/tex].
[tex]\begin{aligned}\frac{5}{14}+\frac{4}{7}\end{aligned}[/tex]
Since the fractions are dissimilar, we need to find the least common denominator first before we can add them. The Least common denominator of 14 and 7 is 14. Divide the least common denominator by the denominators and multiply the results by each fraction. Do this individually.
[tex]\begin{aligned}\frac{14 \rightarrow \text{LCD}}{14 \rightarrow \text{denominator of the first fraction}}&=\boxed{1} \:\text{multiply this result by the first fraction}\end{aligned}[/tex]
[tex]\begin{aligned}\frac{5\times{1}}{14\times{1}}=\frac{5}{14}\end{aligned}[/tex]
[tex]\begin{aligned}\frac{14 \rightarrow \text{LCD}}{7 \rightarrow \text{denominator of the second fraction}}&=\boxed{2} \:\text{multiply this result by the first fractio}\end{aligned}[/tex]
[tex]\begin{aligned}\frac{4\times{2}}{7\times{2}}=\frac{8}{14}\end{aligned}[/tex]
We now have two similar fractions, namely, [tex]\begin{aligned}\frac{5}{14}\end{aligned}[/tex] and [tex]\begin{aligned}\frac{8}{14}\end{aligned}[/tex]. Add these two similar fractions to get the final answer.
[tex]\begin{aligned}\frac{5}{14}+\frac{8}{14}=\frac{5+8}{14}=\boxed{\frac{13}{14}}\end{aigned}[/tex]
Thus, the three pieces of lace are [tex]\begin{aligned}\frac{13}{14}\end{aligned}[/tex] meters.
To learn more about combining fractions, visit the following websites
- Adding Fractions: https://brainly.ph/question/2177186
- Adding and Subtracting Fractions: https://brainly.ph/question/6173467
- Finding the Original Fraction: https://brainly.ph/question/2310625
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