HOW TO FIND 1/2 + 1/4 + 1/8

     

Laura received her Master"s degree in Pure Mathematics from Michigan State University, và her Bachelor"s degree in Mathematics from Grand Valley State University. She has trăng tròn years of experience teaching collegiate mathematics at various institutions.

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Dr. Chan has taught computer and college màn chơi physics, chemistry, & math for over eight years. Dr. Chan has a Ph.D. In Chemistry from U. C. Berkeley, an M.S. Physics plus 19 graduate Applied Math credits from UW, and an A.B. With honors from U.C .Berkeley in Physics.

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Adding Fractions

In everyday life, we encounter scenarios in which we need to địa chỉ three fractions. Suppose you want to ride your bike to your friend"s house. To get there, you must first ride 1/2 of a mile down Elm Street, then 1/4 of a mile down Maple Street, & finally 1/8 of a mile down Oak Street. Before you head out, you want to know how far you have khổng lồ ride.

You can địa chỉ cửa hàng the distances on each street, or 1/2 + 1/4 + 1/8. If we"re adding fractions that have the same denominator such as 1/4 & 2/4, all we have to do is add together the numerators khổng lồ find the result. Since 1 + 2 = 3, our numerator is 3. The denominator, 4, stays the same. Thus, 1/4 + 2/4 = 3/4.

So, how do we địa chỉ fractions with different denominators? To vị this, we have to add a step lớn our procedure. Before we địa chỉ the numerators, we have lớn convert our fractions so that they have the same denominator.


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0:03 Adding Fractions 1:01 Finding a Common Denominator 2:26 One Example of Adding… 4:59 Another Way to lớn Solve 6:23 Lesson Summary
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Finding a Common Denominator

A common denominator is the same denominator in two or more fractions. The common denominator will be the least common multiple of the denominators of the fractions. The least common multiple (abbreviated LCM) of a group of numbers is the smallest positive number that all of the numbers in the group divide into evenly. To lớn find this, it"s helpful to menu multiples of each of the numbers.

Let"s say we want to find a common denominator for the fractions 1/3 & 2/5. We need to lớn find the least common multiple of 3 and 5. We can danh sách the multiples of each number:

Multiples of 3 are: 3, 6, 9, 12, 15, 18, & so on Multiples of 5 are: 5, 10, 15, 20, và so on

The first number in common in these two lists is 15, so the least common multiple of 3 and 5 is 15.

If we wanted to add 1/3 & 2/5, we would first need lớn convert both fractions khổng lồ denominators of 15. How vì we change the denominator of a fraction without changing the value of that fraction? To bởi vì this, we have to lớn multiple both the numerator and denominator by the same number. To lớn change 1/3 into 15ths, we look at what we would need to lớn multiple 3 by khổng lồ get 15. 3 times 5 is 15, so if we multiple the numerator of the fraction (1) by the same number (5) we get 5. 1/3 is equal khổng lồ 5/15.

One Example of Adding 3 Fractions

Let"s practice these steps to lớn find out how far you have khổng lồ ride your bike to get lớn your friend"s house. We want to add 50% + 1/4 + 1/8. There are a couple of ways khổng lồ go about adding three fractions:

The associative property states (a + b) + c = a + (b + c). This means that it doesn"t matter which fractions we showroom together first. We can địa chỉ any two of the fractions together and then add the result lớn the third fraction. Let"s start by adding một nửa and 1/4. First we need a common denominator. This will be the least common multiple of the denominators in the fractions. In our case, we want to find the least common multiple of 2 & 4:

Mutliples of 2 are: 2, 4, 6, 8, 10, và so on Multiples of 4 are: 4, 8, 12, 16, và so on

Comparing the list, we see that 4 is the least common multiple of 2 và 4. Next, we need lớn make 4 the denominator of both fractions. We don"t have to vị anything lớn 1/4 since it already has this denominator. Khổng lồ make 4 the denominator of 1/2, we need khổng lồ multiply both the numerator & denominator by 2, since 2 times 2 equals 4. When we vì chưng this, we find that 50% is equal to 2/4. Now, we"re ready to showroom our fractions. Remember, to địa chỉ cửa hàng two fractions with the same denominator, simply add the numerators: the denominator stays the same. When we địa chỉ cửa hàng 2/4 và 1/4, we showroom 2 + 1 = 3 to find the numerator. Since the denominator is 4, we find that 2/4 + 1/4 = 3/4.

We"re almost there! Now, we need to địa chỉ cửa hàng our third fraction, 1/8, khổng lồ the result. We want khổng lồ find 3 phần tư + 1/8. Again, we have to first find a common denominator by determining the least common multiple of 4 & 8:


Multiples of 4 are: 4, 8, 12, 16, và so on Multiples of 8 are: 8, 16, 24, and so on

We see that 8 is the least common multiple of 4 & 8. Since 8 is already the denominator for 1/8, we just need to manipulate 3 phần tư so that it also has the denominator 8. To bởi this, we multiply both the numerator and denominator by 2. This gives us 6/8. Now, we địa chỉ the numerators of 6/8 và 1/8: 6 + 1 = 7, which means that ba phần tư + 1/8 = 7/8. Thus, by first adding một nửa plus 1/4 và then adding 1/8 lớn the result, we find that 50% + 1/4 + 1/8 = 7/8.

Another Way to lớn Solve

Another way to lớn solve this equation is to địa chỉ all three fractions at once. To do this, we must find a common denominator for all three fractions. In this case, we would start by find the least common multiple of 2, 4, and 8:

Multiples of 2 are: 2, 4, 6, 8, 10, và so on Multiples of 4 are: 4, 8, 12, 16, và so on Multiples of 8 are: 8, 16, 24, & so on

8 is the smallest number each of these numbers divides into evenly. Now, we just need khổng lồ make 8 our common denominator. The denominator of 1/8 is already 8, so we leave it alone. Lớn get a denominator of 8 for 1/2, we multiple the numerator & denominator by 4, giving us 4/8. To lớn get a denominator of 8 for 1/4, we multiple the numerator & denominator by 2, giving us 2/8. Now we have three fractions with the denominator of 8. We need to showroom 4/8 + 2/8 + 1/8. We simply địa chỉ the numerators: 4 + 2 + 1 = 7. Once again, we find that một nửa + 1/4 + 1/8 = 7/8.

Both methods yielded the same result, whether we địa chỉ cửa hàng two fractions first & then địa chỉ cửa hàng the last one lớn the result, or địa chỉ all three together at once, the answer is the same. You"d have khổng lồ ride your xe đạp 7/8 of a mile to lớn get from your house to lớn your friend"s house.

Lesson Summary

When adding fractions, the fractions must have a common denominator. To change fractions so that they have a common denominator, we first find the least common multiple, or the smallest positive number that all of the numbers in the group divide into evenly. We find this by making a menu of the multiples of each denominator. Once we"ve found a common denominator, we convert our fractions by multiplying both the numerator and denominator by the same number, so that the fraction does not change its value. Then, we simply showroom together the numerators and keep the denominator the same to give us our result. Because of the associative property, which states that numbers can be added in any order, it does not matter which fractions we địa chỉ together first. We can also showroom all three at once. Knowing how to showroom fractions is very useful for real-world applications.


Practice Adding Fractions

These questions will give you practice adding fractions. Answer the questions, & then kiểm tra your work using the answers in the Answer Key.

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Question 1

What is một nửa + 1/4 + 1/8 equal lớn (in lowest terms)?

a) 7/8

b) 7/4

c) 5/8

d) 7/16

Question 2

What is 50% + 1/4 + 1/8 + 1/7 in lowest terms?

a) 57/56

b) 57/58

c) 58/59

d) 56/57

Answer Key

To địa chỉ fractions like 1/2 + 1/4 + 1/8, you take the largest denominator (D) và try to lớn convert every fraction khổng lồ an equivalent fraction with that denominator. Before doing that, it might be possible lớn reduce some fractions lớn smaller denominators if the denominator can be divided by the numerator.

Answer 1

a) 7/8

Find largest denominator:

D=2(4)(8)= 64

Convert to equivalent fractions, add, and reduce to lớn lowest terms:

1/2 + 1/4 + 1/8 = 32/64 + 16/64 + 8/64 = (32 + 16 + 8) / 64 = 56/64 = 7/8

Answer 2

a) 57/56

Find the largest denominator:

D=2(4)(8)7 = 64(7) = 448

Convert to equivalent fractions:

1/2 + 1/4 + 1/8 + 1/7 = (1/2)448/448 + (1/4)448/448 + (1/8) 448/448 + (1/7) 448/448 = 224/448 + 112/448 + 56/448 + 64/ 448